GB2322200A - A borehole measurement system employing electromagnetic wave propagation - Google Patents

Abstract

This invention is directed toward the determination of geophysical parameters of earth formations penetrated by a borehole. In particular this invention relates to determining parameters of the earth formations such as water filled porosity, dielectric constant of the dry formation and resistivity of the connate liquid in the formation. The borehole instrument has at least one pair of transmit and receive antennae, as shown there are four transmit 203,205,207,209 and two receive antennae 211,213, equispaced about a central position. The transmitters are energised at at least two frequencies by numerically controlled oscillators 223,225 to transmit waves into the borehole and adjacent formations. The waves are received 231 and measurements of real and imaginary components of the received signals are taken. By using a mixing model, such as a complex refractive index model, of the relationship between measurements and the selected formation parameters, the nature of the earth formation composition can be determined.

Description

A BOREHOLE MEASUREMENT SYSTEM EMPLOYING ELECTROMAGNETIC WAVE PROPAGATION FIELD OF THE INVENTION This invention is directed toward the determination of geophysical parameters of earth formations penetrated by a borehole. The invention is more particularly directed toward the determination of geophysical properties from measures of electromagnetic properties of earth formations in the vicinity of a borehole either during the drilling of the borehole or subsequent to the drilling of the borehole.

BACKGROUND OF THE ART A measure of geophysical parameters of earth formations penetrated by a borehole, as a function of depth within the borehole, is commonly referred to in the oil and gas industry as a "well log". The first well log was measured or "run" in 1927 and consisted of a measure of the spontaneous potential (SP) properties of earth formation penetrated by the well borehole. The log was run after the borehole was drilled using a borehole instrument operating on an electrical wireline. The wireline served as a means of conveying the borehole instrument or "logging tool" along the borehole and also as an electrical path for transmitting data from sensors within the borehole instrument to the surface of the earth. During the intervening decades, the wireline well logging art has grown in sophistication and complexity, employing electromagnetic, acoustic, nuclear and mechanical technologies to determine geophysical parameters of interest.

Probably the most important geophysical parameters to the producer of hydrocarbons are the hydrocarbon (or water) saturation of the formation, the porosity of the formation, and the permeability of the formation. These parameters are, in tum, used to determine (a) if hydrocarbon is present in the formation, (b) how much hydrocarbon is present, and (c) the ease in which the hydrocarbon can be extracted or "produced" from the formation.

During the past two decades well logs of increasing complexity and sophistication have been measured while drilling the borehole. The advantages of measurements-while-drilling (MWD) logs are well known in the art. Electremagnetic, nuclear and acoustic techniques have been employed in MWD systems which are approaching the accuracy and precision of their wireline counterparts.

Electromagnetic induction techniques have been used for a number of years in wireline and MWD logging operations to determine the resistivity and other electromagnetic parameters of earth formations penetrated by a borehole. One or more transmitters within a borehole induction logging instrument induce an alternating voltage into the borehole and the earth formation in the vicinity of the instrument. The amplitudes and phases of the signals produced by these alternating electromagnetic fields are measured by one or more receivers within the borehole instrument.

Resistivity and other electromagnetic properties are computed from the basic amplitude and phase measurements. Using the basic premises that formations saturated with hydrocarbon are more resistive than formation saturated with saline water, the presence and amount of hydrocarbon Sin place" is determined.

The accuracy and precision of hydrocarbon measures computed from measures of formation resistivity are controlled by the accuracy and precision of the underlying resistivity measurements. Error in resistivity measurements, whether wireline or MWD, arise in prior art systems from a number of sources. These sources of error are discussed briefly under the following categories: 1. INSTRUMENT CALIBRATION In prior art systems, borehole instruments or logging tools, both wireline and MWD, are typically calibrated at the well site (or in the laboratory) using an "air-hang" calibration operation, during which the transmitter and receiver antennas of the logging tool are utilized to transmit and receive electromagnetic signals which propagate through the atmosphere around the tool. These air-hang calibration operations provide no data whatsoever about the operation of the tool once it is run into the wellbore andSoperated in the wellbore environment. Calibration values obtained during the air-hang may not apply for the wellbore environment, or the logging tool may go out of calibration once it is run into the wellbore.

Prior art borehole instruments typically include a considerable number of analog electrical and electronic components in both the transmitting and receiving circuits, which tend to introduce an error component when subjected to changes in temperature. This type of error component is typically identified as a Mthermal drift" error component. In prior art devices, this thermal drift error component introduces substantial inaccuracies in measurements, which can reduce the overall accuracy of the logging instrument.

Many prior art MWD logging tools claim to be able to provide some indication of the size and shape of the borehole, during operations which are generally characterized as "calipering1 operations. Such calipering operations depend upon the ability to detect slight changes in the amplitude attenuation or phase shift in the logging measurements which is attributable to changes in the borehole size. A variety of factors are taken into account during calipering operations, including the diameter of the logging tool, the resistivity of the drilling fluid or "mud", the diameter of invasion of the drilling mud into the formation, the resistivity of the formation and drilling mud in the invaded zone, and the resistivity of the formation for uninvaded portions of the formation. Calibration errors and thermal drift error components, along with the other inaccuracies inherent in utilizing such a large number of variables typically dwarf the changes in resistivity of the borehole, and render prior art borehole calipering operations techniques essentially meaningless.

Another problem typically encountered during logging operations is undesirable magnetic field mutual coupling which may occur between two or more receiving antennas. Viewed broadly, the magnetic mutual coupling between receivers can be considered a loss of information attributable to the magnetic interaction of the receivers, and which can be considered to be an error component. More particularly, mutual coupling arises when a propagating electromagnetic field generates a current in a particular receiver, and the current which is generated in a particular receiver itself generates a propagating electromagnetic field which is combined with the primary or interrogating" electromagnetic field to influence the amount of current generated in one or more adjacent receiving antennas.

In summary, some of the principal technical problems associated with borehole instruments and particularly MWD logging tools include: (1) the inability to obtain a meaningful and accurate calibration, (2) the difficulty of obtaining the calibration, (3) the inability to determine when a tool goes out of calibration during logging operations, (4) the considerable impact on accuracy of thermal drift error components, (5) the inability to obtain accurate borehole caliber data utilizing a logging tool, principally due to the combined effect of error components associated with the variables utilized to derive borehole caliper data, and (6) the effects of undesired magnetic field mutual coupling between receiving antenna in a logging apparatus.

2. SERIAL PROCESSING OF MEASURED DATA As mentioned previously amplitude and phase measurements are used to compute the resistivity and other electromagnetic properties of the formation and borehole in the vicinity of the borehole logging instrument.

It is rather common practice to use two or more transmitter-receiver pairs with different spacings along the axis of the borehole. It is also quite common practice to operate one or more transmitters at different frequencies. Both practices are directed toward obtaining electromagnetic measurements of differing radial depths of investigation into the formation, near borehole and borehole regions. These measurements are then combined to obtain resistivity measurements which have been corrected for adverse environmental conditions such as formations invaded by drilling fluid, formations of limited vertical thickness, the diameter of the borehole, the resistivity arrd other electromagnetic properties of the drilling fluid, and the like. The environmental corrections are performed sequentially or "serially" in the prior art. Serial environmental correction tends to propagate error associated with each correction thereby maximizing the error associated with the environmentally corrected resistivity measurement.

It is known in the art that measurements made at different transmitter receiver spacings and at different frequencies exhibit different vertical resolutions. Prior art has matched the vertical resolutions using various convolution and deconvolution techniques prior to combining multiple measurements. This is, again, referred to in the art as serial data processing. U.S. Patent 4,609,873 to Percy T. Cox, et al teaches the use of a wireline logging system comprising at least three transmitter coils and at least two receiver coils to determine resistivity and dielectric constant of a subsurface formation adjacent to a drilling fluid invaded zone. The transmitters are operated at a single frequency of 30 MHz. Amplitude and phase measurements are made and serial processing of the data is employed. At relatively low transmitter frequencies, serial processing introduces only negligible errors. At higher transmitter frequencies in the 2 MHz range or higher, vertical resolution is affected not only by the physical arrangement of the transmitter receiver combinations, but also significantly by the electromagnetic properties of the borehole environments and the formation. The functional dependence of vertical resolution and transmitter frequency is addressed in the publication "2-MHz Propagation Resistivity Modeling in Invaded Thin Beds", W. Hal Meyer, The Log Analyst, July-August 1993, p.33 and *Inversion of 2 MHz Propagation Resistivity Logs", W. H.

Meyer, SPWLA 33rd Annual Logging Symposium, Paper H, June 14-17, 1992. Stated another way, prior art serial processing of data can introduce significant error at transmitter frequencies in the range of 2 MHz and higher.

In order to obtain accurate and precise parametric determinations at these frequencies, it is necessary to compute the parameters of interest and to make the required corrections, including corrections for the effects of differing vertical resolutions, simultaneously.

3. BOREHOLE PARAMETER DETERMINATIONS The prior art correction of resistivity measurements for the adverse effects of environmental corrections, and in particular for borehole conditions, has been discussed briefly in the previous section. In order to make valid corrections for borehole conditions, it is usually necessary to know the borehole or near borehole conditions which include borehole diameter, the electromagnetic properties of the drilling fluid, the degree of invasion of the drilling fluid, and the like.

Borehole and near borehole parameters also provide other extremely useful information. As an example, the drilling fluid invasion profile is indicative of the permeability of the formation. As a further example, the physical properties of the borehole such as rugosity and ellipticity can be related tb the mechanical properties of the rock matrix and to the effectiveness of the drilling operation. A knowledge of rock matrix properties is extremely useful in specifying subsequent completion activities such as possible fracturing and even perforating programs. As a still further example, a knowledge of borehole conditions can often be used to increase efficiency of the borehole drilling operation such as modifying drilling parameters to increase bit penetration rates. Prior art has traditionally viewed borehole parameters as sources of error or "noise" in desired information measurements. Efforts to quantify borehole parameters have, in general, been pursued only to the extent required to obtain reasonable corrections to the formation parameters which have been considered the "signal".

4. QUANTIFICATION OF ERRORS -Error in resistivity or other electromagnetic properties of the formation, near borehole and borehole parameters can arise from many sources. As discussed previously, instrument calibration is a major source of error in prior art devices. In addition, algorithms or "models" used to convert raw amplitude attenuation and/or phase shift measurements into the desired formation and borehole parameters of interest can introduce error in certain borehole and formation conditions. Errors of both types can be compensated for properly only if error is first clearly identified and quantified. Prior art systems have not been directed to the identification and quantification of error, especially in real time. Error analysis, if performed at all, is usually performed by the analyst long after the well has been logged.

5. ADDITIONAL SOURCES OF ERROR In addition to the above sources of error, fundamental problems exist in the conversion of measures of resistivity into measures of hydrocarbon saturation. As mentioned previously, formation resistivity has historically been the primary parameter of interest in MWD and wireline logging since it is used to delineate hydrocarbons from saline waters.

Resistivity measurements can not be used to delineate hydrocarbons from relatively fresh waters due to a lack of contrast in the resistivities of the two fluids. Hydrocarbon and water, whether saline of fresh, exhibit different dielectric constants. A simultaneous measure of formation dielectric constant and formation resistivity has been used in wireline logging to delineate between hydrocarbon and water (fresh or saline) saturated formations. This technique has not, however, been used in MWD logs.

SUMMARY OF THE INVENTION The invention is directed toward the measure or "logging" of electromagnetic properties of earth formation penetrated by a borehole.

Electromagnetic wave propagation techniques are used to determine parameters of interest of the formation and borehole in the vicinity of a borehole instrument. The borehole instrument contains one or more transmitter-receiver pairs operating at one or more frequencies. The borehole instrument is preferably conveyed along the borehole by means of a drill string. The invention is, therefore, primariiy directed toward MWD operations but is also applicable to wireline logging. Measures of amplitude attenuation and phase shift are preferably transmitted to the surface for processing and transformation into parameters of interest using a model of the response of the logging instrument and suitable computing means.

Alternately, the transformation of the amplitude and phase measurements can be made with processing means contained within the borehole instruments, and the parameters of interest are transmitted to the surface, or stored within the borehole instrument for subsequent retrieval at the surface.

One objective of the invention is to provide (7 logging system which yields accurate and precise measures of amplitude attenuation and phase shift of electromagnetic radiation induced within the formation by the transmitter elements of the borehole instrument. This, in tum, results in more accurate and precise formation and borehole parameters of interest which are computed from the basic amplitude and phase measurements using the instrument response model. More specifically, the downhole instrument utilizes digital circuitry which minimizes errors resulting from thermal drift of the electronics of the system. In addition, calibration of the system before, during and after logging is improved thereby further reducing equipment related type error. The system also corrects for mutual coupling of receiver antennas within the borehole instrument thereby further reducing systematic error in the basic amplitude and phase measurements and the parameters of interest computed therefrom. These features, in combination, are not offered in prior art systems.

Another objective of the invention is the reduction of error in the determined parameters of interest resulting from environmental corrections.

Simultaneous or "parallel", rather than serial, data processing methods are used to transform the basic amplitude attenuation and phase shift measurements into formation and borehole parameters of interest. Parallel data processing reduces the propagation of error associated with the correction of data for individual environmental parameters. Serial processing is widely used in prior art MWD and wireline logging systems.

Xfet another objective of the invention is the determination of borehole as well as formation parameters of interest. Such borehole parameters can be used as indicators of the overall efficiency of the drilling program. In addition1 measured borehole parameters such as borehole rugosity, caliper and ellipticity can be used to estimate mechanical properties of the penetrated formation which, in turn, can be used as designed parameters in future well completion programs. Accurate determinations of borehole parameters result in more accurate and precise correction of formation parameters for environmental borehole conditions. Prior MWD and wireline systems have directed little effort to the specific determination and use of borehole parameters.

Still another objective of the invention is the provision of means for identifying and quantifying total error associated with parameters of interest. Such determinations can be used to assign a quality factor to the logged parameters as well as serve as an indicator of equipment or instrument response model problems in certain formation and borehole conditions. Such extensive error indication systems are not available in prior art systems.

A still further objective of the invention is to measure simultaneously the resistivity, dielectric constant and the porosity of the formation in the vicinity of the well bore. A measure of formation dielectric constant is needed to delineate hydrocarbon bearing zones from, fresh water or low salinity water bearing zones Simultaneous measures of resistivity, dielectric constant and porosity are not known to have been made with a MWD logging system.

Additional objectives, features and advantages will become apparent in the detailed description of the invention and appended drawings which follow.

BRIEF DESCRIPTION OF THE DRAWINGS So that the manner in which the above cited features, advantages and objects of the present invention are attained and can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. It is noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments.

Fig. 1 depicts the invention in a measurement-while-drilling embodiment; Fig. 2 illustrates a more detailed view of transmitter, receiver and a control circuit subassembly of the borehole instrument portion of the system; Fig. 3 is a block diagram view of the transmission and reception systems of the logging-while-drilling apparatus of the present invention; Fig. 4 is an electrical schematic of the receiving circuits of the block diagram of Fig. 3; Fig. 5 is a block diagram view of the numerically-controlled oscillators of the block diagram of Fig, 3; Fig. 6 is a block diagram view of the digital signal processor of the block diagram of Fig. 3; Figs. 7A, 7B, and 7C, are high level flowchart representations of tool operation in accordance with the preferred embodiment of the present invention; Fig. 8 is a high level flowchart representation of a digital calibration operation in accordance with the present invention; Fig. 9 is a graphical depiction of the amplitude, frequency, and phase shift data derived through a digital calibration operation; Figs. 10A, 10B, and 10C graphically depict a variety of comparison operations which can be performed utilizing data derived from a digital calibration operation; Fig. 11 is a simplified block diagram view of circuit and data processing components which can be utilized to measure the undesired mutual coupling between particular antennas; Fig. 12 is an equivalent electrical circuit for the circuit of Fig. 11; Fig 13 is a block diagram of the technique for eliminating mutual coupling; Fig. 14 is a detailed electrical schematic of the block diagram of Fig 13; Figs. 15A, 15B, 15C, 16A, 16B, and 16C depict types of measurements obtained with the circuit of Fig. 14; Fig. 17 is a flowchart representation of the technique of eliminating the corrupting influence of mutual coupling and antenna draft; Fig. 18 illustrates measured amplitude and phase resistivities across a relatively thin formation bounded by formations of essentially infinite vertical extent; Fig. 19 is a graphical depiction of an algorithm for serially correcting apparent resistivity for the effects of invasion of the drilling fluid; Figs 20A and 20B are graphical depictions of algorithms for serially correcting phase and amplitude resistivity measurements, respectively, for the effects of finite bed thickness; Fig. 21 graphically illustrates the interdependence of apparent phase and amplitude resistivity, true formation resistivity, and instrument-borehole eccentricity for a borehole fluid of resistivity of 20 ohm meters; Fig. 22 graphically illustrates the interdependence of apparent phase and amplitude resistivity, true formation resistivity, and instrument-borehole eccentricity for a borehole fluid of resistivity of 0.2 ohm meters; Fig. 23 shows apparent resistivity logs determined at four transmitter frequencies and recorded as a function of depth within a well borehole; Fig. 24 shows apparent dielectric constant logs determined at four transmitter frequencies and recorded as a function of depth within a well borehole; Fig. 25 illustrates the variation of measured relative dielectric constant and conductivity as a function of transmitter frequency; Fig. 26 depicts a plot of computed variations in dielectric constant as a function of transmitter frequency and a comparison of theoretical values with measured values at four different transmitter frequencies; Figs. 27A and 27B illustrate the variation of the real portion of effective dielectric constant and the real portion of effective formation conductivity as a function of water resistivity, at various formation porosities; and Fig. 28 is a graph which depicts how amplitude attenuation and phase shift measurements can be used to determine borehole diameter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT The invention employed in a MWD environment is illustrated in a very general manner in Fig. 1. Elements shown in Fig. 1 will be discussed in detail in subsequent sections of this disclosure. The drill bit 31 is attached to borehole instrument 36 which, in the MWD embodiment, is preferably a metallic drily collar which, in turn, is mounted on the wellbore drill string 37.

