CA1163021A - Method and apparatus for constituent analysis of earth formations - Google Patents

Abstract

METHOD AND APPARATUS FOR CONSTITUENT
ANALYSIS OF EARTH FORMATIONS
ABSTRACT OF THE DISCLOSURE
The composition of an earth formation is investigated by repetitively irradiating the formation with bursts of neutrons and measuring an energy spectrum of the scattering gamma rays resulting from such irradiation. The measured spectrum is thereafter analyzed by comparing it with a composite spectrum, made up of standard spectra, measured in a controlled environment, of constituents postulated to comprise the formation. As a result of such analysis, the proportions of the postulated constituents in the formation are determined. Where the measured spectrum is subject to degradation due to changes in the resolution of the detector, a filtering arrangement effects modification o. the standard spectra in a manner which provides for a more accurate determination of the constituents of the formation.

Description

BACKGROUND OF THE INVENTION
Field of Invention The present invention relates in general to nuclear well logging, and pertains in particular to improved methods and apparatus or analyzing inelastic scattering gamma ray energy spectra to provide more accurate infor-mation of the composition of earth formations surrounding a well borehole.
The Prior Art Heretofore, various techniques have been utilized to process gamma ray energy spectra for formation constituent analysis. In the case of in-elastic scattering gamma ray energy spectra, it is known that analysis of thespectra to identify the contributions thereto due to carbon and oxygen pro-vides useful information of the presence of oil in a formation. Additional information concerning the composition of the formation, such as its lithol-ogy for instance, is however frequently required before an unambiguous deter-mination of the presence of oil can be made. A suitable lithology indicator for this purpose might comprise the ratio of inelastic scattering gamma ray contributions for calcium and silicon.
The derivation of the foregoing information concerning carbon, ox-ygen, calcium and silicon, and possibly other constituents of the formation, depends upon accurate constituent analysis of the formation gamma ray spec-tra. An important and basic technique for performing such analysis is dis-closed in United States patent No. 3,521,064 issued July 21, 1970 to Moran et al. In accordance with the teaching of this patent, a detected gamma ray energy spectrum for a formation of unknown composition is compared with a composite spectrum made up of weighted standard spectra of the constituents postulated to comprise the formation. The weight coefficients for the standard spectra which give the best fit of the composite spectrum to the unknown spectrum, as determined, for example, by the method of least squares, represent the relative proportions of the constituents in the

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formation. By appropriate selection of the standard spectra, the proportions of the constituents of interest, such as carbon, oxygen, calcium, silicon, etc., may be obtained, from which the desired information regarding oil con-tent may be derived.
It has further been proposed in United Kingdom Patent No. 2,012,419 listing Russell C. Hertzog, Jr. and William B. Nilligan as inventors January 16, 197~, that a background energy spectrum be generated from gamma rays de-tected during periods between neutron bursts and be utilized to provide one or more standard background spectra for use in the analysis of the inelastic scattering gamma ray spectra. The standard background spectra is then up-dated on a repetitive basis to reflect the current background component in the detected inelastic scattering gamma ray spectrum. The standard back-ground spectra is then updated on a repetitive basis to reflect the current background component in the detected inelastic scattering gamma ray spectrum.
The measured inelastic spectrum is thereafter analyzed by comparing it with a composite spectrum, made up of standard spectra of constituents, including ; the background spectra, postulated to comprise the formation, to determine the proportions in the formation of the postulated constituents.
The spectral standards, except for a background standard, as em-ployed in the aforementioned application are generated illustratively, in known laboratory formations or test pits at standard conditions of tempera-ture, pressure and detector resolution. The measured spectrum, on the other hand, is obtained in borehole wells having temperatures which vary from bore-hole to borehole as well as along the length of any one borehole. As a re-sult of such temperature variations and the age of the detector crystal, the output of gamma-ray detectors employed in obtaining the measured spectrum is subject to variation and deterioration in resolution. For example, where a sodium iodide (NaI) detector is employed, the spectral resolution of the out-; put is known to deteriorate ~peak width increase) from a measured seven per-cent peak full width at half maximum (0.662 Mev) at 20C ~room temperature) to over ten percent peak full width at half maximum at 150C.

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Since the derivation of the foregoing information concerning constituents of the formation, depends upon accurate constituent analysis of the formation gamma ray spectra, the weight coefficients for the standard spectra which give the best fit of the composite spectrum to the unknown spectrum, e.g., as determined in accordance with the technique of the aforementioned U.S. Patent No. 3,521,064, will not, in effect, represent the relative proportions of the constituents in the formation if detector resolution is significantly different when the standard spectra are generated and when the measured spectrum is obtained.

