CA2673243C - Logging systems and methods with tilt compensation for sector-based acoustic tools - Google Patents

Abstract

Various disclosed acoustic logging systems and methods compensate for logging tool tilt relative to the borehole axis. Some method embodiments include: generating an acoustic signal that propagates along a borehole in a formation; receiving a signal from each of a set of azimuthally-arranged acoustic transducers; processing the signals to compensate for logging tool tilt; and determining a property of the formation based at least in part on the compensated signals. Some tool embodiments include an internal controller that processes signals from different directions to determine and correct time offsets that are attributable to logging tool tilt. Thereafter, the tilt-compensated signals can be used to measure formation and borehole parameters which may be associated with position and displayed in the form of borehole logs and/or images.

Description

Logging Systems and Methods with Tilt Compensation for Sector-Based Acoustic Tools BACKGROUND
Oil field operations demand a great quantity of information relating to the parameters and conditions encountered downhole. Because drillers and operators are forced to operate remotely from the underground formations and reservoirs they wish to exploit, their access to relevant information is limited. Consequently, there is a demand for tools that provide new types of information, more accurate information, or more efficient collection of information. Examples of information that may be collected include characteristics of the earth formations traversed by the borehole, and data relating to the size and configuration of the borehole itself. This information is usually recorded and displayed in the form of a log, i.e. a graph of the measured parameter as a function of tool position or depth. The collection of information relating to conditions down-hole, which commonly is referred to as "logging", can be performed by several methods includ-ing wireline logging and "logging while drilling" (LWD).
In wireline logging, a probe or "sonde" is lowered into the borehole after some or all of a well has been drilled. The sonde hangs at the end of a long cable or "wireline" that provides mechanical support to the sonde and also provides an electrical connection between the sonde and electrical equipment located at the surface of the well. In accordance with existing logging techniques, various parameters of the earth's formations are measured and correlated with the position of the sonde in the borehole as the sonde is pulled uphole.
In LWD, the drilling assembly includes sensing instruments that measure various pa-rameters as the formation is being penetrated, thereby enabling measurements of the formation while it is less affected by fluid invasion. While LWD measurements are desirable, drilling operations create an environment that is generally hostile to electronic instrumentation, teleme-try, and sensor operations.
Acoustic logging tools can be employed in both wireline logging and LWD
environ-ments. Acoustic well logging is a well-developed art, and details of acoustic logging tools and techniques are set forth in A. Kurkjian, et al., "Slowness Estimation from Sonic Logging Wave-forms", Geoexploration, Vol. 277, pp. 215-256 (1991); C. F. Morris et al., "A
New Sonic Array Tool for Full Waveform Logging," SPE-13285, Society of Petroleum Engineers (1984); A. R.
I

Harrison et al., "Acquisition and Analysis of Sonic Waveforms From a Borehole Monopole and Dipole Source . . . " SPE 20557, pp. 267-282 (September 1990); and C. V.
Kimball and T. L.
Marzetta, "Semblance Processing of Borehole Acoustic Array Data", Geophysics, Vol. 49, pp.
274-281 (March 1984).
An acoustic logging tool typically includes an acoustic source (transmitter), and a set of receivers that are spaced several inches or feet apart. An acoustic signal is transmitted by the acoustic source and received at the receivers which are spaced apart from the acoustic source.
Measurements are repeated every few inches as the tool passes along the borehole.
The acoustic signal from source travels through the formation adjacent the borehole to the receiver array, and the arrival times and perhaps other characteristics of the receiver re-sponses are recorded. Typically, compressional wave (P-wave), shear wave (S-wave), and Stoneley wave arrivals and waveforms are detected by the receivers and are processed. The processing of the data is often accomplished by an uphole computer system or may be processed real time by a processor in the tool itself. Regardless, the information that is recorded is typically used to find formation characteristics such as formation slowness (the inverse of acoustic speed), from which pore pressure, porosity, and other formation property determinations can be made. In some tools, the acoustic signals may even be used to image the formation.
Acoustic logging tools generally perform well. However, as measurement electronics are improved and tool resolution improves, anomalous slowness measurements are being more commonly observed. Such measurements may unnecessarily confuse interpreters or lead to customer dissatisfaction with the logging tools. It has been discovered that these anomalous measurements may be the result of tool tilt.