This assembly is shown suspended in a wellbore 34 which penetrates the earth formation 32. A means for rotating the drill string 37 is identified by the numeral 40. The drill string 37 and the borehole instrument 36 are axially hollow such that drilling fluid or "mud" may be pumped downward there through and out ports of the drill bit 31 and retumed to the surface by way of the drill string-borehole annulus identified as 34a. The mud circulation system, including mud pumps at the surface, are not shown. It is well known in the art that the mud provides a means for returning drill bit cuttings to the surface, cools and lubricates the drill bit 31 b, and provides hydrostatic pressure to contain intemal pressures of formations penetrated by the drill bit 31. Four transmitter antenna coils of one or more turns are identified by the numerals 207, 209, 205, and 203. The axes of the coils are coincident with the axis of the borehole instrument 36. The coils are electrically insulated from and slightly recessed within the outer diameter of the drill collar thereby comprising integral elements of the collar assembly. Two receiver antenna coils are identified by the numerals 213 and 211. The geometries of these coils are quite similar to the geometries of the transmitter coils and again comprise integral elements of the borehole instrument 36. Transmitter coils are preferably arranged symmetrically on either side of the midpoint between receiver coils 213 and 211. Power sources and control circuitry for the transmitters and receivers are indicated schematically as a subassembly 201 of the borehole instrument 36 for purposes of discussion. In embodiment of the invention as a MWD device, the control circuits are preferably located within pressure and fluid tight compartments within the wall of the borehole instrument 36 which is preferably a drill collar. Data recorded by the receivers can be either transmitted in real time to the surface using drilling fluid pulsing means (not shown) or alternately can be recorded with recording means downhole (not shown) for later retrieval. For the real time data transmission embodiment, signals from the receivers are transmitted to the surface by a path means generically denoted by the numeral 46, transferred to a CPU for processing and correlated with depths from a drill collar depth indicator 43, and output to recorder 44 which displays the computed parameters of interest as a function of depth at which the input measurements were made. A model 45 of the response of the transmitter-receiver pairs, in varying borehole and formation conditions, is provided to convert amplitude attenuation and phase shifts measured by the receiver elements into formation and borehole parameters of interest. The model is preferably based derived from theoretical calculations of the responses of the transmitter-receiver pairs, and also derived from measured responses of the transmitter-receiver pairs in known test formation and borehole conditions. The model can alternately be stored within memory (not shown) of the CPU 42. An alternate embodiment of the invention comprises a processor unit (not shown), with response model stored within, mounted within the drill collar 36 to perform data processing downhole.

Memory capacity is usually limited in MWD borehole instruments. In order to most effectively utilize memory capacity, it is often desirable to process measured data downhole and store processed results rather than the more voluminous measured data.

Various elements, features and methods of the invention will be discussed in detail in the following sections. It should be recalled the although the preferred embodiment of the invention is MWD logging, the invention can be alternately embodied for wireline ligging or any logging operation involving the conveying of a measuring instrument along a borehole.

1. THE BOREHOLE INSTRUMENT The borehole logging instrument 36, preferably a drill collar, comprising the transmitter-receiver coil array, is shown in greater detail in Fig. 2. The two receiver coils are denoted by the numerals 213 and 211.

Transmitter toils 207 and 209 are longitudinally spaced distances 23 and 21, respectively, from the midpoint 25 between the receiver coils 213 and 211. The transmitter coils 205 and 203 are likewise longitudinally spaced distances 23 and 21 , respectively, from the midpoint 25. Again, power sources and control circuitry for the transmitters and receivers are shown schematically as a subsection 201 of the borehole instrument 36. In the preferred embodiment, the circuitry, which will be described in detail in the next section, is contained within pressure and tight compartments within the wall of the borehole instrument 36. The symmetrical spacing pattern of transmitters and receivers about a point 25 midway between receivers 213 and 211 is preferred but not a necessary condition for the embodiment of the invention.

1.1 Transmission and Reception Systems Fig. 3 provides a block diagram view of the exemplary logging instrument or "tool" 36, with the subassembly 201, illustrated previously in Fig. 2 and constructed in accordance with the present invention. Logging tool subassembly 201 includes upper transmitters 203, 205, lower transmitters 207, 209, and intermediate series resonant receiving antennas 211, 213. Central processor 215 is preferably a microprocessor device which is utilized to coordinate the operation of the components of logging tool 36 and subassembly 201, to record and process the data obtained from measurements made by intermediate series resonant receiving antennas 211, 213, and to interact with a mud pulse telemetry data transmission system (not shown) preferably carri controlled oscillator 223. Processor 219 is provided and dedicated for the control of numerically controlled oscillator 225. Central processor 215 communicates with processors 217,219 via data buses 241, 243 respectively. Numerically controlled oscillators 223, 225 are adapted to receive a binary command signal as an input, and to produce an analog output having particular frequency, phase, and amplitude attributes. The frequency, phase, and amplitude attributes are determined at least in part by the command signals applied from processor 217, 219 to the input of numerically controlled oscillators 223, 225, and the data contained in various registers within numerically controlled oscillators 223, 225.

Numerically controlled oscillators 223, 225 provide the analog signal to transmitting circuits 227, 229 respectively. The components which make up transmitting circuits 227, 229 will be described in greater detail in connection with a technique of the present invention of quantifying the undesirable magnetic field mutual coupling between particular antennas.

Receiving antennas 211, 213, communicate through analog receiving circuit 231 with the first and second data input channels of a digital signal processor 221. The digital signal processor 221 receives data at the first and second inputs after it is converted from analog form to digital form by analog-to-digital converters 220, 222, and records the data elements in a circular memory buffer. Central processor 215 pulls data from the buffers in a prescribed and predetermined manner in order to sample the current which is generated in receiving antennas 211, 213 in response to the propagation of electromagnetic signal through the adjoining formation. As is conventional, the resistivity of the formation surrounding the logging tool 36 and subassembly 201 may be determined by either (1) determining the amplitude attenuation of an electromagnetic wave propagating through the formation adjoining receiving antenna 211 and receiving antenna 213, or (2) by determining the phase shift between the electromagnetic signal propagating through the formation adjoining receiving antenna 211 and 213, or from both. These measurements comprise a relative measurement of the amplitude attenuation and a relative measure of the phase shift.

The present invention also allows other techniques for quantifying the electromagnetic field which propagates through the formation surrounding logging tool 36. Since precise control can be obtained with the present invention over the frequency, phase, and amplitude of the electromagnetic wave generated by transmitting antennas 203, 205, 207, and 209, the present invention allows the measurement of the absolute amplitude attenuation of electromagnetic signal between any particular transmitting antenna 203, 205, 207, and 209 and any particular receiving antenna 211,213. Furthermore, the logging tool 36 of the present invention allows for the absolute measurement of the phase shift of an electromagnetic signal between any particular transmitting antenna 203, 205, 207, 209 and any particular receiving antenna 211, 213. Prior art devices do not allow such optional techniques for determining amplitude attenuation and phase shift, since prior art devices are unable to determine easily and precisely the frequency, phase, and amplitude of a signal generated at any particular transmitting antenna.

The operation of numerically controlled oscillators 223, 225 is clocked by the output of reference clock 237, which is preferably 12 MHz.

The operation of receiving circuit 231 is controlled by the output of numerically controlled oscillator 231, which is also clocked by the output of the reference clock 237, which is 12 MHz. Thus, a clocking pulse is provided to numerically controlled oscillator 223, 225 at a frequency identical to that which is provided to numerically controlled oscillator 223, which establishes the operating frequency of receiving circuit 231. Digital signal processor 221 is clocked by the output of divide-by circuit 239, and thus samples the output of receiving circuit 231 at a particular frequency which is much less than that utilized to energize transmitter antennas 203, 205, 207 and 209.

Numerically controlled oscillator 233 produces a phase-locked sine-wave signal with a center frequency of 1.995 MHz, that is used as a local oscillator signal by a receiving circuit (not shown) located in the wall of the logging tool 36.

Reference is now made to Fig. 4. The overall function of the circuitry depicted in block diagram and schematic form in Fig. 4 is to respond to the local oscillator signal and one of the two receiver coil output signals to produce a receiver phase output signal relative to the transmitter and a receiver amplitude output signal. A conventional pre-amp circuit generally indicated at 271 responds to the receiver pick-up signal and its output is applied to a mixer circuit arrangement generally indicated at 273. Mixer circuit arrangement 273 includes an integrated circuit 275 that suitably is implemented by an integrated circuit manufactured and sold by Motorola and other companies under the designation MC 1596.

Because the frequency of the pick-up signal and the local oscillator signals are phase-locked to a common frequency reference and differ by 6 KHz, the intermediate frequency (1F) produced by mixer circuit arrangement 273 is at 6 KHz. A band pass tuning circuit arrangement generally indicated at 277 passes the 6 KHz IF signal to an amplifier circuit arrangement generally indicated at 279. An active band pass filter circuit arrangement generally indicated at 281 provides further band pass filtering and provides a signal to an analog-to-digital converter, which supplies a digital input to a particular input channel of digital signal processor 221 (of Fig. 3).

Fig. 5 is a block diagram view of the numerically-controlled oscillators 223, 225, 233 of Fig. 3. Since the numerically-controlled oscillators are identical, only numerically-controlled oscillator 223 will be discussed and described. In the preferred embodiment of the present invention, numerically-controlled oscillator 223 comprises a CMOS, DDS modulator manufactured by Analog Devices of Norwood, Massachusetts, which is identified by Model No. AD7008. The numerically-controlled oscillator 223 includes a thirty-two bit phase accumulator 301, a sine and cosine look-up table 303, and a ten-bit digital to analog converter 305.

Clock input 307 is provided to receive a clocking signal from a device which is external to the numerically-controlled oscillator 223. The particular numerically-controlled oscillator of the present invention is adapted to accept clock rates high as 20 MHz to 50 MHz, but can accommodate much lower clock rates. The device purports to have a frequency accuracy which can be controlled to one part in four billion. Numerically-controlled oscillator 223 includes a thirty-two bit serial register 309 which receives serial data at serial data input pin 311, which is clocked into the register in accordance with a clock signal which is supplied to serial clock input 313. A thirty-two bit parallel register 313 is also provided which receives parallel binary data from MPU interface 315. Data bus 317 includes sixteen digital input pins identified as DO through D15. The chip select pin 321 is utilized when writing to the parallel register 313. The write pin 319 is also utilized when writing to the parallel register 309. The transfer control address bus 323 is utilized to determine the source and destination registers that are used during a transfer. A source register can be either the parallel assembly register 313 or the serial assembly register 309. The destination register can be any one of the following registers: the command register 325, the FREQO register 327, the FREQ1 register 329, the phase register 331, the IQMOD register 333. The command register is written to only through the parallel assembly register 313. The contents of the command register determine the operating state of the numerically-controlled oscillator 223. In the preferred device utilized in the present invention, the command register is a four bit register.

The content of this register determines the operating state of the numericallycontrolled oscillator. Table 1 provides an overview of the possible operating states of the numerically-controlled oscillator 223 which is utilized in the present invention. During logging operations, the logging apparatus of the present invention is programmed to provide commands from processors 215, 217, 219 (of Fig. 6) with eight-bit commands, so the "CR0" bit is 0.

Normal operation is desired. so the "CR1" bit is 0. In the present invention, amplitude modulation is bypassed, so the "CR2" bit is 0. In the present invention, the synchronizer logic is enabled, so the "CR3" bit is 0. The FREQO register 327 defines the output frequency of the numericallycontrolled oscillator 223, when the FSELECT pin is 1, as a fraction of the frequency of the clock signal applied to clock pin 307. The FREQ1 register 329 defines the output frequency of the numerically-controlled oscillator 223, when FSELECT equals 1, as a frequency of the clock signal applied to clock pin 307. The contents of the phase register 331 are added to the output of the phase accumulator 301. The IQMOD register 333 is not utilized in the present invention.

The operations which can be performed with the registers by supplying command signals to transfer control address bus 323 are set forth in tabular form in Tables 2 and 3. Three basic operations can be performed.

The contents of the parallel assembly register 313 can be transferred to command register 325; the contents of the parallel assembly register can be transferred to a selected destination register, in accordance with the destinations identified in Table 3; and the contents of the serial assembly register 309 can be transferred to a selected destination register.

The load register pin 335 is utilized in conjunction with the transfer control address bus 323 to control loading of intemal registers from either the parallel or serial assembly registers 309, 313. The test pin 337 is utilized only for factory testing. The reset pin 339 is utilized to reset the registers. The reset pin in particular is utilized to clear the command register 325 and all the modulation registers to 0. The current output pins 341, 343 are utilized to supply an altemating current to a selected end device. In the particular embodiment of the present invention, only one of these outputs is utilized for a particular transmitting antenna, since one current is the compliment of the other current. The compensation pin 342 is utilized to compensate for the intemal reference amplifier. The voltage reference pin 343 can be utilized to override an intemal voltage reference, if required. The full-scale adjust pin 345 determines the magnitude of the full scale current at output pins 341, 343. The ground pin 347 provides a ground reference, while the positive power supply pin provides power for the analog components within numerically-controlled oscillator 323. The frequency select pin 354 controls frequency registers FREQO register 327 and FREQ1 register 329, by determining which register is used in the phase accumulator 301 by controlling multiplexer 353. The contents of phase register 331 is added to the output of phase accumulator 301 at sumer 355. The IQMOD registers 333 are provided to allow for either quadrature amplitude modulation or amplitude modulation, so the sine and cosine outputs of lookup table 303 are added together at sumer 357, and are unaffected by the IQMOD registers 333. The output of sumer 357 is provided to digital-toanalog converter 305, which creates an analog signal having a frequency which corresponds to either the contents of the FREQO register 327 or the FREQ1 register 329, a phase which is determined by the output of sumer 355 which is provided as an input to look-up table 303, and an amplitude which is determined by full scale control 359 which is set by full scale adjust pin 345 and reference voltage pin 343. Therefore, the numericallycontrolled oscillator of Fig. 5 can provide an analog output having a precise frequency attribute, phase attribute, and amplitude attribute. Since the device is extremely accurate, it is possible to provide a driving current for the transmitting antennas 203, 205, 207, 209 of Fig. 3 which is controlled precisely. In the preferred embodiment of the present invention, one of transmitting antennas 203, 205 is operated at 400 KHz, while the other of transmitting antennas 203, 205 is operated at 2 MHz. The same is true for antennas 207, 209, with one being operated at 400 KHz and the other being operated at 2 MHz. However, the processors 215, 217, 219 can be programmed to provide any particular frequencies for the transmitting antennas. This will be used to good advantage as will be described below in connection with a calibration routine.

In operation, a command signal is supplied to the FSELECT pin 351 to determine which frequency will be utilized for energizing a particular transmitting antenna. The FREQO register 327 and FREQ1 register 329 may be preloaded with two particular frequencies (such as 400 KHz and 2 MHz).

The binary signal applied to the FSELECT pin 351 determines the operation of multiplexer 353, which supplies the contents of either FREQO register 327 or FREQ1 register 329 of the input of phase accumulator 301. Phase accumulator 301 accumulates a phase step on each clock cycle. The value of the phase step determines how many clock cycles are required for the phase accumulator to count two 7t radians, that is, one cycle of the output frequency. The output frequency is determined by the phase step multiplied by the frequency of the signal applied to the clock input pin 307 divided by 232. In practice, the phase accumulator 301 is cleared, then loaded with the output of multiplexer 353. Then, a predefined time interval is ailowed to pass, during which the signal applied to clock input pin 307 steps the output of phase accumulator 301 through an incrementally increasing phase for the particular frequency. In other words, phase accumulator steps from 0 phase to 180 for a particular frequency. At any time, the output of phase accumulator 301 may be altered by a phase offset which is supplied by phase register 331. Phase register 331 may be loaded in response to commands from processors 215, 217, 219. The phase value is supplied as input to look-up table 303, which converts the output of the phase accumulator 301 (and any desired offset) into a digital bit stream which is representative of an analog signal. This digital bit stream is supplied as an input to the 10-bit digital-to-analog converter 305 which also receives amplitude information from full scale control 359. The digital-to-analog converter 305 supplies an analog output with a particular frequency attribute, phase attribute, and amplitude attribute. For example, an output of 2 MHz, with 15- of phase, and a particular peak amplitude current may be provided as an input to a particular transmitting antenna.

Fig. 6 is a block diagram view of the digital signal processor 221 of Fig. 3. In the preferred embodiment of the present invention digital signal processor 221 comprises a DSP microcomputer manufactured by Analog Devices of Norwood, Massachusetts, which is identified as Model No.

ADSP-2101. This is a single-chip microcomputer which is utilized for highspeed numeric processing applications. Its base architecture 379 is a fully compatible superset of the ADSP-2100 instruction set. The base architecture includes three independent computational units: shifter 371, multiplier/accumulator 373, and arithmetic and logic unit (ALU) 375.