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SUMM~RY OF THE INVENTION
One aspect of the present invention is directed to a method for investigating the composition of an earth formation traversed by a well bore through comparison of a measured spectrum of radiation received from the formation with standard spectra, said measured spectrum being observed by means including a detector, said standard spectra being related to constitu-ents postulated to have contributed to said measured spectrum and generated by means including a detec~or, said method comprising the steps of a) deriv-ing said measured spectrum, b~ comparing the standard spectra with the measured spectrum to obtain a satis~actory fit o~ the standard spectrum to a linear combination of the standard spectra, and characterized by: prior to step b) modifying said standard spectra in a manner w~ich reduces the differ-ence between the detector resolution extant during detection of said measured spectrum and the detector resolution extant during generation of said stand-ard spectra.
Another aspect of the present invention is directed to apparatus for investigating the composition of an earth ormation tra~ersed by a well bore through comparison of a measured spectrum of radiation received from the formation with standard spectra, said measured spectrum being observed by means including a de~ec-tor, said standard spectra being related to constitu-ents postulated to have contributed to said measured spectrum and generated by means including a detector, said apparatus comprising a) means for deriv-ing said measured spectrum, b) means for comparing the standard spectra with the measured spectrum to obtain a satisfactory fit of the standard spectrum to a linear combination of the standard spectra, and characterized by:
c) means for modifying said standard spectra in a manner which reduces the difference between the detector resolution extant during detection of said measured spectrum and the detector resolution extant during generation of said standard spectra~

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BRIEF DESCRIPTION OF THE DRAWING
In the accompanying drawing:
Fig. 1, is a schematic view of an embodiment of logging apparatus constructed in accordance with the present invention, Fig. 2, is a simplified flow chart useful in the programming of a circuit arrangement in the embodiment of Fig. 1, and Fig. 3, is a simplified flow chart useful in the programming of a circuit arrangement in connection with the embodiment of Fig. 1.

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DETAILED DESCRIPTION
In the drawing, a representative embodiment of the invention in-cludes a fluid-tight, pressure and temperature resistant well tool or sonde 10 that is adapted to be suspended in a well bore 12 by an armored cable 14 for investigating a subsurface earth formation 16. The well bore 12 is il-lustrated as cased, including the usual annulus of cement 18 and steel casing 20, and as containing a well fluid 21. Although no tubing is shown in the well bore, the tool if desired may be sized for through-tubing use. It will be understood that the invention has application also to open hole logging.
The sonde 10 includes a pulsed neutron source 22 and a radiation detector 24. The neutron source 22 is preferably of the accelerator type de-scribed in United States patent No. 3,461,291 issued August 12, 1967 to Goodman and Uni~ed States Patent No. 3,546,512 issued December 8, 1970 to Trentrop. This type of neutron source is particularly adapted to generate discrete bursts of high energy or fast neutrons, e.g., at 14 MeV of con-trolled duration and repetition rate.
The detector 24 may be of any construction appropriate to the de-tection, illustratively, of gamma rays and to the production of a pulse sig-nal in response to each detected gamma ray having an amplitude representative o~ the energy detected gamma ray. Generally, such a detector includes a scintillation crystal 26 which is optically coupled to a photomultiplier tube 28. The crystal is preferably of the thallium-activated sodium iodide type, though other suitable crystal types such as thallium sodium-activated cesium iodide, may be used. Alternatively, a solid state detector, having for ex-ample a germanium crystal, might be employed. A neutron shield 30 may be po-sitioned between the source 22 and the detector 24 to reduce bombardment of the detector by neutrons emanating directly from the source.
Electrical power for the sonde 10 is supplied through the cable 14 from a source of power (not shown) at the surface. Suitable power source ~not shown) are also included in the sonde 10 for the purpose of driving the neu-tron source 22, the detector 24 and other downhole electronics. The sonde 10 may be surrounded by a boron carbide impregna-ted sleeve 32 located generally in the region of the source 22 and detector 24. The sleeve 32 acts as a shield to minimize the detection of gamma radiation originating from neutron interactions in the immediate vicinity of the source and detector.
An amplifier 34 acts on the output pulses from the photomultiplier 28. The amplified photomultiplier pulses are thereafter applied to a pulse height analyzer ~PilA) 36, which may be of any conventional type such as a single ramp (Wilkinson rundown) type. It will be understood to include the usual pulse height discriminators, for selection of the gamma ray energy range to be analyzed, and linear gating circuits, for control of the time por-tion of the detector signal train to be analyzed.
PHA 36 segregates the detector pulses into predetermined channelsaccording to their amplitude and supplies signals in suitable digital form representing the amplitude of each analyzed pulse. The digital outputs of PHA 36 are stored in a buffer memory 37 and then transferred to telemetering and cable interface circuits 38 for transmission over cable 14 to the surface.
At the surface, the cable signals are received by signal processing and cable interface circuits 40. It will be understood that the circuits 38 and 40 may be of any suitable known construction for encoding and decoding, multiplexing ` and demultiplexing, amplifying and otherwise processing the signals for trans-mission to and reception by the uphole electronics. Appropriate circuits are described, for example, in United States Patent No. 4,012,712.
The operation of the sonde 10 is controlled by signals sent downhole from a master programmer 42 located at the surface. These signals are re-ceived by a reference pulser 44 which, in response thereto, transmits control signals to the neutron source 22 and to the PHA 36.
Upon receipt of the reference pulses, the pulsing circuit generates a sharp fire pulse thereby causing the source 22 to emit a corresponding sharp burst of fast neutrons. For purposes of constituent analysis of inelastic scattering gamma ray spectra in accordance with the present invention, the neutron bursts are preferably of short duration, e.g. 18 microseconds, and are repeated at short intervals, e.g. every 100 microseconds, so as to provide satisfactory statistics in the ~ ~3~
spect.um analysis procedure.
The control signals transmitted from the reference pulser d4 to the PHA 3~ enable :he linear gating circuits of the PHA during at least two different time intervals in relation to each neutron burst, a first int~rval, an inelastic gate substantially coincident with the respective neutron bursts and the second interval a capture gate at a time between neutron bursts.
The detector pulses applied to the PH~ 36 during the inelastic gate correspond predominately to inelastic scattering gamma rays and the detector pulses applied to the PHA 36 during the capture gate correspond predominately to gamma rays resulting from neutron interactions other than inelastic scattering interactions. For the high burst-rate timing sequence usually employed the detector pulses generated during the capture gate will include components due to gamma rays produced by (1) thermal neutron capture of neutrons from precedlng bursts and by (2) capture neutrons which are generated in the borehole environment by the slowing fast neutrons.
The sonde 10 further includes a temperature sensor d6 which may be of any construction appropriate to the detection of borehole temperatures and to the production of an output signal representative of such temperature~ Advantageously, such sensor 46 supplies its output signal in suitable digltal form to telemetering and interface circuits 38 for transmission over cable 14 to the surface.
The inelastic scattering gamma ray spectrum and the neutron capture gamma ray spectrum are generated by data acquisition buffers 50 and 57, respectively, which, under the control of the master programmer 42, accumulate the approprlate counts-per-channel signals from the signal proc~ssing and cable interface circuits 40. Additional buffers may ~e provided to accumulat~ other spectra, for example, two capture acquisition ouffers may be provided, one to accumulate an epithermal capture spectrum and the other to accumulate a thermal capture spectrum.
Cpecifically, the inelas.ic spectrum acquisition burfer 56 accumulates the inelastic scattering gamma ray counts-per-channel slgnals for a period long enough to give a statlstically satis~actory spectrum, e.g., on the order of 1~ microseconds, an~
is then instructed by the master progr~mme~ 42 to , 3~