BRIEF DESCRIPTION OF THE DRAWINGS
A better understanding of the various disclosed embodiments can be obtained when the following detailed description is considered in conjunction with the following drawings, in which:
Fig. 1 shows an illustrative logging while drilling environment;
Fig. 2 shows an illustrative wireline logging environment;
Fig. 3 shows an illustrative acoustic logging tool;
Fig. 4 shows the sectorization of an illustrative acoustic receiver;
Fig. 5 illustrates an off-center and tilted acoustic logging tool;
Figs. 6A and 6B show illustrative waveforms received in opposing sectors of the tool of Fig. 5;

2

3 PCT/US2007/012087 Fig. 7A and 7B are slowness-time semblance graphs illustrating the effects of tool tilt;
Fig. 8 is a flow diagram of an illustrative acoustic logging method with tilt compensation;
Fig. 9 is a block diagram of an illustrative computer system suitable for implementing aspects of the disclosed methods.
While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. lt should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular fonn disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

DETAILED DESCRIPTION
Disclosed herein are various logging systems and methods with tilt compensation for sec-tor-based acoustic logging tools. Some method embodiments include: generating an acoustic signal that propagates along a borehole in a formation; receiving a signal from each of a set of azimuthally-arranged acoustic transducers; processing the signals to compensate for logging tool tilt; and determining a property of the formation based at least in part on the compensated signals. Some tool embodiments include an internal controller that processes signals from different directions to detemiine and correct time offsets that are attributable to logging tool tilt.
Thereafter, the tilt-compensated signals can be used to measure formation and borehole parame-ters which may be associated with position and displayed in the form of borehole logs and/or images.
Fig. I shows an illustrative logging while drilling (LWD) environment. A
drilling plat-form 2 supports a derrick 4 having a traveling block 6 for raising and lowering a drill string 8. A
kelly 10 supports the drill string 8 as it is lowered through a rotary table 12. A drill bit 14 is driven by a downhole motor and/or rotation of the drill string 8. As bit 14 rotates, it creates a borehole 16 that passes through various formations 18. A pump 20 circulates drilling fluid through a feed pipe 22 to kelly 10, downhole through the interior of drill string 8, through orifices in drill bit 14, back to the surface via the annulus around drill string 8, and into a reten-tion pit 24. The drilling fluid transports cuttings from the borehole into the pit 24 and aids in maintaining the borehole integrity.
An acoustic LWD too126 is integrated into the bottom-hole assembly near the bit 14. As the bit extends the borehole through the formations, logging tool 26 collects measurements relating to various formation properties as well as the tool orientation and various other drilling conditions. The logging tool 26 may take the form of a drill collar, i.e., a thick-walled tubular that provides weight and rigidity to aid the drilling process. A telemetry sub 28 may be included to transfer tool measurements to a surface receiver 30 and to receive commands from the sur-face. In some embodiments, the telemetry sub 28 does not communicate with the surface, but rather stores logging data for later retrieval at the surface when the logging assembly is recov-ered.
At various times during the drilling process, the drill string 8 may be removed from the borehole as shown in Fig. 2. Once the drill string has been removed, logging operations can be conducted using a wireline logging too134, i.e., a sensing instrument sonde suspended by a cable 42 having conductors for transporting power to the tool and telemetry from the tool to the surface. An acoustic logging tool 34 may have pads and/or centralizing springs to maintain the tool near the axis of the borehole as the tool is pulled uphole. A logging facility 44 collects measurements from the logging tool 34, and includes a computer system 45 for processing and storing the measurements gathered by the logging tool.
Fig. 3 shows an enlarged view of an illustrative acoustic logging too126 in a borehole 16.
The logging tool 26 includes an acoustic source 52, an acoustic isolator 54, and an array of acoustic receivers 56. The source 52 may be a monopole, dipole, quadrupole, or higher-order multi-pole transmitter. Some tool embodiments may include multiple acoustic sources or one acoustic source that is configurable to generate different wave modes. The acoustic source may be made up of piezoelectric elements, bender bars, or other transducers suitable for generating acoustic waves in downhole conditions. The contemplated operating frequencies for the acoustic logging tool are in the range between 0.5kHz and 30kHz, inclusive. The operating frequency may be selected on the basis of a tradeoff between attenuation and wavelength in which the wavelength is minimized subject to requirements for limited attenuation.
Subject to the attenua-tion limits on performance, smaller wavelengths may offer improved spatial resolution of the tool.
The acoustic isolator 54 serves to attenuate and delay acoustic waves that propagate through the body of the tool from the source 52 to the receiver array 56. Any standard acoustic isolator may be used. Receiver array 56 includes multiple sectorized receivers 58 spaced apart along the axis of the tool. Although five receivers 58 are shown in Fig. 3, the number can vary from one to sixteen or more.
Each sectorized receiver 58 includes a number of azimuthally spaced sectors.
Referring momentarily to Fig. 4, a receiver 58 having eight sectors A1-A8 is shown.
However, the number of sectors can vary and is preferably (but not necessarily) in the range between 4 and 16, inclu-