Program sequencer 369 supports a variety of operations including conditional jumps, subroutine calls, and returns in a single cycle. Data address generator 367 includes two address generators. Digital signal processor 221 includes serial port 381 which includes two input channels: input channel 383, and input channel 385. Timer 387 provides timing signals for the data processing operation. and receives as an input a clock signal from divide-by circuit 239 (of Fig. 3). External address bus 289-and external data bus 391 allow digital communication between digital signal processor 221 and central processor 315 of Fig. 3. Memory 393 includes program memory 395 and data memory 397. As is typical with digital signal processors, data memory 397 defines at least two circular buffers associated with serial ports 383, 385, which are designed to receive asynchronous digital data, and store it indefinitely or for a predetermined time interval. The digital signal processor 221 receives digital inputs at channel inputs 383, 385 from an analog-to-digital converter, such as is depicted in the circuit of Fig. 4. The receiving circuit of Fig. 4 receives a current which is representative of the response of a particular receiving antenna 211, 213 to electromagnetic radiation propagating through the borehole. This electrical signal is processed through the circuit components of Fig. 4, and is provided as an input to digital signal processor 221. In the preferred embodiment of the present invention, receiving antenna 211 is identified with a particular input channel of digital processor 221, while receiving antenna 213 is identified with the other input channel of digital signal processor 221.

Central processor 215 (of Fig. 3) utilizes external address bus 389 and extemal data bus 391 to address a particular input channel and read digital data into central processor 215 for processing. In the preferred embodiment of the present invention, digital signal processor 221 can sample data from receiving antennas 211, 213 at a very high sampling rate, which can be read periodically by central processor 215 which processes the data to determine the amplitude attenuation and phase shift of the electromagnetic signal which is propagated through the borehole. One particular routine for calculating amplitude attenuation and phase shift is set forth in greater detail herebelow, in connection with a discussion of the error cancellation feature of the present invention. In broad overview, central processor 215 can pull a selected amount of data from each channel of digital signal processor 221, and from that data calculate the amplitude attenuation and phase shift of the electromagnetic wave as it propagates through the wellbore and past receiving antenna 211 and receiving antenna 213. In the preferred embodiment of the present invention, an upper transmitter transmits an interrogating electromagnetic signal of a particular frequency which propagates downward past receiving antennas 211, 213. Then, a particular one of lower transmitting antennas 207, 209 propagate an interrogating electromagnetic signal upward. Measurements from receiving circuit 231 are stored in the input channels of digital signal processor 221, and read by central processor 215 in a manner which allows for the calculation of amplitude attenuation and phase shift.

Another important feature of the present invention arises from the fact that a precise energizing current can be utilized to energize a particular one of transmitting antennas 203, 205, 207, 209. This will establish the frequency attribute, phase attribute, and amplitude attribute of the electromagnetic interrogating signal. Therefore, a single receiving antenna can be utilized to make the measurement of the electromagnetic interrogating signal as it passes through the wellbore. The amplitude and phase of that interrogating signal can be recorded in memory, and compared with values in memory for the energizing current. This allows a single receiving antenna to be used to provide an accurate measure of amplitude attenuation between that particular receiving antenna and the particular transmitting antenna, and the phase shift of the interrogating signal between the transmitting antenna and the receiving antenna. Of course, the amplitude attenuation and phase shift of the electromagnetic interrogating signal as it passes through the formation is indicative of the resistivity of the well bore and surrounding formation Figs. 7A, 7B, and 7C provide high level flowchart representations of logging operations performed in accordance with the preferred embodiment of the present invention. Fig. 7A depicts logic steps which are performed by central processor 215. Fig. 7B represents operations controlled by processors 217, 219. Fig. 7C depicts operations controlled by digital signal processor 221 and central processor 215. The transmission operations begin at block 401. Processor 215 performs a calibration operation upon receiving antennas 211, 21 3, as will be discussed in greater detail elsewhere in this application. After the calibration operations are performed central processor 215 instructs processor 217 to energize transmitting antenna 203 with a 400 KHz current. Then, in accordance with block 407, central processor 215 instructs processor 219 to energize transmitting antenna 209 with a 400 KHz current. Next, central processor 215 instructs processor 217 to energize transmitting antenna 205 with a 2 MHz current, in accordance with block 409. Then, in occurrence with block 411, central processor 215 instructs processor 219 to energize transmitting antenna 207 with a 2 MHz current. The process stops at block 413. In actual practice, transmission operations will be performed continuously over predefined intervals.

Fig. 7B depicts the control operations performed by processors 217, 219 to cause numerically controlled oscillators 223, 225 to energize particular transmitters. The process begins at block 415. It continues at block 417, wherein the processor 217 or 219 clears the registers in numerically controlled oscillators 223 or 225 by providing the appropriate instruction. Then, in accordance with block 419, processor 217 or 219 loads a predetermined value to the FREQO register and the FREQ1 register.

These values determine the frequency of the energizing current which is supplied toW particular transmitting antenna. Then, in accordance with block 421, processor 217 or 219 loads a predetermined phase value to the phase register of numerically controlled oscillator 223 or 225. Processor 217 or 219 then provides a binary command to the FSELECT input pin of numerically controlled oscillator 223 or 225 to select a particular frequency of operation. Then, in accordance with block 425, a particular time interval is allowed to pass. This time interval determines how many cycles of energizing current are applied to a particular transmitting antenna. The process ends at software block 427. Typically, each time processor 217 or 219 is instructed by central processor 215 to energize a particular transmitting antenna, the steps of Fig. 7B are performed.

Fig. 7C depicts in flowchart for the reception operations. The process begins at block 429. The process continues at block 431, wherein the current within receiving antennas 211,213 are sampled by receiving circuit 231. Then, in accordance with block 433, these samples are loaded to the appropriate input channels 283, 285 of digital signal processor 221.

In accordance with block 435, central processor 215 fetches selected samples from the memory buffers associated with the digital signal processor input channels. In accordance with block 437, optionally, samples may be modified to offset for error components due to "miscalibration" of the antenna, which will be described in greater detail elsewhere in this application. Next, in accordance with software block 439, the digital samples may be digitally filter with either a low-pass digital filter, high-pass digital filter, or a bandpass digital filter. Alternatively, the samples can be averaged over predefined intervals to provide stability to the samples and eliminate the influence of spurious or erroneous samples. Next, in accordance with block 441, the amplitude attenuation and phase shift are calculated, as is described elsewhere in this application. Finally, the process ends at block 443.

1.2 Antenna Calibration Operations The invention provides several novel calibration features of the receiver antennas. The utilization of microprocessors and numerically controlled oscillators (see Fig. 3) in the present invention allows for very precise calibration measurements to be made of the transmission and reception of the interrogating signal either outside the borehole, or preferably in the borehole during logging operations. This is accomplished by having a calibration program resident in memory of processors 217, 219, or in central processor 215, which causes a numerically-controlled oscillator to step or sweep through a particular frequency range. This is accomplished by sequentially providing a command signal from processors 217, 219 to numerically controlled oscillators 223, 225 which establishes a frequency for the energizing current which is supplied to a particular transmitting antenna. Additionally, a command is supplied from processors 217, 219 to numerically controlled oscillators 223, 225 to establish the phase characteristic of the signal. In practice, the frequency sweep should include a fairly wide range of frequencies. Normal reception operations are conducted while a particular transmitter is swept through a range of frequencies. The data is recorded, and provides a combined measure of the response of the transmitting antenna and receiving antenna.

In the preferred embodiment of the present invention, each transmitting antenna coil is swept through a predetermined frequency range, while the receiving antennas are sampled. The result is eight sets of data, one for each possible transmitter/receiver combination, which quantifies the operating condition of the particular transmitting antenna and the particular receiving antenna. Malfunctions in a particular receiving antenna or transmitting antenna can be determined by comparisons between the eight data sets. For example, with reference to Fig. 3, supposing that transmitting antenna 203 is damaged or out of calibration. The data set which establishes the operating condition of transmitting antenna 203 and receiving antenna 211 can be compared with the data set which establishes the operating conditions of transmitting antenna 203 and receiving antenna 213 to determine that transmitting antenna 203, and not a particular receiving antenna, is damaged or out of calibration. The identification of a damaged or uncalibrated antenna is an important diagnostic tool. It can be utilized during logging operations to drop one or more of the transmitting or receiving antennas out of the normal operating cycle, once it has been detected that it is damaged, in order to maintain high quality logging information. Altematively, the calibration data can be used in post-logging operations to modify, interpret, or manipulate the logging data to correct for intervals of measurement during which a particular transmitting antenna was damaged or fell out of calibration.

Fig. 8 provides a high level flowchart representation of calibration operations, which of course is set forth in the context of the flowcharts of Figs. 7A, 7B, and 7C. The process begins at block 445. The process continues at block 447, wherein the calibration operation is initiated by central processor 215. Then, in accordance with block 449, a particular transmitting antenna is selected; in accordance with block 451, a particular receiving antenna is selected. The calibration operations will be performed utilizing this particular transmitting antenna and this particular receiving antenna. The resulting data will provide information about the operating condition of both of these antennas. In accordance with block 453, an energization frequency is set. This is accomplished by providing an appropriate command to numerically controlled oscillator 223. Then1 in accordance with block 455, the transmitting antenna is energized. In accordance with block 457, the receiving antenna is sampled, and the data is stored in memory. At block 459, one or more of the processors determine whether all the frequencies have been swept through. If not, the process continues at again, at a higher frequency than the previous frequency utilized. However if it is determined block 459 that all frequencies have been used, the process ends at block 461. In the preferred embodiment, a particular frequency range is stepped through in increments of fractional portions of 1 Hertz. For practical purposes, the calibration operation can be considered to be a sweep through all frequencies within a predetermined frequency range. The data that is recorded in memory can be anaiyzed in a manner discussed below to assess the operating condition of the transmitting antenna and the receiving antenna.

Fig. 9 provides a depiction of an example of the type of data that can be acquired during a calibration operation. Of course, during logging operations, the data will not be recorded or depicted in graphical form. Instead, a data array will be defined which includes information about the amplitude and phase attribute of the receiving antenna's response at a particular frequency. The graphical depiction in Fig. 9 is provided for purposes of exposition. In the view of Fig. 9, the amplitude of the response of the transmitting and receiving antenna is depicted by curve 463. In Fig. 9 the phase of the response of the transmotting and receiving antenna is depicted by curve 465. In order to determine when malfunctioning is occurring, it is necessary that a normal operating condition be preestablished. This should be done with regard to a range of acceptable operating conditions. The graph of Fig. 9 depicts normal operation over a range of 300 KHz to 3.3 MHz. In the view of Fig. 9 , peaks 467, 469, 471, 473 define two resonant frequencies for the transmitting and receiving antennas, with resonances occurring at 400 KHz and 2 MHz, since the particular antennas utilized to generate this calibration graph were resonant at both 400 kHz and 2 MHz. From the information contained in the measurements made when the tool is operating normally, parameters can be established to alert of malfunctioning. Figs. 10A, 10B, and 10C graphically depict three techniques for detecting antenna malfunction. The first technique for detecting antenna malfunction is depicted in Fig. 10A wherein peak 475 is representative of either an amplitude or phase peak for normal operations. In contrast, peak 477, which is generated as a result of calibration operations during logging, indicates to the operator that a shift in the resonant frequency has occurred. A range of acceptable resonant frequencies can be established. If the measurement falls outside an acceptable range, a determination can be made that either the transmitting antenna or the receiving antenna is malfunctioning. Fig. 10B depicts another technique for detecting malfunctioning antennas. Peak 479 represents normal operations, while peak 481 represents a measurement made during logging. The antenna Q for the actual measurement differs significantly from the antenna Q of the normal operating state. A change in the antenna Q can thus be used to indicate malfunctioning.

1.3 Correction for Changes in Antenna Impedance and Antenna Mutual Coupling When an interrogating signal is received at the receiver antenna, the electrical parameters which quantify the signal, phase and amplitude, are functions not only of the desired signal from the transmitter, but are also functions of the antenna impedance. Antenna impedance can change during tool operation as a function of temperature and pressure.

Since this functional form of this change may not be known a priori, the present invention devises a method to measure the effects of these functional changes upon the desired signal.

Fig. 11 provides an electrical schematic depiction of an equivalent circuit which depicts the relationship between antenna impedance and an antenna transfer function. This can be utilized to explain the parameters which affect the impedance of a receiver in a logging tool. In this electrical schematic, the impedance of a receiving circuit is identified as Rr. The voltage Ein across the receiver circuit input represents the receiving antenna's response to the measurement of the propagating electromagnetic field. Zin represents the impedance of the receiving antenna as seen from the receiver electronics. The impedance includes Rant which is the resistive component of the receiving antenna, Ca which is the capacitive component of the receiving antenna, and La which is the inductive component of the receiving antenna. This equivalent circuit is mutually magnetically coupled to the steel drill collar logging tool subassembly Rsub, the surrounding formation Rfoih-tation, and the transmitter. The sub is essentially a resistive component which is mutually coupled through inductive component Ls to the receiving antenna denoted by the mutual coupling Mat. The formation is essentially a resistive component which is coupled magnetically to the receiving antenna through inductor Lf via mutual inductance Mat. The voltage induced in the receiving antenna from the transmitter is the desired signal, and the effect of the formation, sub, and antenna impedance upon the measurement of this voltage are variables for which this invention accounts.

The transmitter is essentially a voltage source which is coupled to the receiving through inductor Lt. The circuit of Fig. 11 can be reduced to the circuit depicted in Fig. 12, with the impedances of the antenna, the subassembly, the formation, and the transmitter represented respectively as: Zantenna, Zsub, Zformation, and Zt. Et is the equivalent voltage source in the receiver circuit due to the transmitter. A current I is induced to flow through this equivalent circuit by voltage source Et. As is depicted in Fig. 12, a voltage Ein is developed across the receiving circuitry as a result of this current flow. The combined effect on the antenna of impedance of the antenna, the drill collar subassembly, the formation, and the transmitter is represented in this view as Zin. The impedance of the receiving antenna, along with the impedances introduced through normal operation and undesired mutual coupling make up the impedance Zin, as is set forth herebelow: (1) Zin = Zantenna + Zsub + Z formation + Zt The transfer impedance for the antenna is represented as: (2) Rr + Zantenna + Zsub + Zformation + Zt = - Et II This transfer impedance states that the total current within the equivalent circuit of Fig. 12 is a function of the voltage of the transmitting antenna Et, and all the impedances of the circuit of Fig. 12. The current can also be stated as a function of Ein and Rr, r as: (3) l=-Ein/Rr The transfer function for the antenna can be determined from these relationships in accordance with equation (4): (4) Transfer Function = Et / Ein =(Rr + Zantenna + Zsub + Zformation +Zt) / Rr Combining equation (1) with equation (4) yields: (5) Transfer function = Et / Ein = (Rr + Zin) / Rr Note that the transfer function is a simple function of the receiver impedance Rr and the measured antenna input impedance Zin.

In the present invention, the particular technique utilized to measure Zin is a conventional "network analysis method." In accordance with this technique, a reflection coefficient p is obtained by measuring the ratio of an incident wave to the reflected wave. Typically, a directional coupler or bridge is used to detect the reflected signal, and a network analyzer is used to supply and measure the signals. In the present invention, the numerically controlled oscillator can serve the functions of the network analyzer, since its output attributes.(frequency, phase, and amplitude) can be precisely controlled, and further since the actual output is measured over a predetermined frequency interval. Directional couplers are devices which are used to separate or sample the traveling electromagnetic wave moving in one direction on a transmission line while remaining virtually unaffected by the traveling electromagnetic wave moving in the opposite direction. Thus, they are typically utilized in analyzing power transmission lines and the like.

They are frequently used in combination with power splitters which receive an input, and provide two equal outputs. In the present invention, both directional couplers and power splitters are utilized to derive the measurements which are utilized in the elimination of the undesired effects of mutual coupling between receiving antennas.

The reflection coefficient is derived from the voltage of the signal reflected from the antenna and the voltage of the signal going into the antenna, in accordance with the following equation: (6) p = reflection coefficient = (voltage of signal reflected from antenna) (voltage of signal going into the antenna) Furthermore, the impedance of the antenna can be derived from the reflection coefficient and the impedance of the directional coupler ZO in accordance with equation (7) as: (7) Zin = ((p + 1) ZO) / (p - 1) Equations (5) and (7) can be combined to determine the transfer function Et/Em in terms of Rr (the impedance of the receiver circuit, which is known), Zo (the impedance of the directional coupler, which is also known), and p (the reflection coefficient, which an be calculated from a measurement of the incident signal and a measurement of the reflected signal) as follows in equation (8): (8) EtlEm = (Rr + ((p + 1)/(p-1))Zo) / Rr From this transfer function, the voltage induced into the receiving antenna by the transmitter, Et, may be determined by simply multiplying the receiver voltage by the transfer function : Et = Emx(EtlEm) corrected by Zantenna, Zsub and Zt.

Fig. 13 provides a block diagram view of the components which interact in the measurement process to eliminate the influence of undesired magnetic field mutual coupling between receiving antennas. Fig.

14 is a more detailed view of the components which cooperate together to make this analysis possible.

With reference first to Fig. 13 , directional coupler 501, directional coupler 503, and numerically controlled oscillator 509 are especially provided to allow for the measurements which can be utilized to eliminate the effects of undesirable magnetic field mutual coupling between receiving antennas 211, 213. As will be described in connection with Fig.