output the spectrum, recycle to zero, and accumulate a new spectrum for a like period. Similarly, the capture spectrurn acquisition buffer 57 accumu-lates the capture gamma counts-per-channel data for a specified period.
Where the capture spectrum is to be used as a standard in the analysis proce-dure for the inelastic scattering spectrum, it is desirable that the capture spectrum have greater statistical reliability than the lnelastic spectrum.
The counting time of the capture acquisition buffer 57 may therefore be longer than the counting time of the inelastic scattering acquisition buffer 56. For example, the accumulation time for the capture spectrum might be four times as long, e.g., on the order of 80 microseconds, as the accumulation time for the inelastic spectrum. Generally, the accumulation time for the capture spectrum should be selected to maintain the background spectrum as current as possible, while at the same time counting for a sufficiently long time to reduce statis-tical errors to permissible limits. It will be appreciated, therefore, that Ihe background spectrum is repetitively updated as the sonde 10 is moved through the well bore, and thus automatically takes into account variations in such factors as sonde environment, sonde performance, source strength and the like which affect the shape of the capture spectrum.
A temperature acquisition buffer 58, also under the control of the master programmer 43, accumulates the temperature data from the signal proces-sing and cable interface circuits ~0. Desirably, the temperature data is ac-cumulated on a continuous basis during the inelastic spectrum accumulation process and an average value associated with each measured inelastic spectrum provided as an output.
Following accumulation in the acquisition buffers 56, 57 and 58, the inelastic scattering spectrum, the capture spectrum and the average tempera-ture value are transferred to storage buffers (not shown) in a circuit ar-rangement 60. The arrangement 60 may comprise a general purpose digital com-puter, such as the PDP-ll computer manufactured by the Digital Equipment Cor-poration, Maynard, Mass., or, alternatively, it may comprise an analog comput-er. In either event, it will be understood that the arrangement 60 is suita-bly constructed to perform the spectrum matching and constituent proportions determining functions described in the aforementioned United States PatentNo. 3,521,064. In addition, the arrangement 60 includes circuits capable of carrying out certain spectrum processing and pre-analysis steps, as described hereinafter, preparatory to the analysis of the inelastic scattering spectrum.
Within the arrangement 60, storage buffers 68 provide output sig-nals representing the previously obtained standard spectra which are applied, through a filter network 69, to the spectrum comparison circuits 70 for com-parison with the inelastic scattering spectrum in the manner of United States Patent 3,521,06~. Prior to inclusion in the standard spectra, the signals representing the capture spectrum where such spectrum is to be used for back-ground correction, however, may be first applied to spectrum processing cir-cuits for selectively carrying out a number of operations on the capture spectrum signals as described in the aforementioned United States application.
Typically, the signals representing the capture spectrum are normalized to the same total count as the other standard spectra to be used in the comparison analysis of the inelastic spectrum. Where the capture spectrum is to be used directly as one of the standards, it will be appreciated that it is already "normalized" to the same detector resolution as the inelastic scattering spec-trum, a transmittal path is provided therefore which by-passes the ~ilter net-work 69.
As described in the aforementioned ~nited States Patent No.3,521,064, the signals representing the unknown inelastic scattering gamma ray spectrum, as accumulated in acquisition buffer 56, are compared with signals representing the weighted standard inelastic spectra to determine the propor-tions of the constituents which provide the combination; i.e.~ the composite spectrum, which most nearly matches the unknown inelastic scattering spectrum.
This comparison is made in the spectrum comparison circuits 70. Preferably, the "least squares" criterion is used to determine when a best fit has been obtained between the composite spectrum and the unknown spectrum. The weights (wi) for the respective standard spectra which produce the best fit represent the proportions of the corresponding constituents in the formation. As indi-cated in the drawing, the comparison circuits 70 generate the constituents i3DZ~

