GB2127148A - Well logging methods and systems - Google Patents

Abstract

Disclosed are a method and a system for well logging in which gamma radiation detected 10 in five energy windows is converted into logs of formation thorium, uranium and potassium (Th, U, K), and logs of borehole barite and potassium chloride (KCl), in a process which makes use of an adaptive filter 24 having a model which accounts for changes in the detected gamma radiation with borehole depth, for the nature of the logging process, and for the composition of the borehole fluid. In a first, simpler embodiment, the adaption of the filter is based on changes with borehole depth in the total amount of detected gamma radiation in the vicinity of the depth level of interest. In a second, more exacting embodiment, the filter is based on a model of both the vertical variations in the Th, U, K concentrations, and the statistical variations in the measurements. In both embodiments a log of Th, U, K is produced. A third embodiment which accounts for environmental effects is based on the second embodiment, but additionally incorporates into the model the effect of the borehole size and the influence of the gamma ray emitters and absorbers located in the borehole fluid on the detected counts of the energy windows. The third embodiment permits the converting of the received radiation information into logs of formation thorium, uranium and potassium, and logs of borehole barite and potassium chloride, by borehole depth. The invention relates to induced as well as natural gamma radiation, and to other types of well logging in which energy windows can be measured, such as sonic well logging. <IMAGE>

Description

SPECIFICATION Well logging methods and systems This invention relates to well logging, in which measurements taken in boreholes are used in searching for and exploiting valuable underground resources such as oil and gas. It is particularly directed to a method and a system related to energy window logs, such as logs of the gamma radiation detected in several energy windows. It is more particularly directed to a method and system for converting energy window logs into logs of selected subsurface materials such as thorium uranium and potassium. It is further directed to a method and system which while converting energy window logs into subsurface materials logs, corrects for the borehole size and corrects for and produces additional logs of the radiation emitters and absorbers in the borehole fluid.The invention relates to logging natural as well as induced gamma radiation, and to other types of logging in which energy window measurements can be taken, such as sonic logging.

In the example of natural gamma radiation logging, a tool capable of detecting gamma radiation in each respective one of several energy windows passes through a selected borehole interval and measures the gamma ray photons detected in the respective windows in each respective one of a succession of small (e.g., 6-inch) depth intervals. The rays are emitted in the radioactive decay of subsurface materials such as thorium, uranium and potassium, each of which emits with a characterstic energy spectrum. The tool output is converted to a log of the respective emitting materials.

The log of materials such as thorium, uranium and potassium is important in the search for and exploitation of underground resources because it is believed that these materials appear in nature with a discernible relationship to geology and rock morphology. As some nonlimiting examples, it is believed that the ratio of thorium to uranium can be used for determining the geochemical faces in sedimentary rocks, the uranium to potassium ratio can be used to estimate the source rock potential of argillaceous sediments and that the thorium to potassium ratio can be used for determining the mineralogical composition of shales.

Perhaps more importantly, it is believed that by using the thorium, uranium and potassium concentrations either individually or in combination it is possible to measure the presence, type, and volume of shale or clay in the formations surrounding the borehole, which is particularly important in the search for and exploitation of oil and gas deposits.

While it is known that thorium, uranium and potassium emit gamma rays with characteristic discrete energy spectra, it is also known that between their emission and their detection those gamma rays undergo various interactions with the formation, the borehole and the tool and that, consequently, their apparent energy spectra as detected are continuous and have a poor energy resolution. Moreover, the borehole often contains borehole fluid (mud) which includes gamma ray emitters such as potassium chloride and gamma ray absorbers such as barite which affect the count rates detected in the energy windows.Additional uncertainties are introduced by the fact that relatively few gamma ray photons can be detected in the respective energy windows at a given borehole depth because the tool must move through the borehole at a sufficiently high speed to allow drilling or production activities to resume as soon as possible, and by the fact that the toll response changes as a function of borehole size.