14, directional couplers 501, 503 are switched in and out of the circuit depending upon whether normal reception operations are desired, or whether a mutual coupling calibration operation is required. Receiver circuits 505, 507 are identical to the receiver circuit depicted in Fig. 4 and described above. This receiver circuit has a characteristic resistance Rr for receiver 505 and Rr for receiver 507. These resistance values are about 50 ohms. The directional coupler 501 in Fig. 14 by provides at least 60dB isolation between forward and backward traveling signals. Receiving antennas 211, 213 have an effective impedance of Zin, which mat change with temperature and pressure. Digital signal processor 221 generates, or passes along, commands to numerically controlled oscillator 509 to provide an energizing signal which may be directed through either directional coupler 501 to receiving antenna 211, or through directional coupler 502 to receiving antenna 213. A certain portion of the energizing signal is accepted by receiving antenna 211 or 213, and a portion is reflected back, through directional coupler 501 to receiver 505, or through directional coupler 503 to receiver 507. The reflected signals are processed by digital signal processor 221, and passed to central processor 215. Digital signal processor 221 may simply provide a circular memory buffer for the storage of data, which is then periodically fetched by central processor 215 for further processing. This activity is represented by the "data out" bus of Fig. 13. In the preferred embodiment of the present invention, each of receiving antennas 211, 213 is analyzed separately.

In broad overview, in the present invention, the technique for correcting a measurement made with a particular receiving antenna for the (corrupting) error component due to undesirable magnetic field mutual coupling is accomplished by making the following measurements over a predefined frequency interval (such as 100 Hertz to 6 MHz): direct an energizing signal to a particular receiving antenna, and measure with precision the amplitude and phase attributes of the incident wave; measure with precision the reflected wave which reflects off of the receiving antenna and back through a directional coupler; calculate the reflection coefficient pfrom the measurements of the incident wave and reflected wave; utilize the calculated value of reflection coefficient p, and the known impedance ZO of the directional coupler, to calculate the input impedance Zin for the particular receiving antenna; utilize Zin and the known (or fixed) impedance of the receiver circuit Rr to calculate the transfer function for that particular antenna.

Note that this determination is made for all operating frequencies of interest.

With specific regard to the preferred embodiment of the present invention, measurements will need to be made for 400 KHz and for 2 MHz, since these are the two operating frequencies are utilized during logging operations.

Note that, in accordance with equation (5), the transfer function provides a measure of the ratio of the voltage venerated in the receiving antenna as a consequence of an interrogating electromagnetic signal (Et) and the voltage detected at the input of the reception circuit (Ein). In other words, the transfer function at a particular frequency equals Et + Ein. This transfer function may be applied to measurements made during logging operations to eliminate the influence of the corruption in the detected voltage (Ein) which is due to magnetic field mutual coupling and thermal (and other) drifts in antenna response. This correction may be accomplished by merely multiplying a detected signal (Ein) times the transfer function value for the receiving antenna at the interrogation frequency which is sensing the interrogating signal. InYhis manner, the measurement is corrected to supply an uncorrupted signal Et for further processing. In the preferred embodiment of the present invention, the mathematical operations which eliminate the corrupting influence of the undesirable magnetic field mutual coupling occur in either digital signal processor 221 or central processor 215.

In other words, for each measurement made by receiving antenna 211, digital signal processor 221 (or central processor 215) automatically fetches a value recorded in memory for the transfer function of receiving antenna 211 at the particular frequency of the interrogating signal which is being utilized. The measurement made utilizing receiving antenna 211 is multiplied by the transfer function value; the resulting product is a measurement value which is corrected for the corrupting influence of undesirable magnetic field mutual coupling between receiving antenna 211 and receiving antenna 213. Conversely, when receiving antenna 213 is utilized to measure an interrogating electromagnetic field, digital signal processor 221 (or central processor 215) fetches the transfer function value for the particular frequency of the interrogating field, and then multiples that value times the measurement obtained from receiving antenna 213. The product is the measurement made with receiving antenna 213 which has been corrected for the corrupting influence of undesirable magnetic field mutual coupling between receiving antenna 213 and receiving antenna 211. The details of operation are set forth below in the description in connection with Fig. 14.

With reference now to the view of Fig. 14, receiving antenna 211 is depicted as being optionally connected through directional coupler 501 to receiver circuit 505 and digital signal processor 221. Receiving antenna 213 is likewise depicted as being optionally coupled through directional coupler 503 to receiver circuit 507 and digital signal processor 221. Receiving antennas 211, 213 are optionally coupled to the output of numerically controlled oscillator 509 through power splitters 519, 521, and 523. Attenuators 511,513,515, and 517 are provided at selected positions within the circuit for load balancing purposes. Preferably, each attenuator provides a 60dB load. In the circuit of Fig. 14, four switches are provided: switch S1, switch S2, switch S3, and switch S4. Each of these switches is under the control of digital signal processor 221 and/or central processor 215 (of Fig. 6). Switches S1, S3 are three-positioned switches, while switches S2, S4 are two-position switches. Each switch is under the binary control of a particular output pin of digital signal processor 221.

Changes in the binary condition of the output pin of digital signal processor 221 will toggle switches S2, S4 between open and closed positions, while switches S1, S3 are toggled between the three positions.

Fig. 14 will now be utilized to describe six basic measurement operations which underlie and allow the technique of the present invention of eliminating the undesired effects of magnetic field mutual coupling between receiving antennas and phase drift due to high wellbore temperatures or pressures.

Step 1: in this step, switch S1 is set in position number two, switch S2 is closed, switch S3 is placed in position number one, and switch S4 is left open. Numerically-controlled oscillator 509 is coupled to receiving antenna 213 through switch S2 to allow an electromagnetic propagating wave to pass between receiving antenna 213 and receiving antenna 211.

Also, in this particular configuration, receiver circuit 507 is connected to receive and monitor the output of numerically controlled oscillator 509 through power splitter 523 and impedance 513 while receiving antenna 213 is energized. Additionally, receiving circuit 505 is connected to monitor the signal originating from receiving antenna 211 in response to the electromagnetic wave which travels from receiving antenna 213 to receiving antenna 211.

Step 2: this step is performed simultaneously with Step 1.

Receiving circuit 505 is coupled through switch S3 through receiving antenna 211, and monitors the response of receiving antenna 211 to the electromagneticxpropagating wave which is generated at receiving antenna 213 (which is operating as a transmitter) and received at receiving antenna 211 (which is operating as a receiver). In Step 2, all the switch positions are identical to those positions of Step 1.

The result of the simultaneous performance of these operations it that channel 1 of digital signal processor 221 records data from receiving antenna 211 through receiver circuit 505, while channel 2 of digital signal processor 221 records the output of numerically controlled oscillator 509 through receiver circuit 507. In the preferred embodiment of the present invention, numerically controlled oscillator 509 is commanded by digital signal processor 221 to step through a predetermined range of frequencies.

The data accumulated on channel 1 and channel 2 of digital signal processor 221 thus defines two data sets: one which records the energizing signals supplied to receiving antenna 213 (the "incident signal"), which is operated as a transmitter, and another which records the response of receiving antenna 211 to that energizing signal.

Fig. 1 5A provides a graphical depiction of data which is recorded on channel 2 of digital signal processor 221, with curve 601 providing a view of the amplitude of the output of the numerically controlled oscillator over the predefined frequency range of f1 to f2, and with curve 601 providing a record of the phase attributes of the output of the numerically controlled oscillator 509 for the range of frequencies from f1 to f2. Together, these values for amplitude and phase provide a measure of the "incident signal". Fig. 15B provides an exemplary view of the type of data which can be recorded on channel 1 of digital signal processor 221, with curve 605 representative of the amplitude response of receiving antenna 211 to the energizing electromagnetic wave provided by receiving antenna 213, over the predefined range of frequencies of f1 to f2, and with curve 607 providing information about the amplitude response of receiving antenna 211 over the same range of frequencies. The information contained in Fig. 15B is similar to that contained in Fig. 9, but provides information about the operating condition of receiving antennas 211, 213. The type of data analysis which is discussed above in connection with Figs. 9, 10A, 10B, and 10C can be performed upon the receiver-to-receiver profile. In other words, the signal recorded on channel 1 provides a measure of the combined response of receiving antenna 211 (operating as a transmitter) and receiving antenna 213 (operating as a receiver) in combination with the impact of the borehole and formation on the signal transmission. Data sets can be created for transmission in one direction (receiving antenna 213 operating as a transmitter, and receiving antenna 211 operating as a receiver) as well as the other direction (receiving antenna 211 operating as a transmitter, and receiving antenna 213 operating as a receiver). The data sets assembled for these operations can be compared with profiles developed in the laboratory for normal operation. Changes or shifts in resonant frequency, antenna Q, or the amplitude of response at a particular frequency can provide important information about whether the receiving antennas 211, 213 are operating as desired, or whether they are damaged or out of calibration.

Step 3: in this step, switch 1 is set in position three, and switch 2 is closed. The positions of switch S3 and switch S4 are are open and are unimportant for this operation. In this operation, numerically controlled oscillator 509 directs an interrogating signal through power splitter 519, power splitter 523, and switch 3 toward directional coupler 503 and receiving antenna 213. A portion of the energizing signal is accepted by receiving antenna 213, and represents the "incident signal", while a portion is rejected by receiving antenna 213 and represents the *reflected signal." The reflected signal is directed through attenuator 511 and switch S1 to receiver circuit 507. Preferably, numerically controlled oscillator 509 is stepped through a predetermined frequency range, and receiver circuit 507 monitors the reflected signal over the particular frequency range, and ports the data into channel two of digital signal processor 221. Fig. 15C provides a graphic depiction of the type of data which is recorded in channel two of digital signal processor 52, with curve 609 representative of the amplitude attributes of the reflected signal and curve 611 representative of the phase attributes of the reflected signal.

In steps 4, 5, and 6, the process is reversed, with receiving antenna 211 serving as the transmitting antenna. This provides information from a different point of view.

Step 4: in this step, switch S3 is set in position two, switch S4 is closed, switch S1 is set in position one, and switch S2 is left open. In this configuration, numerically controlled oscillator 509 may be stepped through a predefined frequency range, and receiver circuit 505 can record the amplitude and phase of the output of numerically controlled oscillator 509 (the "incident signal"), and provide this to channel one of digital signal processor 221. Fig. 1 6A provides a view of the type of amplitude 613 and phase 615 data which may be recorded during this operation.

Step 5: This step is performed simultaneously with step 4. With the same particular switching configuration of Step 1, receiving antenna 211 is supplied with an energizing signal, causing an electromagnetic wave to propagate toward receiving antenna 213. Receiving antenna 213 responds to the propagating electromagnetic signal, and this response is monitored by receiver circuit 507 and recorded on channel two of digital signal processor 221. Fig. 198 graphically depicts the amplitude response curve 617 and the phase response curve 619, both over the predetermined frequency range.

Step 6: in this step, switch S3 is set in position three, switch S4 is closed, switch S1 is set in position 1, and switch S2 is left open. In this particular switching configuration, the energizing signal provided by numerically controlled oscillator 509 is directed toward receiving antenna 211. A portion of the energizing signal is accepted by receiving antenna 211, and a portion is reflected. The reflected portion is routed through attenuator 517 and switch S3, where it monitored by receiver circuit 505, and recorded to channel one of digital signal processor 221. Fig. 1 6C provides a graphical depiction of the data sets which are maintained in channel one of digital signal processor 221 in graphic form.

In the preferred embodiment of the present invention, the data from these operations are arranged in data arrays, to allow for the use of conventional data manipulation operations in order to detect or identify particular attributes of the data set, such as maximum responsiveness, minimum responsiveness, rates of change of the data, and the relative position of particular data attributes. Diagnostic operations can be performed utilizing these data sets. For example, the responses recorded in data sets corresponding to the information displayed in graphical form in Figs. 15A and 16A may be compared. Since the numerically controlled oscillator 509 has "phase coherency," the amplitude and phase measurements of the data sets of Figs. 15A and 16A should be identical. The failure to find similarity, or the discovery of dissimilarity, can serve to diagnose a variety of mechanical problems, including broken switches, a malfunctioning receiver, or other component failure. For an altemative example, the data sets which are visually represented in Figs. 15B and 16B may be compared. The curves of Figs. 15B and 16B should be identical, since they represent the combined response of the receiving antennas and the borehole region intermediate the receiving antennas.

Fig. 17 is a flowchart depiction of the preferred technique of the present invention for correcting for the undesired corrupting influence of (1) magnetic field mutual coupling between receiving antennas, and (2) any drift in antenna response. The process begins at flowchart block 615. In block 653, a particular transmitter is energized with a current having a particular frequency to generate an electromagnetic field which propagates through the borehole, and which is detected at receivers 211, 213, in accordance with software block 655. Then, in accordance with software block 657, digital signal processor 221 or central processor 215 fetch transfer function values for the particular operating frequencies for (a) the mutual coupling impact of receiving antenna 211 on receiving antenna 213, and (b) the mutual coupling impact of receiving antenna 213 on receiving antenna 211. Then, in accordance with software block 659, the transfer function value of the impact of receiving antenna 211 on receiving antenna 213 is applied to the measurements made with receiving antenna 213. Then, the transform value for the impact of receiving antenna 213 on receiving antenna 211 is applied to the measurements made with receiving antenna 211. Then, in accordance with software block 661, resistivity values for the formation are calculated using the corrected measurements, and the process ends at block 663. These operations are performed for every measurement made during logging operations. The transfer functions associated with transmission operation frequencies of 400 KHz are utilized to correct for mutual coupling and thermal error components present during 400 KHz logging operations, while the transfer functions associated with 2 MHz are utilized to correct for the influence of mutual coupling and drift components during 2 MHz transmission operations.

1.4 Logging Calculations The following section illustrates how the present invention is used to derive an accurate measure of the amplitude attenuation and the phase shift of the interrogating electromagnetic signal which travels through the borehole and surrounding instrument comprising two transmitters and two receivers is used to illustrate data processing methods. The derivation of resistivity of the formation, resistivity of the borehole, characteristics of the formation and borehole, and data processing using a borehole instrument comprising four transmitters and two receivers will all be discussed in subsequent sections.

First, consider four transmitter-to-receiver signals: (Transmitter 1 [X1] to Receiver 1 [R1]): A11 ei#11 (Transmitter 1 [X1] to Receiver 2 [R2]): A12 ei#12 (Transmitter2 [x2j to Receiver 1 [R1]): A21 eier2, (Transmitter 2 [X2] to Receiver 2 [R21): A22 ei22 The measured amplitudes are made up of: (9) Amn = Xm Rn atmn where Xm = transmitter output variation Rn = receiver sensitivity variation atmn = true amplitude (transmitter M to receiver N); and the measured phases are made up of: (10) #mn = #Xm + #Rn + #tmn where Xm = transmitter phase (output) variation Rn = receiver phase variation tmn = true phase (transmitter M to receiver N) The foregoing general equations correspond to the following more specific equations: A11 = X1 R1 atil A12=X1 R2 at12 A21 = X2 R1 at21 A22 = X2 R2 at22 11 = #x1 + R1 +11 #12 = #X1 + #R2 + #t12 #21 = #X2 + #R1 + #t21 #22 = #X2 + #R2 + #t22 Taking ration of the various transmitter-to-receiver signals produces the following: For Transmitter 1 (A12 ei#12/A11 ei#11) = (A12/A11)e i(#12 - #11) and for Transmitter 2: (A21 ei#21/A22 ei#22) = (A21/A22)e i(#21 - #22) Multiplying the above equations and taking the square root gives: (11) [(A12A21/A11A22)] exp (i (#12+#21-#11-#22)/2) Straightforward algebraic manipulation of equations (9) through (11) yields: (12) [(ati2 at21 / at1 1 at22)]112 exp(i (#t12+#t21-#t11-#t22)/2) because all the system variables drop out of the measurement.

Therefore, by using two transmitters and two receivers, systematic variables can be removed from both the attenuation (amplitude) and from the phase velocity (phase difference) terms.

Within the context of the preferred embodiment of this invention, in which a sampled data processing means produces a signal as a function of formation resistivity based on phase-representing signals, the following analysis demonstrates certain matter relevant to the stability feature.

Consider two consecutive samples: Sample A and Sample B.

During Samplir A, a first transmitting coil is energized to cause a wave to propagate through the formation in a direction such that the wave passes a first receiving coil (R1), and later passes a second receiving coil (R2), and induces each receiver coil to produce a signal. During Sample B, a second transmitting coil is energized to cause a wave to propagate through the formation in a direction such that the wave passes a second receiving coil (R2), and later passes the first receiving coil (R7), and induces each receiver coil to produce a signal.

Let MR2A represent the measured phase of the signal produced by receiver coil R2 during Sample A; let oMR1A represent the measured phase of the signal produced by receiver coil R1 during Sample A; let MR1 B represent the measured phase of the signal produced by receiver coil R1 during Sample B; and let MR2B represent the measured phase of the signal produced by receiver coil R2 during Sample B.

The MR2A signal depends on the phase of the wave at the location of R2, and in general, has an error component attributable to various phase shifts including those introduced by the tuned receiver coil, cabling from the receiver coil to the receiver, and the receiver itself. Let TR2A represent the true phase of the wave at the location or R2 during Sample A, and let R2E represent the error component so introduced.

(13) oMR2A = oTR2A + oR2E Similarly, the oMR1A signal depends on the phase of the wave at the location or R1, and in general, has its own error component. Let ATRIA represent the true phase of the wave at the location of R1 during Sample A, and let #R1E represent the error component so introduced.