weights (wi) and transmit signals representative thereof to a recorder 72.
The recorder 72 includes the conventional visual and magnetic tape components for making the customary record of logging signals as a function of depth.
The usual cable-following mechanical linkage 74 for driving the recorder 72 in synchronism with the cable 14 is provided for this purpose. Advantageous-ly, suitable ratios of such constituent weights, e.g., the carbon/oxygen ra-tio and the calcium/silicon ratio, may be formed and recorded as a function of tool depth. The output signals from the signal processing and cable interface circuits 40 may also be recorded directly on tape in the manner indicated in the drawing for further processing and review.
In order to better understand the principles of the present inven-tion represented in the accompanying drawing, detector resolution and factors affecting it will be presently examined in some detail.
The peak-full-width-at-half-maximum resolution (R) of a detector re-sponse at a given energy (E) and temperature ~T) can be generally expressed as:
R(E,T) = Ao(T) + Al(T)E + A2(T)E + ... +A (T)E (1) where the coefficients Ai are temperature dependent constants that describe the detector resolution dependence on the incident gamma ray energy E. For any one particular detector, the coefficients Ai will also be dependent on the degradation of the resolution due to the age of the detector crystal. It will be appreciated that for a typical, undamaged detector at room temperature, on-ly the first two terms of equation (1) will contribute significantly to the expression describing detector resolution.
F.quation (1) provides a general expression for detector resolution with temperature dependency. The resolution of a given spectrum measured for example as T can be expressed as R(E,T ). It will be appreciated, however, that this expression of resolution becomes inadequate in describing detector resolution at other temperatures which differ significantly from T . There-fore, to derive an expression of detector resolutions at temperatures which differ significantly from T , some filtering process which reflects the changes in resolution becomes desirable.

In the practices of the present invention, advantage is taken of the general Gaussian shape of the peaks of a detector measured spectrum -to effcct a convolution of the spectrum obtained at 1' by a Gaussian of resolution G~E,T) to produce a new spectrum at the new temperature ~T) with a resolution given by the expression:
R~E,T) = R~E,T ) -~G(E,T) (2) where G(E,T) = G (T) + Gl(T)E + G2(T)E + -- +G (T)E (3) and the coefficients Gi are temperature dependent constants.
Therefore, given a set of standard spectra measured by a detector and having respective spectra obtained at T by a detector having an output spectrum resolution expressed as R(E,T ), one is able to effect a modification of those spectra for any temperature condition through a filtering process which effects a Gaussian convolution of the obtained spectra. Of course, a determination of the appropriate values of the filter operators Gi becomes es-sential for effecting the desired modification.
The energy spectrum of any one of the standard spectra exists in a digital or analog computer as 256 contiguous channels, with the particular shape of the spectrum defined by the counts stored in locations corresponding to respective channels. This spectrunl can be effectively degraded (i.e., broadened), by convoluting a broadening function with the stored spectrum.
The broadening function is generally of the form F (~E,E,T) = EXP ((2.77 ~E )/G(E,T) ) (~) Where ~E is a variable energy interval defined over an integral num-ber of contiguous spectral channels.
The new, broadened spectrum is obtained from the following relation-ship:
~E ~E
new (~ SOld (E+~) F(~E,E,T))/ (~ F(~E,E,T)) (5) Where SneW(E) is the new average count rate in a spectral chalmel centered about the energy E;
S ld(E+~E) is the average count rate of the existing spectrum, in a spectral channel centered about the energy E+~E; and ~E is an integral multiple of the channel width. The sum over ~E in ~3~