4 sive. Each sector may include a piezoelectric element that converts acoustic waves into an electrical signal that is amplified and converted to a digital signal. The digital signal from each sector is individually measured by an internal controller for processing, storage, and/or transmis-sion to an uphole computing facility. Though the individual sectors can be calibrated to match their responses, such calibrations may vary differently for each sector as a function of tempera-ture, pressure, and other environmental factors. Accordingly, in at least some embodiments, the individual sectors are machined from a cylindrical (or conical) transducer. In this fashion, it can be ensured that each of the receiver sectors will have matching characteristics.
When the acoustic logging tool is enabled, the internal controller controls the triggering and timing of the acoustic source 52, and records and processes the signals from the receiver array 56. The internal controller fires the acoustic source 52 periodically, producing acoustic pressure waves that propagate through the fluid in borehole 16 and into the surrounding fonna-tion. At the borehole boundary, some of the acoustic energy is converted into shear waves that propagate along the interface between the borehole fluid and the formation. As these "interface waves" propagate past the receiver array 56, they cause pressure variations that can be detected by the receiver array elements. The receiver array signals may be processed by the internal controller to determine the true formation shear velocity, or the signals may be communicated to the uphole computer system for processing. The measurements are associated with borehole position (and possibly tool orientation) to generate a log or image of the acoustical properties of the borehole. The log or image is stored and ultimately displayed for viewing by a user.
The processing methods applied to the acoustic tool measurements commonly assume that the acoustic logging tool is centered, or at least that the logging tool axis parallels the borehole axis. In practice, however, the logging tool can move off-center and become tilted relative to the borehole axis as shown in Fig. 5.
In Fig. 5, the acoustic logging tool is offset by 2 inches and tilted at 2.5 relative to the axis of a 10 inch borehole through a 50 s/ft fonnation. Such tilts, alone or in conjunction with off-centering, have been found to cause anomalous slowness measurements. The tool tilt pro-duces a gradual shortening of the tool-to-borehole wall offset on one side of the tool, and a gradual lengthening of the offset on the opposite side of the tool. As a consequence, the acoustic waves 62 propagating along one side of the borehole may appear to be propagating past the receiver array at a greater velocity than the acoustic waves 64 propagating along the opposite side of the borehole.
Fig. 6A shows a set of amplitude versus time waveforms 62 recorded from (say) the A3 sectors of each receiver in the receiver array. The receivers are located at 3, 3.5, 4, 4.5, and 5 ft

5 from the acoustic source, and various slowness value slopes are shown to aid interpretation. Fig.
6B shows the set of amplitude versus time waveforms 64 recorded from A7, the sector opposite A3 and tilting away from the borehole wall.
In both figures, the time scale is from 68 to 1832 s. Each of the waveforms is shown for a corresponding receiver as a function of time since the transmitter firing. (Note the increased time delay before the acoustic wave reaches the increasingly distant receivers.) After recording the waveforms, the internal controller typically normalizes the waveform so that they have the same signal energy.
To identify waves and their slowness values, the internal controller or uphole processing system may calculate the time semblance E(t,s) as a function of slowness and time for the data.
This information in turn may be used to determine various formation properties, including wave propagation velocity and dispersion of acoustic waves. The equation for the time semblance E(t,s) is:

N Z

E(t, s) = N' N Z (1) ~x; (t -sd;) ;-~ -In the above equation, N is the number of receiver elements, and hence is also the num-ber of recorded waveforms, x;(t) is the waveform recorded by the ith receiver, d; is the distance of the ith receiver from the transmitter, and s is the slowness. In Equation 1, the quantity (t-sd;) is the relative time at the ith receiver for a given slowness s.
Semblance values E(t,s) range between zero and one. Values near one indicate a high correlation between the various recorded waveforms at the given time and slowness, and hence indicate the presence of a propagating wave having that slowness value. Values near zero indicate little correlation between the various waveforms at the given time and slowness value, and hence provide no indication of a propagating wave having that slowness value.
Fig. 7A shows a plot of the time semblance E(t,s) as a function of time and slowness for the waveforms of Fig. 6A, and Fig. 7B shows a similar plot for the waveforms of Fig. 6B. Of particular interest in measuring formation slowness are the first-arrival peaks, i.e., the peaks in the lower left corner, corresponding to the fastest waves. The graph on the right shows the maximum semblance value found for a given slowness value.
In Fig. 7A the first arrival peak 72 has a maximum semblance value at 41.7 s/ft, while in Fig. 7B the first arrival peak has a maximum semblance value at 58 s/fft.
Thus, when com-pared with the formation slowness of 50 s/ft, the receiver sectors tilting toward the borehole

6 wall measure a reduced slowness (i.e., a faster propagation speed), and the receiver sectors tilted away from the borehole wall measure an increased slowness (i.e., a slower propagation speed).
If, in each receiver, all the sector measurements were combined, the resulting semblance calcula-tions would have revealed an unnecessarily broad distribution of propagation speeds, possibly having a peak at an incorrect value.
Fig. 8 is a flow diagram of an illustrative acoustic logging method with tilt compensation.
The acoustic logging tool is inserted in the borehole, and as the drilling process progresses or as the wireline sonde is pulled, the logging tool moves along the borehole as indicated in block 82.
ln block 83, the logging tool's internal controller periodically fires the acoustic transmitter and collects sector-specific measurements from each of the receivers in the receiver array.
As indicated by block 84, the internal controller processes the measurements to deter-mine the tool tilt effect, and may further calculate the tool offset and tilt relative to the borehole axis. In some embodiments, the internal controller determines tool offset and tilt by first sum-ming the sector-specific measurements for each receiver to obtain each receiver's full radial response. The internal controller then measures the time semblance as given in equation (1) to determine a first arrival window, i.e., a time window in which the transmitted acoustic signal first reaches each of the receivers. A suitable window length might be 100 s, centered on the time value for the first-arrival peak and shifled for subsequent receivers in accordance with the slowness value for the first-arrival peak.
Having identified the time window for each receiver, the intemal controller analyzes the sector-specific signals to determine a time offset between the waveforms of the different signals.
The internal controller may employ a threshold crossing or a peak-detection technique to meas-ure a time offset for each sector-specific signal, e.g. relative to the center or leading edge of the time window. (As a refinement, the peak detection may be performed on an envelope of the sector specific signals, the envelope being determined by rectification and low-pass filtering.) Alternatively, the internal controller may select one of the sector-specific signals as a reference and perform a semblance or correlation calculation to determine the time offset of the other waveforms relative to the reference signal. The time-offset determination is performed between the sectors for each of the receivers.
In block 85, the internal controller determines whether a tilt effect correction is needed.
ln some embodiments, the maximum time offset (or the average time offset magnitude) is compared to a threshold, and corrections are deemed unnecessary when the threshold is not exceeded. For those corrections deemed necessary, the internal controller applies individual time

7 shifts to the sector-specific signals to correct for tilt and to potentially correct for tool de-centralization.
In some embodiments, the measured time offset is simply corrected by a corresponding time shift. In other embodiments, a more sophisticated processing technique is employed to determine the appropriate time shifts. In some embodiments of the correction process, the internal controller determines a tilt effect model that best fits the measured time-offsets. In some embodiments, the tilt effect model assumes a time offset that varies sinusoidally as a function of azimuth, and has the same size and orientation for each of the receivers so that, e.g., the time offset is the same in sector A1 of each receiver. With the size and orientation of the time-offset as model parameters, the internal controller determines a least-squares fit to the measured time offsets. In other embodiments, the tilt effect model includes an time-offset dependence due to a tool-offset parameter to account for de-centralization of the tool relative to the borehole axis.
The time-offsets determined by the best-fitting model are corrected by appropriate time shifts to the measured sector-specific signals, thereby correcting for tilt and "pushing" the summed receiver signal to the center of the borehole.
Though the foregoing discussion determines the corrections for the receiver array as a whole, the same approaches can be applied independently to each receiver in the array to achieve similar results with reduced complexity. If sufficient computing resources are available to deal with additional complexity, the method may be refined to track tool movement from measure-ment to measurement and to use the movement information to refine estimates of tool tilt and position effects.
In block 87, the corrected (if correction was needed) sector-specific signals are processed to measure formation slowness, measure acoustic anisotropy, perform acoustic imaging, evaluate cement bonding, and/or to determine the borehole shape and size in accordance with existing techniques. Formation slowness can be measured using the techniques outlined in U.S. Patent 7,089,119, entitled "Acoustic Signal Processing Method Using Array Coherency".
Acoustic anisotropy can be measured using the techniques outlined in U.S. Patent 6,188,961, entitled "Acoustic Logging Apparatus and Method". Acoustic imaging can be performed by mapping attenuation or intensity measurements to borehole wall pixels in a fashion similar to the tech-niques outlined in U.S. Patent 6,021,093, entitled "Transducer configuration having a multiple viewing position feature". With a short-distance acoustic source, or straightforward modifica-tions to account for different travel paths, borehole calipering can be performed using the techniques outlined in G.J. Frisch and B. Mandal, "Advanced Ultrasonic Scanning Tool and