(14) #MR1A = #TR1A + #R1E During Sample A, the MR1A signal and the MR2A are simultaneously processed to produce a DeltaA signal that represents the difference in phase between these two signals (i.e., #MR1a - MR2A).

(15) Delta A = (TR2A- #TR1A) + (R2E - R1 E) The component of the DeitaA signal representing the true phase difference (TR2A - #TR1A) is a function of the resistivity of the formation in the region between the two receiver coils. Let F(Rapp) represent this component.

(16) DeltaA = F(Rapp) + (R2E - oR1 E) Similarly, during Sample B, the MR2B signal and the #MR1B are simultaneously processed to produce a DeltaB signal that represents the difference in phase between these two signals (i.e., MR2B - oMR1B).

(17) #MR1B = #TR1B + #R1E (18) #MR2B = #TR2B + #R2E (19) DeltaB = (#TR1B - #TR2B) + (#R1E - #R2E) The component of the DeltaB signal representing the true phase difference (TR1B - TR2B) is a function of the resistivity of the formation in the region between the two receiver coils; i.e., it equals F(Rapp).

(21) DeltaB = f(Rapp) + (RiE - # R2E) The Delta A signal is recorded so that it can be retrieved and processed with the Delta B signal.

By adding Equations (19) and (20), it follows that: DeltaA + DeltaB=2 * F(Rapp) + oR2E - oR1E - oR2E + oRIE , and (21) F(Rapp) = 1/2 * (DeltaA + DeltaB) In other words, a computed signal representing the sum of the consecutive samples is a function of formation resistivity, and error components such as oR1E and R2E do not introduce errors into this computed signal.

2. PARALLEL PROCESSING OF MEASURED DATA As discussed briefly is a previous section, it is desirable to transform signals measured by the one or more receivers into parameters of interest using simultaneously using "parallel" processing. Consider again the four transmitter-two receiver embodiment of the borehole logging instrument shown in Fig, 2. The near spacing dn between transmitter and receiver array is denoted by the numeral 23 and the far spacing df is denoted by the numeral 21. Both the near spacing distances 23 and far spacing distances 21 are measured with respect to the midpoint 25 between the receivers 213 and 211. Point 25 is commonly referred to as the "measure point" of the borehole instrument. For transmitter frequency a) 1 the phases of the signal detected at receivers 213 and 211 resulting from the sequential transmission from transmitters 209 and 205 are combined algebraically to obtain Rp,n,1. More specifically, a first phase shift computed from the difference in the responses of receivers 213 and 211 resulting from the activation of transmitter 207 is algebraically averaged with a second phase shift computed from the difference in the responses of receivers 213 and 211 resulting from the activation of the transmitter 205 to yield Rp,n,1.

The amplitudes of these received signals are simultaneously measured and combined yielding Ra,n,1. More specifically, a first amplitude attenuation is computed from the ratio of the responses of receivers 213 and 211 resulting from the activation of transmitter 207 is algebraically averaged with the ratio of the responses of receivers 213 and 211 resulting from the activation of transmitter 205 to yield Ra,n,1. Again for a transmitter frequency 1. the phase of the signals received at receivers 213 and 211 resulting from the sequential transmission from transmitters 209 and 203 are combined algebraically in a similar manner to obtain Rp,f,1. The amplitudes of these signals are likewise simultaneously measured and combined in a similar manner yielding Ra,f,1. The above sequence is repeated with a second transmitter frequency 02 yielding Rp,n,2, Ra,n,2, Rp,f,2 and Ra,f,2. The end result is eight apparent resistivity measurements comprising amplitude and phase shift measured at two transmitter-receiver spacings and at two transmitter frequencies.

Fig. 18 illustrates hypotheticai measurements of resistivity across a thin formation bed denoted by the numeral 51 using a single transmitter and two receivers. This bed of vertical extent 56 is bounded on either side by formation of essentially infinite vertical extent identified by the numeral 61. In the example, the vertical extent 56 of bed 51 is 4.0 feet. The true resistivity of the bed is 10 ohm meters as illustrated by curve 50 and the bed is invaded to a depth of di = 60 inches. With the resistivity of the invaded zone Rxo = 2.0 ohm meters as illustrated by curve 52. The resistivity of the surrounding or shoulder formation, RSHOULDER = 0.5 ohm meters, is illustrated by curve 60. The shoulder formations are not invaded by the drilling fluids.

Curves 53 and 54 illustrate the apparent phase and amplitude resistivities measured across the bed boundaries at a transmitter frequency of c91 = 2 MHz. Using previously defined nomenclature, curve 53 is computed from the difference of the two receivers and is denoted by Rp,f,l and curve 54 is calculated from the ratio of the two receivers and is denoted by Ra,f, 1.

Similar curves are generated at a second frequency 02 but are not shown.

It can be seen that the maximum or peak values of curves 53 and 54 within zone 51, denoted by the numerals 58 and 57, respectively, are 2.23 and 2.07 ohm meters, respectively. Both apparent resistivity measurements diverge greatly from the actual or true resistivity of Rt = 10 ohm meters. Fig.

19 is a graphical representation of an algorithm for correcting apparent resistivity meWsurements made at a frequency of 2 MHz for the effects of invasion in formations of infinite vertical extent. The algorithm was derived using theoretical transmitter-receiver array calculations well known in the art.

Using values for di = 60 inches, Rxo = 2.0 ohm meters and the maximum phase and amplitude values of 2.23 and 2.07 ohm meters, respectively, the resulting "corrected" value for true resistivity, Rcor = 2.09 ohm meters, still exhibiting significant divergence from the actual bed resistivity value of 10.0 ohm meters. Bed boundary corrections are applied to the maximum phase and amplitude resistivity measurements 58 and 57 using correction algorithm derived from theoretical transmitter-receiver response calculations well known in the art and depicted graphically in Figs 20A and 2OB, respectively, using a bed thickness of 4.0 feet. Ra denotes apparent resistivity measurement in using the charts. These corrected values are then serially corrected for invasion, again using the synthetic data depicted graphically in Fig. 18. After applying both bed boundary corrections and invasion corrections serially, the resulting "corrected" value for true resistivity is Rcor = 5.2 ohm meters which still exhibits significant deviation from the true resistivity value of 10.0 ohm meters. It is apparent that serially corrections for the hypothetical example at a frequency of 2 MHz is totally inadequate.

Similarly, the same sequence of corrections using corresponding amplitude and phase resistivities made at 02 = 400 MHz can also be shown to be totally inadequate. Serially corrections for additional parameters (not shown) such as borehole diameters, resistivity of the drilling fluid, dielectric effects and formation anisotropy also yield inadequate corrections at either transmitter frequency for true resistivity.

The current invention utilizes the eight previously defined measurements of apparent resistivity along with the comprehensive model of the response of the borehole instrument in a variety of formation and borehole conditions to simultaneously determine formation and borehole parameters of interest. The process is generally defined by the matrix equation: (22) [R] = [T1 x pq where [R] is a 1 x 8 matrix representing eight measures of apparent resistivity at multiple frequencies and transmitter spacings as defined previously, and [X] is a 1 x 8 matrix representing 8 parameters of interest to be determined.

For the example being considered, Rt, Rxo, SHOULDER. di and the thickness of the zone 56 are included as elements of the matrix [X]. [T1 is an 8 x 8 transform matrix based upon the comprehensive model of the borehole instrument response in a variety of borehole and formation conditions, examples of which are shown graphically in Fig.s 19, 20A, and 20B. As an example, [T1 comprises the response functions for the borehole instrument across bed boundaries, the responses characteristics as a function of invasion, and response functions for all other borehole and formation parameters discussed previously in this disclosure. The values of the elements of [T1 will depend upon resistivity and will, therefore, depend upon the matrices [X] and [R]. As a result of this functional dependence, equation (22) is not a simple linear matrix equation. US. Pat. No. 5,144,245 to M. M.

Wisler, assigned to the assignee of this disclosure, describes such a model and is hereby entered by reference. A non-linear regression scheme is used to invert the equation (22) yielding (23) [X] = [T] x [R] where 1T'] is the inversion of the response matrix [Ti. The matrices on the right hand side of eguation (23) are therefore either representative of measured quantities ([R]) or are known from theoretical calculations (["j).

Solving equation for [X], which includes Rt as an element, a corrected value of Rt = 10 ohm meters is obtained for the hypothetical example shown in Fig.

18. The fact that sets for two transmitter frequencies are used in the present invention contributes to the convergence of the measured and true formation resistivities when compared to the previous computations using only measurements at 2 MHz. Equally important in the conversion is that the current invention employs simultaneous inversion of the measurements at multiple frequencies and multiple spacings. The errors introduced at higher frequencies resulting from serial processing are thus avoided.

3. DETERMINATION OF BOREHOLE PARAMETERS Previous discussions defined the uses of measured borehole and near borehole parameters. The drilling fluid invasion profile is indicative of the permeability of the formation. In addition, physical properties of the borehole such as rugosity and ellipticity can be related to the mechanical properties of the rock matrix and to the effectiveness of the borehole drilling operation using the preferred MWD embodiment of the invention. Further, knowledge of rock matrix properties is extremely useful in specifying subsequent completion activities such as possible fracturing and even perforating programs. Finally, a knowledge of the condition of the borehole, the drilling program can often be modified to increase efficiency such as modifying drilling parameters to increase bit penetration rates.

Referring again to Fig. 2, the transmitters are activated sequentially at a first frequency. The phase shift and amplitude attenuation of the induced electromagnetic signals are measured at each receiver, with respect to the transmitter outputs as previously described, yielding sixteen basic signal measurements (Eight amplitude attenuation and eight phase shift measurements). The procedure is then repeated at a second transmitter frequency yielding an additional eight measurements of amplitude attenuation and eight measurements of phase shift. A total of thirty two uncorrected "raw" measurements are therefore obtained for each cycle of transmitter activations as the borehole instrument 36 is conveyed along the borehole 34. Each phase shift and amplitude attenuation, being uncorrected by means previously mentioned, is greatly affected by the borehole and the near borehole environs. These raw measurements are used, therefore, to determine borehole characteristics such as borehole diameter, rugosity and eccentricity as well as providing means for correcting apparent resistivity measurements for these borehole effects. Stated another way the invention not only provides formation resistivity measurements corrected for perturbing effects of the borehole as previously described, but also provides means for quantifying these corrections thereby providing useful information on the physical properties of the borehole. These borehole properties, in turn, can be related to such parameters as mechanical properties of the rock matrix, shallow invasion profiles, and the effectiveness of the drilling program. The vertical resolution of the thirty two measurements are, in general, different and vary from measurement to measurement when borehole conditions are rapidly varying with respect to the transmitter-receiver array spacings 21 and 23. It is necessary to apply deconvolution techniques in order to "match" the vertical resolution of all sixteen measurements prior to combining these data using means previously mentioned. Resolution matching is not an independent data processing step as is often the case in prior art, but is an integral step in the calculation of all parameters of interest.

It should be understood that other transmitter-receiveroperating frequency combinations can be utilized. As an example, two transmitters and four receivers with the transmitters operating at two frequencies will also yield thirty two raw measurements. Expanding the variability concept even further, an array of one receiver, operating at two frequencies, and eight receivers will also yield a total of thirty two raw measurements of amplitude and phase, as will one receiver and one transmitter operating at sixteen frequencies. The transmitter-receiver frequency combination can also be varied to yield a raw measurement total greater than or less than thirty two with a corresponding increase or decrease in the number of parameters of interest that can be uniquely determined.

Referring again to Fig. 2, the transmitters 209, 207, 205 and 203 are activated sequentially at a given frequency 6)1. The phase and amplitude of the induced electromagnetic signal are measured at each receiver transmitter pair thereby yielding a total of eight measurements of amplitudes and eight measurements of phase which will be identified as Ai and Pi, respectively, where (i = 1,...,8). The procedure is then repeated at a second transmitter frequency 02 yielding an additional eight measurements of amplitude and eight measurements of phase which will be identified as A and Pi, respectively, where (i = 9,...,16). The above defined cycle is repeated as the borehole instrument is conveyed along the borehole. In summary, thirty two parameters are measured as a function of instrument depth within the borehole.

The processing of measured data can best be visualized by matrix operation wherein the previously defined sixteen raw amplitude and sixteen raw phase measurements are multiplied by a non-square matrix which transforms these thirty two measurements into the parameters of interest. The parameters of interest can be selected and varied by a user, and can include traditional formation evaluation related parameters such as resistivity and dielectric constant as well as near borehole parameters such as the radial extent of invasion of the formation by drilling fluid and the resistivity of the invaded zone. Furthermore, borehole parameters such as borehole diameter, eccentricity and ellipticity can be quantified as well as the resistivity of the fluid contained within the borehole. The number of parameters of interest must be limited to thirty two or less in the preferred embodiment. In an alternate embodiment, the number of parameters of interest can be greater than the number of raw data measurements. This condition yields an underdetermined set of equations requiring that initial estimates be supplied for the number of parameters of interest exceeding the number of raw data measurements. Regression techniques are then used to minimize the discrepancy between tool response predicted by the model and the set of measured raw data. The preferred embodiment employing thirty two measured parameters will directed to toward the measurement of borehole and near borehole parameters. For purposes of illustration, it will be assumed that five borehole or near borehole parameters are to be determined. These will be denoted Bn, where n = 1,....,5. The matrix operation is written as (24) m x [M] = [B] where

The matrix m is a transform which represents a comprehensive model of the borehole instrument response with the borehole, near borehole, and formation conditions being variables. Since the elements Ti,j are predicted by the model, the borehole parameters to be determined, Bn (n=1,....,5), can be calculated directly from the measured parameters represented by the matrix [M]. Using the fonnalism of equation (24), it is essential that the model represented by m yield parameters of interest (the "unknowns") as a function of the downhole instrument response (the measured quantities).

Jian-Qun Wu and Macmillian M. Wisler ("Effects of Eccentering MWD Tool on Electromagnetic Resistivity Measurements", SPWLA, 31st Annual Logging Symposium, June 24-27, 1990) disclose a method for calculating the effects of a borehole logging tool being eccenterred in a borehole upon resistivity measurements and is hereby entered by reference.

As an example of this work, Fig. 21 illustrates the variations of apparent resistivity 75a computed from phase shift measurements (denoted by curves 74) and amplitude ratio measurements (denoted by curve 76) resistivities, as a function of logging instrument-borehole eccentricity, for true formation resistivity 70 of 0.2, 2.0 and 20 ohm meters and with a borehole fluid resistivity 72 of 20 ohm meters. The transmitter frequency is 2 MHz. A similar plot is shown in Fig. 22 for a borehole fluid resistivity of 0.2 ohm meters and all other parameters remaining the same. In these examples, functional relationships have been developed which yield apparent resistivity values 75a that will be measured by the borehole instrument 36 (the measured quantities) as a function of true formation resistivity 70, borehole resistivities 72, and eccentricity 75b, which are the "unknown" quantities to be determined with means and methods of this invention. The responses are computed using a model developed around basic electromagnetic wave propagation principles using borehole geometry. The calculations have been verified experimentally. J.-Q. Wu, M. M. Wisler and J. F. Towle ("Effects of Arbitrarily Shaped Boreholes and Invasion on Propagation Resistivity Measurements in Drilling Horizontal Wells", Progress in Electromagnetic Research Symposium, Pasadena, California, July 14, 1993) likewise discloses means for determining the measured response of borehole instruments in terms of circular and non circular invasion profiles and also in terms of instrument eccentricity within the borehole. Again measured quantities are expressed in terms of unknown parameters of interest. Stated another way the cited reference discloses means for calculating the forward problem which if incorporated in the comprehensive model, the current invention would cast the matrix equation (24) in the reverse direction yielding equation (28) (28) [T'] x [B] = [M] where

The solution of equation (29) for [B] requires a regression scheme which is in general non-linear. That is, values of the parameters of interest, namely the elements of [B], are iterated until the elements of [Ml calculated from equation (29) converge upon the actual measured values Ai and Pi (i = 1 16). It is again emphasized that the other borehole and near borehole parameters are included in the model. Such additional parameters might include borehole diameter and resistivity of the invaded zones. Those parameters detailed in Figs. 21 and 22 are presented as examples to illustrate the concepts of the data prncessiitg method. The additional characteristics of the response of the downhole instrument, obtained by mathematical modeling, are likewise incorporated as elements of the matrix [T1.

4. DETERMINATION OF ERRORS ASSOCIATED WITH PARAMETERS OF INTEREST The current invention provides means and methods for determining error which can be related to uncertainty associated with measured parameters of interest. Again, the user of the information, or log "analyst", selects the parameters of interest which might include the resistivity (or conductivity) of the formation, the dielectric constant of the formation, or perhaps the degree to which drilling fluids invade the formation in the vicinity of the borehole. As mentioned previously, the analyst's primary interests are usually the determination of the hydrocarbon saturation, porosity and permeability of the formations penetrated by the borehole. It is highly desirable to make such measurements while drilling or soon after the drilling of the well borehole so that critical economic decisions concerning the amount and producibility of hydrocarbons in place can be made. Based upon this information, the well will either be completed or abandoned. The accuracy and precision of measured parameters selected to make such critical decisions are also of prime importance. The error measurements provided by the invention can also be used to indicate equipment malfunctions of both the electrical and mechanical types. Although prior art teaches means and methods of measuring a wide range of geophysical parameters using electromagnetic techniques, little, if any, emphasis is placed upon determining the quality of the measurements. Usually the analyst can only rely on past experience in assigning, at best, qualitative estimates of the quality of the measurements obtained from the borehole instrument and associated system. Any error analysis is usually performed long after the measurements are made and usually not at the well site.