equation (5) includes all ~E values for which F~E,E,T) is greater than a given limit, such as 0.1.
With reference again to the drawing, circuit arrangement 60 repre-sents one embodiment of the present invention. For purposes of illustration we may assume that a detected radiant energy spectrum conveyed from inelastic spectrum buffer 56 to spectrum comparison circuit 70 is to be analyzed for the formation constituents contributing thereto. We will further assume that this spectrum is measured by a detector of unknown resolution and at a given temperature T as provided to the spectrum comparison circuits 70 by the tem-perature acquisition buffer 58. Since this is an initial analysis of the mea-sured spectrum, we may further assume that the filter operators generator 74 is in a reset state and therefore provides an output to -filter network 69 such that the standard spectra provided from the inelastic standard spectra store 68 through filter network 69 to spectra comparison circuits 70 undergo no mod-ifica~ion. In comparison circuits 70 the measured spectrum is compared with a composite spectrum made up of weighted standard spectra, as provided from the inelastic standard spectras store 68, of constituents postulated to comprise the formation. The weight coefficients (wi) for the standard spectra which give the best fit, i.e., reduces the fit discrepancy of the composite spectrum to the measured spectrum) as determined, for example, by the method of least squares, provides one measure of the relative proportions of the constituents of the formation. It will be appreciated of course that one may then obtain a difference indication corresponding to the fit discrepancy between the mea-sured spectrum and the composite spectrum. This difference indication is thereafter compared with a value chosen as being satisfactory for the spectral analysis process. If the difference indication is of a magnitude which is larger than that chosen value then an output of the spectrum comparison cir-cuits 70 is applied to the filter operators generalor 74 so as to generate filter operators representing the effects of detector resolution degradation on an obtained spectrum. The generation of these filter operators will be subsequently discussed in more detail. For purposes of the present discus-sion~ it will be sufficient to note that the output of filter operators gener-ators 7~ when applied to filtcr network 69 effect a modification o:E the stan-dard spectra passing through the filter network :Erom the inelastic standard spectra store 68 to the spectrum comparison circuits 70. It will be appre-ciated therefore, that after the - 13a -generation of these operators spectrum comparison circuits 70 will receive a new set of standard spectra which are modified to reflect detector resolution changes. This new set of spectra is then employed, in spectrum comparison circuits 70, in the constituent analysis process to provide yet another set of weight coe~ficients for the modified standard spectra as a measure of their relative proportions of the constituents o~ the ~ormation. A dif~erence indication between this new composite spectrum and the measured spectrum can then be obtained and compared to the chosen value. It will be appreciated then that this process, of generating modified standard spectra is further repeated until a set of weight coefficients for a particular modification of the standard spectra is found which gives the best fit of the composite spectrum to the measured spectrum, i.e., the difference indication for that particular set of standard spectra is less then the chosen value. This set of weight coefficients then represents a measure of the relative proportions of the constituents in the formation which is adjusted ~or variations in detector resolutions between the measured spectrum and the standard spectra. These weight coefficients are thereafter provided as an output from the spectrum comparison circuits and applied to the recorder 72.
As discussed above, the degradation in resolution of a spectrum measured by a crystal is dependent on the energy of the incident radiation; i.e., the degradation response is dependent on energy. Furthermore, this energy dependency is not fixed for any one crystal but is ~urther subject to variations as a function of temperature and the age of the crystal. It will be appreciated, therefore9 that knowledge of a particular energy dependency of the resolution of a crystal at a given temperature and time in the life of the crystal, is of little use when either the temperature or the age of the crystal changes. Therefore, it is incumbent, for a more accurate analysis of formation constituents~ in accordance with the practices of the aforementioned U.S. Patent No. 3,521,061l, that spectral shapes of the standard spectra reflect a detector resolution which is relatlvely close to the detector resolution extant when the measured spectrum is obtained.
Filter operators Gi, which in effect, determine the extent of spectral broadening and the energy dependence of such broadening, may be generally determined by sequentially, upon a c~mmand frcm .he spectrum comparison circui~s to .he ,ilter operators generator 74, changing one of the filter operators wnile holding the other of the filter operators constant and pQrforming a ~inimum chi-square search for the optimum set of operators set which reduces the difference between the measured spectrum and a composite spectrum ormed of weighted, modified standard spectra. Obviously, this process is relatively time consuming since it depends on the sequential changing of the operators and often requires that the whole process be repeated for each filter operator until the difference between the measured spectrum and the best modified composite spectrum is less than a given desirable value. This process will have to be f!~rther repeated for significant changes in temperatures to wnich the detector is subjected to during measurement intervals in which the radiation spectrum is obtained.
Once these filter operators are obtained, it will be appreciated that, for a given temperature range, for example +5C, these same filter operators will effect the desired nor~alizations of the spectral standards with respect to the measured spectrum. Should the sonde temperature, as communicated by buffer 58, during a measurement in~erval exceed the temperature range of the previously deter~ined set of filter operators, a new set of operators is generated by the above mentioned process. ~asically, the spectrum comparison circuits 70 inc~ude means for determining an initial temperature range and for modifying that temperature range whenever the temperature at which a ne-~ spectrum is measured differs from the limits set for that range. Once a new spectrum is measured at a temperature T2 which differs rom the limits previously defined, e.g., Tl + 5C, Tl - 5C, the spectrum comparison circuits 70 provide an output to filter operators generators to effect generation of a new set of filter operators which will effect, in network 69, the cesired "normalization" between the measured spectrum and the standard spectra. These operators remain unchanged for all subsequent spectra measured at temperatures T which are within the limi~s T2 + 5C, T2 ~ 5C.
In order to avoid the time consuming process of dete~ining filter operators for the normalization procQSS
outlined above, the appropriatQ set of filter operators, ~hich provides the desired normalization of the standard spectra, - comorising a li.eal- co~ination of coef'icienta, associated with resoective, monotonically increasir.g func.ions o~ the energy of the incident gamma rays which modify the standard spectra, may be determined by examining only two of the filter operators. A
first one not associated with any energy dependence and a second one associated with a term corresponding to the square of the incident gamma ray energy. An initial set of ~ilter operators which modify the standard spectra, is determined by varying only the first coefficient and performing a minimum chi-square search for the optimum filter operators over a low energy portion or window of the measured spectrum. These low and high windows have width of the order of 30 and 80 channels r~spectively and are therefore small relative to the width of the wnole measured spectrum. This initial set of filter operators is thereafter finalized by varying the second coefficient and performing ~et anothe~ minimum chi-s~uare search for the optimum filter operators over a high energy portion of the measured spectrum.
During this second search operation care is taken to ensure that the finalized set of filter operators provide the same or similar modification result for the standard spectra over the low energy portion of the spectrum as did the initial set of filter operators, for example, by varying the first coefficient.
The optimum filter operators generated for the analysis of a particular measured spectrum are, thereafter, employed for the analysis of subsequent measured spectra over an interval of the well borehole where changes in temperature do not exceed certain limits. Where changes in temperature exceeding the certain limits are detected during spectrum measurement, a new set of filter operators is generated, as discussed above, so as to improve the accuracy of the earth formation constituent analysis process.
-- With reference now to Fig. 2, a simplified flow diagram is sho~n as illustrative of the operations oerformed within arrangement 60, in accordance wi.h one embodiment of the oresent invention. These operations consist mainly of three l~a,or paths.
A first path reflects the search of filter ooerators, GQ~ Gl/
G2... etc. which provide for a minimum chi-square fitting of a modified composite sDectrum to a measured spectrum. A second path effects a search for welaht coefficients which provide for a least squares fitting of a measured spectrum to a composi.e 3~