8 Evaluation Methods Improve and Standardize Casing lnspection", SPWLA 42"d Annual Logging Symposium, June 17-21, 2001.
In block 88, the measurements determined from the processing operations of block 87 are associated with tool position measurements. If the logging tool includes a navigation package, this associate may be performed by the intemal controller or the downhole telemetry transmitter.
Alternatively, or in addition, this association may be performed by an uphole computer system that collects position information from surface instruments and combines it with the telemetry data. The measurements, once associated with position, are stored in the form of a log or image and updated as new information becomes available. In block 89, the uphole system displays the log and/or images to a user. The user may be a driller, a completions engineer, or other profes-sional needing information regarding the well. The process of Fig. 8 repeats as logging contin-ues.
lt is noted here that the actions of Fig. 8 are shown in a sequential order for explanatory purposes. However, the disclosed method may in practice have multiple operations occurring concurrently and in different orders as suited to the needs of the users.
Although the bulk of the method is described as being performed by an internal controller of the acoustic logging tool, this is not a requirement. To the contrary, the processing steps can be performed in a surface computing facility once the sector-specific signals have been acquired and communicated to the surface by a computer such as that shown in Fig. 9.
Fig. 9 is a block diagram of an illustrative computer system suitable for determining and correcting for logging tool tilt and offset. The computer of Fig. 9 includes a chassis 90, a display 91, and one or more input devices 92, 93. The chassis 90 is coupled to the display 91 and the input devices 92, 93 to interact with a user. The display 91 and the input devices 92, 93 together operate as a user interface. The display 91 often takes the form of a video monitor, but may take many alternative forms such as a printer, a speaker, or other means for communicating informa-tion to a user: The input device 92 is shown as a keyboard, but may similarly take many alterna-tive forms such as a button, a mouse, a keypad, a dial, a motion sensor, a camera, a microphone or other means for receiving information from a user. In some embodiments, the display 91 and the input devices 92, 93 are integrated into the chassis 90.
Located in the chassis 90 is a display interface 94, a peripheral interface 95, a bus 96, a processor 97, a memory 98, an information storage device 99, and a network interface 100. The display interface 94 may take the form of a video card or other suitable interface that accepts information from the bus 96 and transforms it into a form suitable for display 91. Conversely, the peripheral interface may accept signals from input devices 92, 93 and transform them into a

9 form suitable for conununication on bus 96. Bus 96 interconnects the various elements of the computer and transports their communications.
Processor 97 gathers information from the other system elements, including input data from the peripheral interface 95 and program instructions and other data from the memory 98, the information storage device 99, or from a remote location via the network interface 100. (The network interface 100 enables the processor 97 to communicate with remote systems via a wired or wireless network.) The processor 97 carries out the program instructions and processes the data accordingly. The program instructions may fucther configure the processor 97 to send data to other system elements, including information for the user which may be communicated via the display interface 94 and the display 91.
The processor 97, and hence the computer as a whole, generally operates in accordance with one or more programs stored on an information storage device 99. One or more of the information storage devices may store programs and data on removable storage media such as a floppy disk or an optical disc. Whether or not the information storage media is removable, the processor 97 may copy portions of the programs into the memory 98 for faster access, and may switch between programs or canry out additional programs in response to user actuation of the input device. The additional programs may be retrieved from information the storage device 99 or may be retrieved from remote locations via the network interface 100. One or more of these programs configures the computer to carry out at least one of the acoustic logging methods with tilt effect correction disclosed herein.
Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. For example, the disclosed methods can be adapted for use with monopole, dipole, quadrupole, and higher-order acoustic transmitters. In some embodiments, the tool tilt is collected from other instruments (e.g., borehole calipers) and employed to determine the appropriate time shifts for the individual sector signals. It is intended that the following claims be interpreted to embrace all such variations and modifications.