Stated another way, prior art does not provide means and methods for determining the quality of electromagnetic based geophysical measurements in real-time or near real-time, although real-time or near real-time economic and operational decisions are made based upon these measurements. This is especially true in electromagnetic type measurements of formation resistivity which weighs so heavily in the decision to complete or abandon the well. The invention provides this ver parameters as described previously. The system of unknown parameters is therefore over determined" in the sense that there is more measured parameters than variable or unknown parameters to be determined. It should be noted that other transmitter-receiver-operating frequency combinations can be utilized as discussed previously. The number of selected parameters of interest must, however, always be less than the number of raw data measurements so that the resulting system of equations is over determined.

Non-linear inversion techniques are used to determine the set of selected unknown parameters which, through the mathematical model, predicts a tool response which most closely matches the thirty two measured raw data points. The predicted tool responses and the measured tool responses will exhibit no discrepancies only if (a) there is no error associated with the measured data and (b) if the model represents without error the response of the instrument in every encountered borehole and formation condition. This is because there are more measured data points than unknown variable parameters in the model. Any degree of non-conformance or "mismatch" of the model data and the measured data is a measure of inaccuracy of either the data or the model or both the data and the model. In all cases the determined non-conformance is treated as a quality indicator for the determined parameters of interest. In other words, an uncertainty is attached to each parameter selected by the analyst based upon the goodness of fit between the model and the measured data.

Referring again to Fig. 2, transmitters 209, 207, 205 and 203 are activated sequentially at a first frequency 1. The phase and amplitude of the induced electromagnetic signal is measured at the receiver nearest to each activated transmitter thereby yielding four measurements of amplitude and four measurements of phase shift. These measured parameters will again be identified as Ai and Pi, respectively, where (i = 1,...,4). The procedures is repeated at a second frequency 02 yielding an additional four measurements of amplitude and four measurements of phase, identified hereafter as Ai and Pi, respectively, where (i = 5,...,8). The entire procedure is then repeated for the receiver farthest from each activated transmitter yielding values of Ai and Pi where (i = 9,...,16). In summary, a total count of thirty two parameters is measured by the borehole instrument 36 during each cycle as it is conveyed along the borehole 34. The above combined procedure of transmitting at frequencies a) 1 and 02, and recording received signals is repeated sequentially as the instrument is conveyed along the borehole.

Parameters of interest related to the formation, near borehole, and borehole are selected by the analyst. These parameters might include formation resistivity, formation dielectric constant, radius of invasion of the drilling fluid, resistivity of the drilling fluid and perhaps the diameter of the borehole. The selected number of parameters must be less than thirty two so that the system of equations described in the following section is over determined thereby permitting uncertainty associated with the selected parameters to be determined. For purposes of illustration, it will be assumed that the analyst selects n parameters to be determined, where n is less than thirty two.

* The processing of the data to obtain the parameters of interest and the determination of uncertainty associated with these parameters can best be described using matrix notation. The system is written as (30) Fr]x[M]=[XJ where

The matrix [T] represents the theoretical response of the borehole instrument calculated using appropriate electromagnetic modeling techniques for a broad range of formation and borehole conditions, the matrix [M] represents the thirty two raw data points measured by the borehole instrument, and the matrix [X] represents the formation and borehole parameters selected by the analyst to be determined. Although the solution of the matrix equation (30) to attain the desired parameters represented by the vector [X] is viewed as linear, in this case the eiement of the matrix [TI can be dependent upon the elements of [X]. The solution of equation (30) wili, therefore, require a non-linear regression solution such as a ridge regression.

Once equation (30) has been solved for [X], an inverse matrix operation is performed to generate a synthetic- matrix of the measured quantities denoted as [M ]. That is, (34) [r]x[X]=[M'] where

The mismatch between the measured parameters, [M], and the synthetic values of the measured parameters [M'] is a measure of quality of the parameters of interest, [X]. If (37) [M') # [M] then there is little uncertainty associated with the computed values [X] indicating that the quality of the measured data [M] and the model representing the response of the instrument m are both good. If, however, (38) [M'] w EM) it can be concluded that either the measured data [M] are of poor quality (due to tool function, calibration error or the like), or the model of the tool response represented IDY [T] is inadequate for the conditions encountered, or both conditions have occurred. Minimization of calibration, thermal drift and antenna mutual coupling errors have been discussed previously. It has been determined that in many cases, the response model is also quite reliable and error in the model is only a minor contributor to the observed error. It follows, therefore, that when [M'] ? [M], the source of the observed error can not be identified. The degree of mismatch of [M'] and [M] is indicative of the magnitude of the uncertainty or error in the computed parameters of interest, [X]. Non-linear regression techniques suitable for application in this invention are described in the publication conversion of 2 MHz Propagation Resistivity Logs" by W. H. Meyer, SPWLA 33rd Annual Logging Symposium, June 14-17, 1992, Paper H.

5. FORMATION PARAMETERS OF INTEREST The transformation of ray data measured by the sensors into apparent resistivities of the formation, near borehole and borehole environs has been discussed in previous sections. The determination of error associated with these quantities has also been discussed. In addition, previous discussions encompassed the general concepts of converting apparent resistivities and other electromagnetic properties into parameters from which "end" information, such as hydrocarbon saturation and porosity of the formation, is derived. Finally, basic problems associated with the determination of hydrocarbon saturation from resistivity measurements alone, in the presence of low salinity or fresh waters, has also been addressed. The following section is devoted to the conversion of tool measurements, whose accuracy and precision have been determined and optimized using previously discussed methods, into "end" parameters which include hydrocarbon saturation and porosity.

5.1 A Review of Physical Principles Phase shift and attenuation measurements in the low MHz frequency range are dependent upon only three electromagnetic properties and the manner in which these three properties are combined and spatially distributed near the borehole transmitter and receiver assembly. The three properties that control, as an example, the propagation of a 2 MHz electromagnetic wave are (1) magnetic permeability, (2) conductivity, and (3) dielectric permittivity. The primary parameter of interest is conductivity (or resistivity) since this is the primary parameter used in hydrocarbon saturation calculations if the connate water is saline. In order to relate the measured phase shift and attenuation measurements made with the borehole instrument to conductivity, assumptions must be made concerning the magnetic permeability and dielectric permittivity of the formation.

Magnetic permeability is defined as the ability of magnetic dipoles in the formation to align themselves with an extemal field. Minerals and fluids commonly found in sedimentary earth formations do not exhibit significant magnetic permeability. In computing resistivities from measurements of amplitude and phase measurements from a device operating in the mid KHz to low MHz frequency range, minimal error is introduced in assuming a value of magnetic permeability to be equal to that of free space, or 1.25 x 10-6 Henrys/meter.

Conductivity is defined as the ability of a material to conduct an electric charge, while dielectric permittivity is defined as the ability of a material to store an electrical charge. Dielectric permittivity is usually expressed in terms of relative dielectric constant, Er, which is the dielectric permittivity E of the substance in question divided by the dielectric permittivity in free space, so = 8.854 x 10-12.

Attention is now tumed to dielectric permittivity and the physical principles behind the effects of this parameter upon attenuation and phase signals measured in a borehole environment. In sedimentary formations, dielectric permittivity arises from the ability of electric dipoles to align themselves with an altemating electromagnetic field induced by the borehole instrument. Water molecules will be used for purposes of discussion. There are three phenomena contributing to Erin a porous earth formation. The first contribution isUhe rotation of dipolar water molecules. The water molecule has a slight positive charge on the side to which are bound the two hydrogen atoms, and a corresponding negative charge on the side of the molecule opposite to the bound hydrogen atoms. In the presence of an applied electric field, the water molecule will rotate to align the positive and negative poles of the molecule with the applied electric field. In an altemating current (AC) field such as that produced by the borehole instrument, the water molecule will rotate back and forth as the polarity of the applied field alternates. During the time period in which the water molecule is in actual rotation seeking to align with the applied field, the movement of the charge represents electrical charges moving in phase with the applied field and are therefore carrying current and contributing to the composite formation conductivity. Once aligned with the field, the polarized water molecules represent fixed or stored charges and thereby contribute to the formation permittivity until the polarity of the altemating applied field is reversed. At this time, the water molecules again rotate contributing again to composite formation conductivity. This sequence, of course, repeats with the cycling of the applied AC field. Ions dissolved in the formation pore water are a second contributor to er in that they will also be set in motion by the applied AC field and migrate in the direction of the field until they encounter a physical obstruction such as a rock grain forming the boundary of the pore space.

Once the ions abut the pore boundary and begin to accumulate, they likewise become fixed or "stored" charges thereby contributing to the formation dielectric permittivity as described by M. A. Sherman, "A Model for the Frequency Dependence of the Dielectric Permittivity of Rock", The Log Analyst, Vol. 29, No. 5, September-October, 1988. Cations attached to cation exchange sites on the surface of certain clay minerals are a third contributor to Er in that they can also move under the influence of an applied AC field.

The movement of cations between various exchange sites produces effects similar to those of free ions in the pore water.

Complicating the issue of dielectric effects is the fact that er values are dependent upon the frequency of the applied field. At low frequencies, dielectric constants can be quite high since the water molecules can easily rotate and align themselves with the field before the polarity of the field reverses. Similarly, dissolved ions can migrate to the boundary of the pore space and accumulate against the pore wall long before the polarity of the field reverses. Likewise, the movement of cations can be completed prior to the reversal of the field polarity. Therefore, at low frequencies, water molecules, dissolved ions and cations spend most of their time in a fixed orientation or position and only a small fraction of the time moving during any given cycle of the applied AC electromagnetic field. At high frequencies, however, the polarity of the applied field will reverse before the three types of mobile charges come to rest. In this situation, the mobile charges spend most of their time moving in phase with the extemal electromagnetic field thereby increasing the conductivity and resulting in a lower dielectric constant. The phenomena of changing dielectric and conductivity values with frequency is known as dispersion. The frequency at which the rotating molecules or mobile ions can no longer keep pace with the oscillating field is known as the "relaxation frequency". The relaxation frequency, relative dielectric constant Er, and conductivity a will depend upon various factors such as porosity, mean pore size, the resistivity of the water Rw, and shale mineralogy as described in the previously cited reference by Sherman.

J. C. Sims, P. T. Cox and R. S. Simpson, "Complex Dielectric Interpretation of 20 MHz Electromagnetic Logs", Paper SPE 15486, 61 st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, October 5-8, 1986, teaches the use of a mixing formula to interpret dielectric log data, but measurements made at only one frequency are employed. U. S. Pat. No. 3,891,916 to R. A. Meador et al teach the use of two frequencies, both much higher than 2 MHz, to determine dielectric constant. Meador et al, however, teach the use of amplitude measurements to determine dielectric constant and resistivity and do not address the problem of dielectric dispersion using two frequencies with both amplitude and phase meassurements. U.S. Pat. No. 5,144,245 to M. M. Wisler discloses the use of the Complex Refractive Index Model (CRIM) as a means for correcting resistivity measurements for dielectric effects where the resistivity amplitude and phase data are taken at a single frequency. K. S. Cole and R.

H. Cole, "Dispersion and Absorption in Dielectrics", Journal of Chemical Physics, Vol. 9. P 341(1941) disclose a model for dielectric dispersion which can be used as a mixing model in a somewhat similar to the previously referenced CRIM model and could be used as an element in the embodiment of the current invention. There are many other mixing and dispersion models that might also be used.

This brief review of pertinent basic physical principles will assist in fully disclosing the means and methods of the invention and advances of the current invention over prior art.

Recall that a major objective of invention is directed toward the accurate measure of the conductivity (or resistivity) of earth formation penetrated by a borehole. As discussed previously, formation resistivity combined with formation porosity and connate water resistivity can be used to compute formation hydrocarbon saturation of a porous formation. The invention is further directed toward the determination of the dielectric constant of the formation. This measurement is used to correct resistivity measurements made at certain frequencies for the adverse effects of the dielectric permiivity of the formation. The invention is directed still further toward the determination of the volume fraction of the formation saturated with water. This measurement, when combined with an independent measure such as a neutron porosity measurement which responds to total formation liquid (water plus liquid hydrocarbon), can be used to determine hydrocarbon saturation of the formation in either fresh or saline water environments. Hydrocarbon saturation can not be determined using resistivity measurements only in fresh water environments since the resistivity of fresh water and hydrocarbon exhibits little contrast.

5.2 TheoretScal Basis Solutions to Maxwell's equations in homogeneous lossy media are a function of a factor commonly referred to as the propagation constant or wave number, defined herein as "K', which contains conductivity, dielectric constant and magnetic permeability terms. A plane wave solution will have the form (39) V = Ceikx where V = a field variable; C = a constant e = the naperian log base = = the square root of -1; x = the distance traveled; and (40) k = [# o r#o#r)+(i# o r#)] where: o = the magnetic permeability of free space; r = the relative permeability (which is 1.0 for free space and most earth materials); ò = the electric permittivity of free space; #r = the relative dielectric constant (which is 1.0 in free space); 0) = the angular frequency of the applied field; and # = the conductivity which is the inverse of resistivity. the term k can be rewritten in terms of a relative complex dielectric constant, er which includes the effect of dielectric constant and conductivity, as

where ko = the wave number in free space; r= 1; and #r = [#r + i#(.1/##o)] We now assume a model of the earth formation wherein there are two layers of different propagation constants k and differing complex relative dielectric constants #r with the first region spanning (1 - ) units of length and the second region spanning 0 units of length. A plane wave incident on the layers and passing through the layers without reflection will have the form (42) eik2#eik1(1-#)=ei(k2#+k1(1-#)] The effective propagation constant for this model, keff, is therefore

Equation (5) is solved for the equivalent relative dielectric constant to obtain

Considering all of the above relationships leading to equation (44), it is apparent that the effective real relative dielectric constant is therefore corrupted by the imaginary parts of the relative dielectric constants of the two regions and likewise the effective conductivity is corrupted by the real parts of the relative dielectric constants. The model is now further related to actual earth formations. The first region is equated to connate water filling the pore space of the rock matrix with the water fractional volume being 0 of the total formation volume. The second region is equated to the rock matrix with the rock matrix fractional volume being (1 - ) of the total formation volume.

Expanding equation (44) to illustrate real and imaginary components and designating terms with respect to the above formation model yields

where the subscripts w and m designate parameters associated with the water and rock components of the formation, respectively. Note that a m is equal to zero. If measurements are made at two known frequencies = = Ct )2, equation (45) yields two independent complex equations.

Because both real and imaginary parts of these equations must be equal, measurements at two frequencies actually yield four independent equations.

The dielectric constant of water, Ew is independent of the salinity of the water thus is a known quantity. The two frequencies are predetermined thus are known. The quantities geff and a eff are measured. The four independent equations can, therefore, be used to solve for the remaining three unknown quantities, namely the porosity , the conductivity of the water Cw and the dielectric constant of the rock Em It is noted that a plurality of transmitter- receiver-operating frequency combinations can be used in embodiments of the invention as long as the chosen combination yields four independent equations relating a eff and èff to Cw, m and . It should also be noted that the dielectric constant of the rock matrix and the dielectric constant of any hydrocarbon contained within the pore space of the rock are essentially equal and the conductivity of each is essentially zero. The computed quantity 0 is therefore the fraction of water within the formation and not necessarily the effective porosity of the formation in the sense commonly used in the art. In order to obtain effective formation porosity, it is necessary to combine the "water filled porosity yielded by the present invention with a second, independent, measure of formation porosity which responds to the total fluid filled porosity. An example of such a second measurement would be a thermal neutron "porosity" measurement which responds to the hydrogen content of the formation. Since most hydrogen in earth formation resides in the pore space rather than the rock matrix and since the response is essentially the same for both water and liquid hydrocarbons, the neutron porosity measurement yields total liquid porosity.

5.3 Longing Example Attention is directed to Fig. 23 which illustrates logs of resistivity, which is the inverse of conductivity, measured at four different transmitter frequencies as a function of depth, in feet, within a borehole. The measurements were made in a test well in which the characteristics of the formations are well known from numerous studies of well log and core data as referenced in "Comparison of MWD, Wireline and Core Data from a Borehole Test Facility", Paper SPE 22735, proceedings of the Society of Petroleum Engineers 66th Annual Conference and Exhibition, pp 741-754, (1991). These "logs" of resistivity clearly illustrate the effects of dispersion effects as a function of the frequency of the induced electromagnetic field.

Attention will be focused on the zones denoted by the numerals 840 and 844 which are shales and the low permeability limestone zone denoted by the numeral 846. Zone 842 is a permeable sandstone, and is therefore invaded by the drilling fluid. Radiai invasion combined with differing depths of investigations for the measurements at different frequencies mask the dispersion effects. Zone 842 will therefore be ignored in this discussion.

Curves 850, 852, 854 and 856 represent resistivities measured at frequencies of 1100 MHz, 200 MHz, 25 MHz and 2 MHz, respectively.