spectrum Pormed from standard spectra modified in accordance with a filtering process dependent on the filter operators derived in the first path. And finally, a third path which bypasses the first path wherever certain temperature conditions are met.
At the start of operations at 80, it will be appreciated that values for the filter operators correspond to zeros so that operations of filter network 69 will eff`ect no modification of the standard spectra. Also an initial temperature Tl, illustratively, -200 G, is chosen so as to assure that the first cycle of operations is conducted thru the first path. Therefore, when at 82 the temperature T of the borehole at a given depth corresponding to that at which a measured spectrum is obtained is compared to a range of temper-atures, Tl - 5 C to Tl + 5 C, it will clearly fall without that range.
The following step at 84 designates Tl equal to T and resets all filter operators Gi, variables i and n equal to zero. Variable i is the subscript of the filter operators and identifies the correspondence of the operator to an incident energy term E which is raised to the power i. The variable n corresponds to the total number of operators to be considered, it being appreciated that the term n may be as large as is desired even though in practice only the first three terms G 1 Gl and G2 significantly contrib-ute to the spectra modification process. The filtering process at 85 operates on the standard spectra ~rom store 68, which in this initial cycle will pass through the filtering prooess unmodified. Subsequently, the measured spectrum from buffer 56 will be compared at 86 with a composite spectrum made up of weighted spectra of constituents postulated to have contributed to the meas-ured spectrum in accordance with the aforementioned U.S. Patent No.3,521,064.
Thereafter, at 88 a measure of the goodness of fit between the composite and measured spectra is derived and stored along with the filter operator subject to variation, in this case Go. At 90, the goodness of fit derived at 88 is observed to determine whether or not it has passed through a minimum. Since this i~ the first cycle of operation, the filter operators generator will incrementally chan~e Gi, i.e., in this case Go, at 92, store this value at 94, and apply the "new" set of operators to filter 85. Of course, this time around when the standard spectra from store 68 are convoluted in filter 85 so as to be modified in accordance with set of` filter operators, the result 3~