Claims (20)

WHAT IS CLAIMED IS:

1. An acoustic logging method that comprises:
generating an acoustic signal that propagates along a borehole in a formation;
providing at least one acoustic sectorized receiver, each receiver comprising a plurality of azimuthally-arranged acoustic transducers at a single axial position of an acoustic logging tool;
receiving a signal from each of the plurality of azimuthally-arranged acoustic transducers to provide a plurality of sector-specific signals for each receiver;
processing the plurality of sector-specific signals to provide compensated signals by determining a time offset between the received signals in order to compensate for a tilt of the acoustic logging tool relative to an axis of the borehole;
and determining a property of the formation based at least in part on the compensated signals.

2. The method of claim 1, wherein the acoustic logging tool comprises an array of two or more axially-spaced receivers, each receiver comprising a plurality of azimuthally-arranged acoustic transducers at a single axial position.

3. The method of claim 2, wherein each receiver comprises at least four azimuthally-arranged acoustic transducers.

4. The method of claim 2, wherein each receiver comprises at least eight azimuthally-arranged acoustic transducers.

5. The method of any one of claims 1 to 4, wherein said processing further comprises finding a model parameter that provides a best fit to the determined time offsets.

6. The method of any one of claims 1 to 5, wherein said formation property is formation slowness.

7. The method of any one of claims 1 to 5, wherein said formation property is selected from a set consisting of acoustic attenuation, acoustic anisotropy, and combinations thereof.

8. The method of any one of claims 1 to 7, further comprising:
associating the formation property with a position and storing the property in the form of a borehole log or image.

9. An acoustic logging tool that comprises:
a tool body having a longitudinal axis;
at least one acoustic sectorized receiver attached to the tool body, each acoustic receiver comprising a plurality of directionally sensitive transducers each oriented in a different azimuthal direction at a single axial position of the tool body;
an internal controller that receives signals from the directionally sensitive transducers to provide a plurality of sector-specific signals for each receiver and processes the plurality of sector-specific signals to provide tilt-corrected signals by determining a time offset between the received signals in order to correct for tilt between the longitudinal axis and a borehole axis.

10. The tool of claim 9, wherein the directionally sensitive transducers are sections of a divided cylindrical or conical piezoelectric element.

11. The tool of claim 9 or 10, wherein the internal controller further determines a formation property based at least in part on the tilt-corrected signals.

12. The tool of claim 11, wherein the formation property is selected from a set consisting of formation slowness, acoustic attenuation, acoustic anisotropy, and combinations thereof.

13. The tool of claim 9 or 10, wherein the internal controller further determines a borehole property based at least in part on the tilt-corrected signals.

14. The tool of claim 13, wherein the borehole property is selected from a set consisting of hole size, hole eccentricity, casing wear, and cement bonding.

15. The tool of any one of claims 9 to 14, wherein as part of correcting for tilt, the internal controller determines time offsets between signals from transducers oriented in different azimuthal directions.

16. The tool of claim 15, wherein as part of correcting for tilt, the internal controller finds at least one model parameter that provides a best fit to the time offsets.

17. The tool of claim 16, wherein the at least one model parameter is one of multiple model parameters including tool offset from the borehole axis and tool tilt relative to the borehole axis.

18. A well logging assembly that comprises:
a telemetry sub; and an acoustic logging tool that provides the telemetry sub with logging measurements derived from tilt-corrected acoustic receiver signals, the acoustic logging tool including:
a tool body having a longitudinal axis;
at least one acoustic sectorized receiver attached to the tool body, each acoustic receiver comprising a plurality of directionally sensitive transducers each oriented in a different azimuthal direction at a single axial position of the tool body; and an internal controller that receives signals from the directionally sensitive transducers to provide a plurality of sector-specific signals for each receiver and processes the plurality of sector-specific signals to provide tilt-corrected signals by determining a time offset between the received signals in order to correct for tilt between the longitudinal axis and a borehole axis.

19. The well logging assembly of claim 18, wherein the acoustic logging tool is a logging while drilling tool, and wherein the telemetry sub stores the logging measurements.

20. The well logging assembly of claim 18, wherein the acoustic logging tool is a wireline tool, and wherein the telemetry sub transmits the logging measurements to an uphole computer.