Knowing that zones 840, 844, and 846 are radially homogeneous (that is, non-invaded by the drilling fluid), it is concluded that the observed dispersion is due to dielectric effects. Fig. 24 illustrates relative dielectric constant measurement over the same formation zones of interest but at different frequencies where curves 870, 872, 874 and 876 represent measurements at 1100 MHz, 200 MHz, 25 MHz, and 2 MHz, respectively. Dielectric dispersion is again quite apparent. The phenomena of both dielectric and conductivity (or resistivity) dispersion and their dependency upon the frequency of the induced field has been discussed in a qualitative or conceptual sense in a previous section. The phenomena can be quantified as illustrated in Fig. 25 which illustrates generalized theoretical dispersion plots for a clean sandstone formation. The dielectric dispersion curve 860 illustrates that in general Er decreases as frequency increases. Conversely, the conduction curve 862 illustrates that conductive dispersion increases with increasing frequency. Both curves 860 and 862 also clearly illustrate frequency ranges at which interfacial relaxation and molecular relaxation occur. To assess whether the variations in the relative dielectric constant Er observed in the logs of Fig. 24 are indeed consistent with dispersion effects, the four values of depicted by curves 870, 872, 874 and 876 at a depth of 1660 feet in the limestone formation 846 were compared in Fig. 26 to a dispersion curve 880 based upon published (M. R. Taherain et al, "Dielectric Response of Water-Saturated Rocks", Geophysics, Vol. 55, No. 12, December 1990) dielectric measurements made on limestone core samples with matrix and connate water resistivities very similar to the limestone of formation 846. The superimposed data points 881, 882, 883, and 884 are average readings of the curves 876, 874, 872, and 870 taken at a depth of 1660 feet in zone 846, respectively. The good agreement between the corederived dispersion curve and the log derived measurements from these two carbonate formations suggest that the differences between the various Er values from the log are indeed due to dispersion. Considering Figs. 23, 24, 25 and 26 in combination, it is apparent that any model which simultaneously extracts dispersion corrected resistivity and dielectric constant values from measurements of phase difference and amplitude ratio at varying frequencies must quantitatively include the frequency of the induced electromagnetic field.

Recall that one of the basic objectives of the invention is to determine conductivity (or resistivity) of the formation which is free of dispersion effects. A second objective is to determine the dielectric constant of the formation which, again, is free of dispersion effects. A third objective is to determine effective water filled porosity of the formation which, when combined with independent measurements of total liquid filled porosity, can be used to determine the hydrocarbon saturation of the formation. A theoretical Complex Refractive Index Model (CRIM) has been developed which relates Er to true formation resistivity and meets the previously stated objectives of the invention. The development of the model begins with the solutions to Maxwell's equations in homogeneous lossy media are a function of a factor commonly referred to as the propagation constant or wave number, defined herein as ikon, which contains conductivity, dielectric constant and magnetic permeability terms. Restating, for completeness, Equation (39) for a plane wave solution yields (39) V = Ceikx where V = a field variable; C = a constant e = the naperian log base = = the square root of 1; x = the distance traveled; and (40) k= [(# o r#o#r)+(i# o r#)] where: c = the speed of light = 2.999 108 (meters/second); SUO= the magnetic permeability of free space = 4 x r= the relative permeability (which is 1.0 for free space and most earth materials); E0 = the electric permittivity of free space = (1/ oc)= 8.854 x 10-12; Er = the relative dielectric constant (which is 1.0 in free space); # = the angular frequency of the applied field; and a = the conductivity.

The term k can be rewritten in terms of a relative complex dielectric constant, which includes the effect of dielectric constant and conductivity, as

where ko = the wave number in free space; Ii r = 1; and the relative complex dielectric constant is #r = [#r + i#(1/##o)] Note that k is defined such that when'the conductivity a goes to zero, the complex relative dielectric constant goes to the relative dielectric constant equals the real relative dielectric constant #r.

We now assume a model of the earth formation wherein there are two layers of different propagation constants k and differing complex relative dielectric constants Ec with the first region spanning (1 - ) units of length and the second region spanning 0 units of length. A plane wave incident on the layers and passing through the layers without reflection will have the form (42) eik2#eik1(1-#)=ei(k2#+k1(1 where the subscripts 1 and 2 denote parameters associated with layers 1 and 2, respectively. The effective propagation constant for this model, keft; is therefore (43) keff=k20 +ki(i-4)) or on terms of the complex dielectric constant defined above

Equation (44) is solved for the equivalent relative dielectric constant to obtain

The model is now further related to actual earth formations. The first region is equated to connate water filling the pore space of the rock matrix with the water fractional volume being 0 of the total formation volume. The second region is equated to the rock matrix with the rock matrix fractional volume being (1 - ) of the total formation volume. Expanding equation (45) to illustrate real and imaginary components and designating terms with respect to the above formation model yields

where the subscripts w and m identify parameters associated with the water and rock matrix components, respectively. Note that #m is equal to zero.

The effective real dielectric constant is therefore corrupted by the imaginary part of the dielectric constants of the two regions, and likewise the effective conductivity is corrupted by the real parts of the relative dielectric constants. That is (47) Er.cff = Re(Ec eff ); and = ò Im(E,, Im) In order to calculate the dielectric constants that we would expect to observe in clean water saturated rocks, it will be assumed that the rocks are composed of two parts which comprise the rock matrix and the connate water. The resistivity of the water and the porosity of the rock matrix are varied within reasonable limits and the dielectric constant of the combination of the two parts, which is the quantity actually sensed by the borehole instrument, is calculated utilizing the two component mixing relationship derived above. The subscripts w and m designate parameters associated with the water and rock parts, respectively.

The relationship of equation (46) can be used to graphically illustrate the functional relationships between the measured quantities and the parameters which are of interest and which are to be determined. Figs.

27a and 27b are presented as typical illustrations of these relationships.

The real part 890 of the effective dielectric constant as defined by equation (46) is plotted in Fig. 27a as a function of the formation water resistivity, denoted on the abscissa as 892, for various porosities 894. The abscissa is logarithmic and the ordinate is linear. These plots are for a frequency #1= 2 MHz. The real part 91 of the formation effective conductivity is plotted in Fig.

27b as a function of formation water resistivity 892, again at Ct)l= 2 MHz and again for varying porosities 894. Both the ordinate and the abscissa are logarithmic. Similar plots can be generated for the real and imaginary components of and Creff at Ol= 2 MHz and likewise plots for both the real and imaginary parts of Ce.ff and at a second frequency W2=400 KHz. These are graphical depictions of a set of four independent equations used to determine the 'unknown" formation parameters of interest, namely the effective conductivity (or resistivity), the effective dielectric constant and the water filled porosity of the formation.

5.4 Determination of Dielectric Constant. Resistivity and Porosity Attention is again directed to Figs. 23 and 24 which show resistivity and dielectric data, respectively. Fig. 23 depicts data from four downhole systems, with the 2 MHz data being measured with a MWD system and the remaining being measured with wireline systems. Fig. 24 depicts dielectric data measured with the same systems. Dispersion of the measurements as a function of frequency is clearly exhibited in both logs.

Based upon the previously discussed principles, the dispersion in the resistivity measurements would be expected to be small at 2 MHz and lower frequencies. Attention is drawn in particular to zone 846 which is known from core data to be impermeable carbonate. Dispersion in this zone can only be attributed to dielectric effects. Zone 842 is a sandstone which is known to be permeable and therefore invaded with drilling fluids prior to running the wireline logs. The observed dispersion in this zone must be attributed to, at least in part, to invasion effects as well as dielectric effects. Data from zone 846 will, therefore, be used to illustrate the determination of dielectric dispersion of resistivity measurements. Attention is further drawn to Fig. 26 which illustrates observed dielectric data superimposed upon laboratory measurements of dielectric constant as a function of frequency published in the previously cited Taherain reference. The curve as illustrated was fitted using the model of Cole and Cole as previously referenced. At a depth of 1660 feet, dielectric constants measured at 2 MHz and 25 MHz are denoted by the numerals 841 and 821, respectively and the corresponding resistivities are denoted by the numerals 838 and 827, respectively. These values of Eeff and eff= 1/Reff are inserted into equation (46) at the respective frequencies, real and imaginary parts of equation (46) are equated yielding set of four equations, and a non-linear regression scheme such as a ridge regression is employed to solve for the resistivity of the water Rw= liCyw = 0.16, the dielectric constant of the rock matrix Em = 9.0, and the formation porosity 0 = 0.05 or 5 %. These are reasonable values for impermeable carbonate and agree well with core data taken in zone 846.

5.5 Borehole Calinering The ability to accurately calculate amplitude attenuation and phase shift, which are uninfluenced by mutual coupling and drift errors, allows for meaningful wellbore calipering operations. An accurate determination of the amplitude attenuation caused by the formation alone or the wave propagating between receiving antennas 211,213, and an accurate measure of the phase difference between receiving antennas 211, 213, can be utilized with a library of graphs or data which are recorded in computer memory. Fig. 28 depicts a graph of phase difference in degrees versus attenuation in dB. With respect to these X- and Y-axes, a plurality of curves are provided. A plurality of curves are provided which correspond to borehole diameter, in inches. In Fig. 28, borehole diameters of 7", 8", 9", and 10" are graphed. A plurality of curves are provided which represent formation resistivity in ohm meters. Fig. 28 depicts formation resistivity measurements of 0.2 ohm meters, 0.5 ohm meters, 1.0 ohm meters, 2.0 ohm meters, and 200 ohm meters. This graph is accurate when the drilling mud has a resistivity of 0.05 ohms meters (Rm). The graph of Fig. 28 is merely an exemplary graph. In practice, a plurality of graphs or data sets are provided for a plurality of mud resistivities Rm.

Provided that the formation resistivity and the mud resistivity Rm are known, the amplitude attenuation and phase shift of the electromagnetic interrogating field can be utilized to determine the diameter of the borehole in the region of the logging apparatus. For example, with reference to Fig. 28, assuming that the formation resistivity is 0.5 ohm meters and the mud resistivity Rm iso0.05 ohm meters, a calculated amplitude attenuation of -66 dB and a phase difference of 55 indicates that the borehole has a diameter of approximately 9". In accordance with the present invention, central processor 215 and digital signal processor 221 can be programmed to periodically or intermittently calculate borehole diameter, and transmit it to the surface utilizing mud pulse telemetry techniques. If the borehole diameter is enlarged to 10", this should be reflected by changes in the amplitude attenuation and phase shift. In contrast, if the borehole narrows in diameter to 8", this would also be reflected in the amplitude attenuation and phase shift measurements. Borehole calipering operations can only be conducted if uncorrupted measurements of amplitude attenuation and phase shift can be obtained. Since the present invention allows for the correction of any corrupting influence of magnetic mutual coupling, or thermal and other types of drift, such measurements can be utilized to accurately determine borehole diameter. In the preferred embodiment of the present invention, a plurality of data sets are provided, each corresponding to a different mud resistivity Rm and a particular formation resistivity. These data sets are contained within the tool model matrix m which was discussed in a previous section. The measurements of amplitude attenuation and phase shift are then utilized to determine borehole diameter.

The above description may make other alternative embodiments of the invention apparent to those skilled in the art. It is therefore the aim of the appended claims to cover all such changes and modifications as fall within the true spirit and scope of the invention.

Table 1 : Command Register Bits

CR0 = 0 Eight-Bit Databus. Pins D15-D8 are ignored and the parallel assembly register shifts eight places left on each write. Hence four succesive writes are required to load th 32-bit parallel assembly register, Figure 6.

= 1 Sixteen-Bit Databus. The parallel assembly register shifts 16 places left on each write. Hence two succesive writes are required to load the 32-bit parallel assembly register, Fig. 5.

CR1 = 0 Normal Operation.

= 1 Low Power Sleep Mode. Internal Clocks and the DAC current sources are turn off.

CR2 = 0 Amplitude Modulation Bypass. The output of the nine LUT is directly sent to the DAC.

= 1 Amplitude Modulation Enable. IQ modulation is enabled allowing AM or QAM to be performed.

CR3 = 0 Synchronizer Logic Enabled. The FSELECT, LOAD and TC3-TC0 signals are passed through a 4-stage pipeline to synchronize them with the CLOCK frequency, avoiding metastability problems.

= 1 - Synchronizer Logic Disabled. The FSELECT, LOAD and TC3-TC0 signals bypass the synchronization logic. This allows for faster response to the control signals.

TABLE 2 AD7008 Control Registers

Register Size Reset State Description COMMAND REG 4 Bits CR3-CR0 All Zeros Command Register. This is written to using the parallel assembly register FREQ0 REG 32 Bits DB31-DB0 All Zeros Frequency Select Register 0. This defines the output frequency, when FSELECT = 0, as a fraction of the CLOCK FREQUENCY.

FREQ1 REG 32 Bits DB31-DB0 All Zeros Frequency Select Register 1. This defines the output frequency, when FSELECT = 1, as a fraction of the CLOCK frequency.

PHASE REG 12 Bits DB-11-DBO All Zeros Phase Offset Register. The contents of this register is added to the output of the phase accumulator.

IQMOD REG 20 Bits DB19-DB0 All Zeros I and Q Amplitude Modulation Register. This defines the amplitude of the I and Q signals as 10-bit two complement binary fractions. DB[19:10] is multiplied by the Quadrature (line component and DB [9:0] is multiplied by the In-Phase (cosine) component.

Table 3 - Source and Destination Registers

TC3 TC2 TC1 TC0 LOAD Source Register Destination Register X X X X 0 N/A N/A 0 0 X X 1 Parallel COMMAND 1 0 0 0 1 Parallel FREQ0 1 0 0 1 1 Parallel FREQ1 1 0 1 0 1 Parallel PHASE 1 1 0 0 1 Serial FREQ0 1 1 0 1 1 Serial FREQ1 1 1 1 0 1 Serial PHASE 1 1 1 1 1 Serial IQMOD

Claims (22)

IN THE CLAIMS:

1. A logging apparatus for use for determining parameters of a borehole and surrounding formation, comprising: (a) a borehole instrument comprising at least one transmitter and at least one receiver; (b) at least one oscillator, which is electrically coupled to said at least one transmitter for selectively energizing said at least one transmitter, which has at least one digital input and an analog output, and which provides a particular analog output from a plurality of available analog outputs at least in part in response to receipt of a particular digital command signal; (c) a controller means for supplying said particular digital command signal from a plurality of available digital command signals in response to program instructions, causing said analog output of said at least one oscillator to be applied to a particular ones of said at least one transmitter thereby inducing a primary electromagnetic field within the borehole and formation environs, utilizing said at least one receiver to measure at least one parameter attributable to said induced primary electromagnetic field, and calculating at least one parameter of said borehole and formation environs; (d) means for conveying said borehole instrument along said borehole; and (e) means for determining the position within the borehole at which said at least one parameter attributable to said induced primary electromagnetic field is measured.

2. The apparatus of claim 1 wherein said at least one oscillator provides an analog signal at said analog output with: (a) a frequency attribute which is determined at least in part by said digital command signal at said at least one digital output; (b) a phase attribute which is determined at least in part by said digital command signal at said at least one digital output; and (c) an amplitude attribute which is determined at least in part by said digital command signal at said at least one digital output.

3. The apparatus of claim 1 wherein said controller means utilizes a combination of a measurement of a phase attribute of said induced primary electromagnetic field and a knowledge of phase of said particular analog output to calculate said value for said least one parameter of said borehole and formation environs.

4. The apparatus of claim 1 wherein said controller means utilizes a combination of a measurement of an amplitude attribute of said induced primary electromagnetic field and a knowledge of amplitude of said particular analog output to calculate said value for said least one parameter of said borehole and formation environs.

5. The apparatus of claim 1 wherein (a) said borehole instrument is conveyed by means of a drill string; (b) said measure of at least one parameter attributable to said induced primary electromagnetic field is transferred to the surface of the earth while said borehole instrument is within the borehole, and (c) said calculation of at least one parameter of said borehole and formation environs is performed at the surface of the earth.

6. A logging method for determining parameters of a borehole and surrounding formation, comprising the steps of: (a) providing a borehole instrument comprising at least one transmitter and at least one receiver; (b) providing at least one oscillator, which is electrically coupled to said least one transmitter for selectively energizing said at least one transmitter, which has at least one digital input and an analog output, and which provides a particular analog output from a plurality of available analog outputs at least in part in response to receipt of a particular digital command signal; (c) providing a controller means for supplying a particular digital command signal from a plurality of available digital command signals in response to program instructions, causing said analog output of said at least one oscillator to be applied to a particular ones of said at least one transmitter thereby inducing a primary electromagnetic field within the borehole and formation environs, utilizing said at least one receiver to measure at least one parameter attributable to said induced primary electromagnetic field, and calculating at least one parameter of said borehole and formation environs; (d) conveying said borehole instrument along said borehole; and (e) determining the position within the borehole at which said at least one parameter attributable to said induced primary electromagnetic field is measured.

7. The method of claim 6 comprising the additional steps of utilizing said at least one oscillator to provide an analog signal at said analog output with: (a) a frequency attribute which is determined at least in part by said digital command signal at said at least one digital output; (b) a phase attribute which is determined at least in part by said digital command signal at said at least one digital output; and (c) an amplitude attribute which is determined at least in part by said digital command signal at said at least one digital output.

8. The method of claim 6 further comprising the step of utilizing said controller to combine measurement of a phase attribute of said induced primary electromagnetic field and a knowledge of phase of said particular analog output to calculate said value for said least one parameter of said borehole and formation environs.

9. The method of claim 6 further comprising the step of utilizing said controller to combine measurement of an amplitude attribute of said induced primary electromagnetic field and a knowledge of amplitude of said particular analog output to calculate said value for said least one parameter of said borehole and formation environs.

10. The method of claim 6 comprising the additional steps of: (a) conveying said borehole instrument by means of a drill string; (b) transferring said measure of at least one parameter attributable to said induced primary electromagnetic field to the surface of the earth while said borehole instrument is within the borehole, and (c) performing said calculation of at-least one parameter of said borehole and formation environs at the surface of the earth.