of least squares fitting at 86 and -the goodness of fit measure at 88 will be different from that previously obtained.
Once the goodness of fit measure passes through a minimum, that minimum is determined at 96 by means of well known techniques such as by fit-ting a parabola through the points defining the pass through the minimum and then determining the minimum of the parabola. The Go associated with such minimum is then stored at 94. Thereafter, n and i are incremented at 98 and the process is sequentially repeated through the first path for Gl, G2 and G3 and these values stored in their respective terms at 94. It will be appreci-ated that when n equals 4 this will signify that all the operators needed forthe filtering process have been determined. Therefore at lO0 the process is continued through the second path through a filter 102 which effects a modifi-cation of the standard spectra from store 68 by convoluting the spectra with a function determined from the output of filter operators store 94, i.e., G , Gl and G2. A composite spectrum formed of weighted, modified standard spectra is then compared to the measured spectrum from buffer 56 to provide a least squares fit therebetween. The weights wi, of the standard spectra which pro-vide the best fit of the composite spectrum to the measured spectrum is there-after provided as an output at 106 which output may be supplied to a recorder or plotter such as 72 in Figure 1.
For subsequent measured spectra having associated temperatures T
within ~5C of the previous measured spectrum~ it may be safely assumed that the already determined filter operators will provide the desired modification of the standard spectra. Therefore, the process bypasses the first path and directly passes through the filter at 102, the least squares fitting at 104 to the output at 106. Where the temperature of the measured spectrum exceeds that of the previously deter~nined limits, the filter operators will have to be determined anew by the method outlined above with reference to the first path.
With reference now to Figure 3, a simplified flow diagram illus-trates yet another embodiment of the present invention which simplifies theprocess o:E obtaining filter operators, i.e., the first path illustrated in Figure 2, which would effect the desired modification of the standard spectra.

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In this embodiment only portions of the measured spectrum are employed in the determination of the operators, mainly a low energy window from 1.59 MeV to 2.55 MeV and a high energy window from 5.73 MeV to 7.33 MeV. Moreover, in accordance with this embodiment not all of the operators need be determined.
Illustratively, only two operators Go and G2 or Go and Gl, may be sufficient for effecting the desired modification of the standard spectra. Of course, more than two operators may be needed and this illustration of the embodiment of the invention is not intended to limit the practice of the invention to any selection of operators. We will assume, for purposes of illustration, that the two operators to be determined are G and G2. Initially at 108 G and G2 are set equal to zero so as not to effect any modificatioll of the standard spectra when such spectra is convoluted in filter network 110. At 112 the portion of the spectrum in the low energy window is compared with a composite ; spectrum formed of weighted spectra of constituents postulated to have con-tributed to the measured spectrum. Thereafter, at 114 a measure of the good-ness of fit between the measured spectrum and the composite spectrum is deter-mined and stored along with the associated Go. At 116 this measure of the goodness of fit is monitored for indications that it has passed through a min-imum. If it has not passed through a minimum, G is incrementally changed at 118 and the new value stored at 120 where it is supplied to filter network 110. This process is repeated, as discussed with reference to Figure 2, un-til the measure of the goodness of fit passes through a minimum. This mini-mum is then determined at 121 as previously discussed and a quantity Z is set equal to Go at 122. The process is then repeated for the determination of G2 in the high energy window of the measured spectrum. Filter network 124, the least squares fitting step at 126, the measure goodness of fit derivation at 128, the passage through a minimum test at 130, the incremental changes of G2 at 132 and the filter operator s~ored at 134, correspond to their counter-parts discussed in reference to the determination of G and will not be fur-ther discussed. However, it will be appreciated that since the desired filter operators should provide the same or similar modification o:E the standard spectra for the low energy window as the Go determined at 120, i.e., Z, a new G is determined at 136 from the relationship:

G = Z - G E
o 2 Low Where EL :is the energy at the mid point of the low energy window.
Once a G2 has been determined, i.e., the G2 associated with a good-ness of fit measure which is at a minimum, the associated G will also be readily identified. These filter operators may then be stored at 138 and fur-ther employed in the determination of the formation constituents in accordance with the process discussed above and shown in the second path of Figure 2.
Although the invention has been described herein with reference to a specific embodiment, many modifications and variations therein will readily occur to those s~illed in the art. For example, the gamma ray energy spec-trum analysis of the present invention may be carried out by comparison of gamma ray spectra obtained in other ways than by inelastic scattering of fast neutrons, such as those produced by thermal or epithermal neutron capture, or by other ways than by neutron irradiation such as natural gamma ray spectra.
Accordingly~ all such variations and modifications are included within the intended scope of the invention as defined by the following claims.