11. A logging apparatus for use for determining parameters of a borehole and surrounding formation, comprising: (a) a borehole instrument; (b) at least one transmitter comprising a transmitter antenna, and an energizing circuit coupled to said at least one transmitter antenna for selectively supplying an energized altemating current to said at least one transmitter antenna of a particular frequency corresponding to a particular supplied command signal, which induces a primary electromagnetic field within the borehole and fomation environs having said particular frequency; (c) at least one receiver comprising a receiver antenna, and a reception circuit for utilizing said receiver antenna in measuring at least one parameter attributable to said induced primary electromagnetic field of a particular frequency; (d) at least one controller member which can be operated in a plurality of modes of operation, including: a transmission mode of operation, wherein said controller provides a plurality of command signals to produce a plurality of primary electromagnetic fields of differing frequencies in a predetermined order, a reception mode of operation, wherein said controller samples receiver measurements made by said reception circuit; and an interrogation mode of operation, wherein said controller supplies a plurality of command signals to produce a plurality of primary electromagnetic fields of differing frequencies in a predetermined order, samples measurements made by said reception circuit, and calculates at least one attribute of the surrounding borehole and formation environs; (e) a mathematical model relating the properties of the surrounding formation and borehole environs to one of the following quantities supplied by the borehole instrument: said samples measurements made by said one or more reception circuits, said at least one attribute of the surrounding borehole and formation environs; (f) means for conveying said borehole instrument along said borehole; and (g) means for determeing the position within the borehole at which said at least one parameter attributable to each of said plurality of induced primary electromagnetic field is measured.

12. The apparatus of claim 11 wherein said at least one controller member is operable in the following additional modes of operation: (a) an analysis mode wherein said at least one controller calculates one or more selected parameters of interest by combining said mathematical model with said sampled measurements to obtain said selected parameters of interest; (b) a calibration mode of operation, wherein said at least one controller member: supplies a plurality of particular command signals to produce a plurality of primary electromagnetic fields of differing frequencies over a predetermined range of frequencies, samples measurements made by said one or more reception circuits, and compares at least one receiving antenna transform attribute to a predetermined measure of an antenna attribute.

13. The apparatus of claim 12 wherein said receiving antenna transform attribute comprises at least one of the following: (a) = a resonance frequency for said at least one receiving antenna; (b) an antenna Q for said at least one receiving antenna; (c) phase shift for said at least one receiving antenna; (d) signal amplitude for said at least one receiving antenna.

14. The apparatus of claim 11 wherein said attributes of the surrounding borehole environs comprise at least one of the following: (a) amplitude attenuation of said plurality of primary electromagnetic field; and (b) phase shift of said plurality of said primary electromagnetic fields.

15. The apparatus of claim 11 wherein: (a) said mathematical model is defined such that, when combined with said sampled measurements made by said one or more reception circuits, yields selected parameters of interest comprising formation parameters, borehole parameters, or formation parameters and borehole parameters; and (b) and wherein the number of pairs of said transmitters and receivers pairs and the number of said particular transmitter frequencies is such that the number of said sampled measurements is equal to or greater than the number of said selected parameters of interest.

16. The apparatus of claim 11 wherein: (a) said mathematical model is defined such that, when combined with said sampled measurements made by said one or more reception circuits, yields selected parameters of interest comprising selected formation parameters; selected borehole parameters; or selected formation parameters and selected borehole parameters, and errors associated with the determination of said selected formation parameters, selected borehole parameters or selected formation parameters and borehole parameters; and (b) wherein the number of pairs of said transmitters and receivers pairs and the number of said particular transmitter frequencies is such that the number of said sampled measurements is greater than the number of said selected parameters of interest.

17. The apparatus of claim 14 wherein said mathematical model is defined such that, when combined with said attributes of the surrounding borehole and formation environs, yields a measure of formation resistivity and formation dielectric constant.

18. The apparatus of claim 11 wherein said borehole instrument is conveyed by means of a drill string.

19. The apparatus of claim 18 wherein said one or more transmitters comprises four transmitters and said one or more receivers comprises two receivers and wherein said transmitters are operated at two particular frequencies.

20. The apparatus of claim 19 wherein the first of said transmitters is operated within the range of 100 KHz to 6 MHz and the second of said two transmitters is operated in the range of 500 KHz to 12 MHz.

21. A logging method for determining parameters of a borehole and surrounding formation, comprising the steps of: (a) providing a borehole instrument; (b) providing at least one transmitter comprising a transmitter antenna, and an energizing circuit coupled to said at least one transmitter antenna for selectively supplying an energized alternating current to said at least one transmitter antenna of a particular frequency corresponding to a particular supplied command signal, which induces a primary electromagnetic field within the borehole and fomation environs having said particular frequency; (c) providing at least one receiver comprising a receiver antenna, and a reception circuit for utilizing said at least one receiver antenna in measuring at least one parameter attributable to said induced primary electromagnetic field of a particular frequency; (d) providing at least one controller member which can be operated in a plurality of modes of operation, including: a transmission mode of operation, wherein said controller provides a plurality of command signals to produce a plurality of primary electromagnetic fields of differing frequencies in a predetermined order, a reception mode of operation, wherein said controller samples receiver measurements made by said reception circuit; and an interrogation mode of operation, wherein said controller supplies a plurality of command signals to produce a plurality of primary electromagnetic fields of differing frequencies in a predetermined order, samples measurements made by said reception circuit, and calculates at least one attribute of the surrounding borehole and formation environs; (e) providing a mathematical model relating the properties of the surrounding formation and borehole environs to one of the following quantities supplied by the borehole instrument: said samples measurements made by said one or more reception circuits, said at least one attribute of the surrounding borehole and formation environs; (f) conveying said borehole instrument along said borehole; and (g) determining the position within the borehole at which said at least one parameter attributable to each of said plurality of induced primary electromagnetic field is measured.

22. The apparatus of claim 21, wherein said data transfer system for transferring of measured data to the CPU comprises one or more electrical conductors contained within the wireline.

22. The method of claim 21 comprising the additional steps of operating said at least one controller member in the following additional modes of operation: (a) an analysis mode wherein said at least one controller calculates one or more selected parameters of interest by combining said mathematical model with said sampled measurements to obtain said selected parameters of interest; (b) a calibration mode of operation, wherein said at least one controller member: supplies a plurality of particular command signals to produce a plurality of primary electromagnetic fields of differing frequencies over a predetermined range of frequencies, samples measurements made by said one or more reception circuits, and compares at least one receiving antenna transform attribute to a predetermined measure of an antenna attribute.

23. The method of claim 22 wherein said receiving antenna transform attribute comprises at least one of the following: (a) a resonance frequency for said at least one receiving antenna; (b) an antenna Q for said at least one receiving antenna; (c) phase shift for said at least one receiving antenna; (d) signal amplitude for said at least one receiving antenna.

24. The method of claim 21 wherein said attributes of the surrounding borehole environs comprise at least one of the following: (a) amplitude attenuation of said plurality of primary electromagnetic field; and (b) phase shift of said plurality of said primary electromagnetic fields.

25. The method of claim 21 comprising the additional steps of: (a) defining said mathematical model such that a combination of said mathematical model with said sampled measurements made by said one or more reception circuits yields selected parameters of interest comprising formation parameters, borehole parameters, or formation and borehole parameters; and (b) selecting the number of said selected parameters of interest such that the number of pairs of said transmitters and receivers pairs and the number of said particular transmitter frequencies produces a number of said sampled measurements is equal to or greater than the number of said selected parameters of interest.

26. The method of claim 21 comprising the additional step of: (a) defining said mathematical model such that, when combined with said sampled measurements made by said one or more reception circuits, yields selected parameters of interest comprising: formation parameters, borehole parameters, or formation and borehole parameters, and errors associated with the determination of said formation parameters, said borehole parameters, and said formation and borehole parameters, and (b) selecting the number of said selected parameters of interest such that the number of pairs of said transmitters and receivers pairs and the number of said particular transmitter frequencies produces a number of said sampled measurements is equal to or greater than the number of said selected parameters of interest.

27. The method of claim 24 comprising the additional step of defining said mathematical model such that, when combined with said attributes of the surrounding borehole and formation environs, yields a measure of formation resistivity and formation dielectric constant.

28. The method of claim 21 wherein said borehole instrument is conveyed by means of a drill string.

29. The method of claim 28 wherein said one or more transmitters comprises four transmitters and said one or more receivers comprises two receivers and wherein said transmitters are operated at two particular frequencies.

30. The method of claim 29 wherein the first of said transmitters is operated at a first frequency within the range of 100 KHz to 6 MHz and the second of said two transmitters is operated a second frequency in the range of 500 KHz to 12 MHz.

31. The method of claim 30 comprising the additional steps of: (a) measuring with said receivers the amplitude attenuation and phase shift of electromagnetic radiation resulting from the energization of said transmitters at said first frequency and said second frequency; (b) combining said amplitude attenuation and said phase shift measurements to determine effective conductivity of the formation and the effective dielectric constant of the formation whereby the adverse effects of the borehole and changes in operating characteristics of said borehole instrument are minimized; (c) providing a mixing model which relates said effective conductivity and said dielectric constant to conductivity of the connate formation fluid, the dielectric constant of the dry formation, and the water filler porosity of the formation, wherein said mixing model provides a set of four independent equations for the said first and second transmitter operating frequencies; (d) solving said set of equations for the conductivity of the said connate formation fluid, said dielectric constant of the dry formation and said water filled porosity of the formation; (e) tracking the depth of said borehole instrument within said borehole thereby relating said measures of amplitude attenuation and said phase shift measurements, and parameters computed therefrom, to the depth within the borehole at which they were measured; and (f) repeating steps (a) through (e) as said borehole instrument is conveyed along the borehole.

32. The method of 25 comprising the additional steps of: (a) providing two transmitters; (b) providing four receivers; (c) operating said two transmitters at two particular frequencies; (d) obtaining a total of thirty two sampled measurements from the said four receivers operating at said two particular frequencies; (e) selecting n parameters of interest to be determined, where n is less than thirty two, and formulating said parameters in the form of a n x 1 parameter matrix; (f) formulating said mathematical model as a model predicting the response of the borehole instrument, in the form of predicted sampled measurements, as a function of selected parameters of interest in the form of a 32 x n formation model response matrix; (g) formulating said sampled measurements in the form of a 32 x 1 data matrix; (h) forming a matrix equation by multiplying said formation model response matrix by said data matrix to obtain a 32 x 1 predicted data matrix which represents the response of said borehole instrument as predicted by said mathematical model in the form of a formation model response matrix; (i) employing a non-linear regression scheme to minimize the discrepancy between said data matrix and said predicted data matrix; and (j) recording the parameters of interest, which are in the form of matrix elements of said parameter matrix, when convergence of said data matrix and said predicted data matrix occurs.

33. The method of 25 comprising the additional steps of: (a) providing two transmitters; (b) providing four receivers; (c) operating said two transmitters at two particular frequencies; (d) obtaining a total of thirty two sampled measurements from the said four receivers operating at said two particular frequencies; (e) selecting 32 parameters of interest to be determined; (f) formulating said mathematical model, as a model which transforms sampled measurements into parameters of interest, in the form of a 32 x n parameter model response matrix; (f) formulating said sampled measurements in the form of a 32 x 1 data matrix; (g) forming a matrix equation by multiplying said 32 x 32 parameter model response matrix by said data matrix to obtain a 32 x 1 parameter matrix, the elements of which represent the parameters of interest to be determined.

34. The method of 26 comprising the additional steps of: (a) providing two transmitters; (b) providing four receivers; (c) operating said two transmitters at two particular frequencies; (d) obtaining a total of thirty two sampled measurements from the said four receivers operating at said two particular frequencies; (e) selecting n parameters of interest to be determined, where n is less than thirty two, and formulating said parameters in the form of a n x 1 parameter matrix; (f) formulating said mathematical model as a model predicting the response of the borehole instrument, in the form of predicted sampled measurements, as a function of selected parameters of interest in the form of a 32 x n formation model response matrix; (g) formulating said sampled measurements in the form of a 32 x 1 data matrix; (h) forming a matrix equation by multiplying said formation model response matrix by said data matrix to obtain a 32 x 1 predicted data matrix which represents the response of said borehole instrument as predicted by said mathematical model in the form of a formation model response matrix; (i) employing a non-linear regression scheme to minimize the discrepancy between said data matrix and said predicted data matrix; and (j) recording the parameters of interest, which are in the form of matrix elements of said parameter matrix, when convergence of said data matrix and said predicted data matrix occurs.

35. The method of claim 21 wherein said at least one receiver comprises a plurality of receivers and wherein the corrupting influence of magnetic mutual coupling between said plurality of receiving antennas is eliminated by the steps of: (a) generating, during the operation of said borehole instrument, at least one transfer function which quantifies said mutual coupling between said plurality of receiving antennas; (b) making measurements, during the operation of said borehole instrument, a particular one of said plurality of receiver antennas; and (c) mathematically combining each of said measurements with information from said at least one transfer function to eliminate the influence of said magnetic coupling.

Amendments to the claims have been tied as follows

1. A method for determining certain parameters of interest by utilizing an electromagnetic propagation device conveyed in a borehole in a formation, comprising: (a) inducing electromagnetic radiation in the formation at at least two frequencies; (b) obtaining a plurality of real and imaginary components of measurements from the electromagnetic device conveyed in the borehole, at said frequencies; (c) defining a plurality of parameters of interest to be determined, at least one such parameter of interest being selected from a group consisting of (i) water filled porosity of the formation, (ii) dielectric constant of a dry formation, and (iii) resistivity of a connate formation fluid; (d) defining a mixing model that relates the plurality of real and imaginary components of measurements to the parameters of interest to be determined; and (e) determining the value of the parameters of interest by utilizing the plurality of real and imaginary components of measurements and the mixing model.

2. The method of claim 1, wherein the at least two frequencies include a 400 kHz frequency and a 2 MHz frequency.

3. The method of claim 1, wherein the mixing model is based on dielectric dispersion.

4. The method of claim 3, wherein the mixing model is a CRIM model.

5. The method of claim 3, wherein said real and imaginary measurements of said induced electromagnetic radiation are recorded as a function of depth within the borehole at which they are measured.

6. The method of claim 5, wherein said values of the resistivity of said connate formation fluid, the dielectric constant of said dry formation, and said water filled porosity of the formation are recorded as a function of depth within the borehole at which said amplitude and phase measurements from which they are computed are measured.

7. The method of claim 6, wherein said borehole instrument is conveyed along the borehole with a drill string.

8. The method of claim 6, wherein said borehole instrument is conveyed along the borehole with a wireline.

9. A method of determining certain parameters of interest by utilizing an electromagnetic propagation device conveyed in a borehole, comprising: (a) inducing electromagnetic radiation in the formation; (b) obtaining at least two real and imaginary components of measurements at a first frequency and a second frequency from the electromagnetic device conveyed in the borehole; (c) defining a plurality of parameters of interest to be determined, at least one such parameter of interest being selected from a group consisting of (i) water filled porosity of the formation, (ii) dielectric constant of a dry formation, and (iii) resistivity of a connate formation fluid; (d) defining a mixing model that relates the real and imaginary components of measurements to the parameters of interest to be determined; and (e) determining the value of the parameters of interest by utilizing the plurality of real and imaginary components of measurements and the mixing model.

10. The method of claim 9, wherein the at least two frequencies include a 400 kHz frequency and a 2 MHz frequency.

11. The method of claim 9, wherein the mixing model is based on dielectric dispersion.

12. The method of claim 11, wherein the mixing model is a CRIM model.

13. The method of claim 11, wherein said real and imaginary measurements of said induced electromagnetic radiation are recorded as a function of depth within the borehole at which they are measured.

14. The method of claim 13, wherein said values of the resistivity of said connate formation fluid, the dielectric constant of said dry formation, and said water filled porosity of the formation are recorded as a function of depth within the borehole at which said amplitude and phase measurements from which they are computed are measured.

15. The method of claim 14, wherein said borehole instrument is conveyed along the borehole with a drill string.

16. The method of claim 14, wherein said borehole instrument is conveyed along the borehole with a wireline.

17. An apparatus, conveyed in a borehole in a formation, for determining certain parameters of interest, at least one such parameter of interest being selected from a group consisting of water filled porosity of the formation, dielectric constant of a dry formation, and resistivity of a connate formation fluid, comprising: (a) a transmitter for inducing electromagnetic radiation in the formation at at least two frequencies; (b) a receiver for measuring the real and imaginary parts of the induced electromagnetic radiation in the formation at each of said frequencies; (c) a mixing module that relates the parameters of interest to said plurality of real and imaginary parts of the induced electromagnetic radiation; (d) a CPU for processing data measured by said receivers using the mixing module wherein the resulting processed data comprises measures of the parameters of interest; (e) a data transfer system for transferring the measurements made by the receivers to the CPU; (f) a depth measuring system for tracking the depth of said borehole instrument within said borehole; and (g) a recorder for recording said processed data as a function of depth within said borehole at which said measured data used to generate said processed data is measured.

18. The apparatus of claim 17, wherein said apparatus is conveyed by a drill string.

19. The apparatus of claim 17, wherein said data transfer system comprises a mud pulse system with said CPU system located at the surface of the earth.

20. The apparatus of claim 17, wherein said data transfer comprises a downhole recorder for recording and storing the measured data in the borehole instrument, and wherein said data transfer system further comprises one or more electrical conductors connecting said downhole recorder to the CPU when the borehole instrument is retrieved at the surface of the earth.

21. The apparatus of claim 17, wherein said apparatus is conveyed by a wireline.