Claims (10)

1. A method for investigating the composition of an earth formation traversed by a well bore through comparison of a measured spectrum of radiation received from the formation with standard spectra, said measured spectrum being observed by means including a detector, said standard spectra being related to constituents postulated to have contributed to said measured spectrum and generated by means including a detector, said method comprising the steps of a) deriving said measured spectrum, b) comparing the standard spectra with the measured spectrum to obtain a satisfactory fit of the standard spectrum to a linear combination of the standard spectra, and characterized by:
prior to step b) modifying said standard spectra in a manner which reduces the difference between the detector resolution extant during detection of said measured spectrum and the detector resolution extant during generation of said standard spectra.

2. The method of claim 1 characterized in that said standard spectra modifying step comprises the steps of:
- generating a set of filter operators and modifying said standard spectra by said fitter operator so as to provide a set of filtered standard spectra;
- generating a composite spectrum made up of weighted, filtered standard spectra which weights provide the best fit between the composite spectrum and the measured spectrum;
- comparing the measured spectrum and the composite spectrum to provide a difference indication corresponding to the fit discrepancy between the measured spectrum and the composite spectrum; and - repeating said set of filter operators generating step, said composite spectrum generating step, and said comparing step for a plurality Or different sets of ?ilter operators to identify an optimum set of filter operators associated with a difference indication having a magnitude which is as small as possible.

3. The method of claim 2 characterized by the steps of:
- obtaining an indication of the temperature of the formation associated with said measured spectrum; and - effecting said set of filter operators generation step, said comparing step and said repeating step only where said obtained temperature indication differs by more than a chosen amount from an indication of temperature associated with a preceding measured spectrum, for which an optimum set of filter operators has been identified.

4. The method of claim 1 characterized in that said standard spectra modifying step comprises the steps of:
- performing a first search over an energy independent operator, said search minimizing chi-square calculated over a low energy portion of the measured spectrum to generate and initial set of filter operators; and - performing a second search over an operator dependent on the square of the energy, said second search minimizing chi-square calculated over a high energy portion of the measured spectrum to generate a final set of filter operators, said second search insisting that the finalized set of filter operators provide the same modification result over the law energy portion of the spectrum as the initial optimum set of filter operators.

5. The method of claim 4 characterized by the steps of:
obtaining an indication of the temperature of the formation associated with said measured spectrum; and effecting said set of filter operators generation steps only where said obtained temperature indication differs, by more than a chosen value, from an indication of temperature associated with a precedent measured spectrum for which an optimum set of filter operators has been identified..

6. Apparatus for investigating the composition of an earth formation traversed by a well bore through comparison of a measured spectrum of radiation received from the formation with standard spectra, said measured spectrum being observed by means including a detector, said standard spectra being related to constituents postulated to have contributed to said measured spectrum and generated by means including a detector, said apparatus comprising a) means for deriving said measured spectrum, b) means for comparing the standard spectra with the measured spectrum to obtain a satisfactory fit of the standard spectrum to a linear combination of the standard spectra, and characterized by:
c) means for modifying said standard spectra in a manner which reduces the difference between the detector resolution extant during detection of said measured spectrum and the detector resolution extant during generation of said standard spectra.

7. The apparatus of claim 6 characterized in that said means for modifying said standard spectra comprises :
- means for generating a set of filter operators and modifying said standard spectra by said filter operators so as to provide a set of filtered standard spectra;

- means for generating a composite spectrum made up of weighted, filtered standard spectra which weights provide the best fit between the composite spectrum and the measured spectrum;
- means for comparing the measured spectrum and the composite spectrum to provide a difference indication corresponding to the fit discrepancy between the measured spectrum and the composite spectrum; and - means for repeating said set of filter operators generation , said composite spectrum generation, and said comparison for a plurality of different sets of filter operators to identify an optimum set of filter operators associated with a difference indication having a magnitude which is as small as possible.

8. The apparatus of claim 7 characterized by:
- means for obtaining an indication of the temperature of the formation associated with said measured spectrum; and - means for enabling said set of filter operators generation means only where said obtained temperature indication differs by more than a chosen amount from an indication of temperature associated with a preceding measured spectrum, for which an optimum set of filter operators has been identified.

9. The method of claim o characterized in that said standard spectra modifying means comprises :
means for performing a first search over an energy independent operator, said search minimizing chi-square calculated over a low energy portion of the measured spectrum to generate an initial set of filter operators; and means for performing a secon? search over an operator dependent on the square of the energy, said second search minimizing chi-square calculated over a high energy portion of the measured spectrum to generate a final set of filter operators said second search insisting that the finalized set of filter operators provide the same modification result over the law energy portion of the spectrum as the initial optimum set of filter operators.

10. The apparatus of claim 9 characterized by:
means for obtaining an indication of the temperature of the formation associated with said measured spectrum; and means for effecting said set of filter operators generation steps only where said obtained temperature indication differs, by more than a chosen value, from an indication of temperature associated with a precedent measured spectrum for which an optimum set of filter operators has been identified..