Some aspects of known gamma radiation well logging are discussed in Marrett, G. et al., "Shaly Sand Evaluation Using Gamma Ray Spectrometry, Applied to the North Sea Jurassic," Proc. SPWLA 17th Annual Logging Symposium, June 9-12, 1976, and Serra, O. et al., "Theory Interpretation and Practical Applications of Natural Gamma Ray Spectroscopy," Proc. SPWLA 21st Annual Logging Symposium, July 8-11, 1980, and additional information can be found in Chevalier et al. U.S. Patent 3,976,878 and Moran et al. U.S. Patent 3,521,064.As discussed in the cited documents, all of which are hereby incorporated by reference herein, it is possible to convert the output of natural gamma radiation logging tool having three or five energy windows into a log ofthorium, uranium and potassium concentrations (Th,U,K), in essence by subjecting the tool output to a filter characterized by a 3X3 or 3X5 matrix which can be empirically derived -- such as by passing the tool through a test borehole containing known concentrations of Thu,U,K arranged to approximate the effect of homogenous beds of infinite depth extent and recording the window responses.If W designates the radiation detected in five energy windows at a given borehole depth level, i.e., W = [W1, W2, W3, W4, W5], and X designates the thorium, uranium and potassium concentrations at the same depth level, i.e., X = [Th,U,K], then the relationship between the windows measurements W and the concentrations X (when no environmental effects are present) can be described by: W = HX + e (1a) wherein H is defined by a 5X3 tool sensitivity matrix which is unique to a given tool and can be empirically derived by passing the tool through a borehole containing known concentrations of Th,U,K in idealized beds, and. = [.1, e2, . . . e5] denotes the statistical errors which are due to the Poisson nature of gamma ray detection.What is of interest normally in the concentrations of Th,U,K as a function of the radiation detected in the windows, and therefore what is of interest is the relationship: X=MW (2a) where M is defined as a 3X5 matrix relating the concentrations of the three materials to the radiation detected in the five energy windows at a given depth level in the borehole. The matrix M is not the inverse of the matrix H because of a nonsquare matrix does not have a direct inverse in the strict sense of the term, but M can be found through a least squares technique relating known concentrations of Th,U,K to measured radiation in the five energy windows for given test conditions. Of course the matrix M need be found only once for a given logging tool.In the case of a particular tool the following empirically derived numeral matrics H and M can be used for a standard (8"-diameter, water-filled) borehole:

10.13660 21.77220 37.47680 3.27358 6.41613 16.59690 H = .61623 1.61744 7.519860 (1b) .32686 .56565 .0 .46439 .16434 .0 .06184 .13764 .00442 .09079 2.46311 M = .10020 -.11665 -.24194 .28841 -1.24674 (2b) -.01856 .04096 .13512 -.14859 .04175 In the known technique, a log of the Th,U,K concentrations is derived by evaluating the relationship (2a) at each depth level in the borehole.Because of the nature of the logging process this estimate of Th,U,K concentrations tends to be noisy, but can be improved by some averaging of the radiation detected in the respective windows over successive borehole depth levels. For example, in order to find the Th,U,K concentrations at a given depth level n in the borehole, the matrix M can be applied to the average of the radiation detected in the five windows for the depth level n and the preceding one, n- 7. The average need not be an arithmetic one, and more of the current depth level can be used than the preceding one. More than two depth levels can be averaged, but there is a limit because the consequence of averaging is a loss of resolution in the direction along the borehole axis.

Additional aspects of gamma radiation well logging, especially a method and system for correcting the log of selected gamma radiation emitting subsurface materials for environmental errors introduced by borehole size and by the gamma ray emitters and absorbers found in the borehole fluid, are discussed in Ellis, D., "Correction of NGT* Logs for the Presence of KCI and Barite Muds", Proc. SPWLA 23rd Annual Conference, 6-8 of July, 1982. As discussed in that document, which is hereby incorporated by reference herein, the gamma radiation emitting subsurface materials logs may be corrected for at least one of: (i) the gamma ray emitter potassium chloride (KCl) in the borehole fluid, and (ii) a gamma ray attenuator (absorber) in the borehole fluid, e.g. barite and/or hematite.Thus the matrix H seen in expression (1 b) and the relationship W = HX + ,seen in (1a) may be modified by considering the measurement of window 1 to be affected in a certain manner not only by radiation from the formation gamma ray emitting materials, but also by radiation from the KCI emitter in the borehole fluid, and by absorption (attenuation) by a strong absorber in the same borehole fluid. The measurements in windows 2 and 3 are affected both by radiation from the KCI in the borehole fluid. The contribution to the measurement in a given window from the KCI in the borehole fluid grows centered and eccentered tools.The contribution W(KCI) to the measurement in a given energy window which is due to KCI in the mud can be represented in the general case as W(KCI) = (KCI) a[1 - eb(r -C)] (3) where a, band care constants which can be derived empirically by tests with a given logging tool in test boreholes having known diameters (r, found by a caliper log) and containing mud with known concentrations of KCI. The following relationships govern the lowerst three energy windows in the non-limiting example of a particular 5-window logging tool, where W(KCI) is the contribution to the measurement in an energy window due to the borehole fluid KCI, KCI is in percent concentration and r is in inches: W1 (KCI) = (KCI) 59.86 (1 - e -.O46(r-3.62)) - (KCI) f1 (r) W2 (KCI) = (KCI) 22.16(1 - e -.078(r-3.62))-- (KCl) f2 (r) (1c) W3 (KCI) = (KCl) 11.22 (1 - e-.1l36(r-3.e2)) - (KCI) f3 (r) The relationship between window measurements and Th,U,K concentrations (related by the logging tool sensitivity matrix H) can be corrected for the influence of the mud filtrate KCI and B in the borehole fluid by accounting for the effect thereon on the lowest three energy windows, in a relationship described by the following expression:

[W1 - (KCl)f, (r)]/B W2 - (KCl)f2 (r) Th W3 - (KCl)f3 (r) = H U (2c) W4 K W5 The five unkowns in expression (2c) are the borehole fluid KCI concentration, the B correction and the concentrations of the three materials Th,U,K in the formations surrounding the borehole; and there are five relationships from which to find them.

In view of the known techniques discussed above for gamma radiation well logging and the corrections thereto for borehole fluid absorbers and emitters, and borehole size, one aspect of the invention relates to improving the log of Th,U,K concentrations derived from the radiation measured in five energy windows, based on the recognition that the concentrations log can be filtered not in a fixed manner but adaptively -- in accordance with changes with borehole depth in the detected radiation and an understanding of the nature of the logging process. More particularly, this aspect of the invention is based on the discovery that a technique which has at least some characteristic of Kalman filtering can be used in connection with gamma radiation well logging when the nature of the logging process is taken into account in accordance with this invention.

In particular, in accordance with an illustrative and nonlimiting example of the invention, the Th,U,K concentrations log is derived by estimating the concentrations for a given borehole depth level through modifying the concentrations estimate for a previous depth level by an amount determined through applying a filter (constructed for the given depth level) to a combination of: (i) the radiation detected in the five energy windows for the given depth level and (ii) an estimate for the radiation in the five energy windows derived by applying the tool sensitivity matrix to the concentrations estimate for the previous depth level.If the filtered estimate for the Th,U,K concentrations for the current depth level n in the borehole is designated by X(n) and the filtered estimate for a previous depth level is designated by X(n-1), the filter gain for the given depth level is designated by K(n), the radiation detected in the five energy windows for the depth level n is designated by W(n) and the sensitivity matrix characterizing the particular well logging tool is designated by H, then one exemplary process in accordance with the invention can be described by the expression: X(n) = X(n-1) + K(n) [W(n) - HX(n-1) (4) In a first, simpler and nonlimiting example of the invention, the filter gain K(n) for a particular borehole depth level n is determined by the behavior of the total detected gamma radiation in the vicinity of the depth level n.If the total detected gamma radiation is stable and smoothly varying in the relevant borehole depth interval, then in this example the effect of the adaptive filter gain K(n) approaches that of averaging the energy windows over a substantial borehole depth interval. However, if the total detected gamma radiation is changing significantly in the relevant borehole depth interval, then the gain K(n) approaches the 3X5 empirically derived matrix M discussed above. Stated differently, the filter adapts such that the previous Th,U,K concentrations estimate tends to dominate when the true concentrations at the relevant depth in the borehole are likely to be constant, and the newly measured energy windows tend to dominate otherwise. In a particular example, the gain K(n) can be the matrix M weighted by a scalar K(n) which varies between a value approaching zero and a value approaching unity.

In a second, more exacting but again nonlimiting example, the invention is implemented in a process which again applies a filter in the manner discussed in connection with expression (4) but the filter gain K(n) for a given depth level n is determined by a 3X3 matrix S characterizing the statistical variations in the filtered estimates of the Th,U,K concentrations, a 3X3 matrix Q characterizing the relevant geological noise, the well logging tool sensitivity matrix H, the matrix H transposed to produce a matrix H', and a 5X5 matrix R characterizing the statistical variations in the radiation detected in the five windows (i.e. the noise E).The manner in which said factors determine the filter gain K(n) in this second exemplary embodiment of the invention can be described by: K(n) = (S(n-1) + Q(n-1)) H' [H [S(n-1) + Q(n1)] H' + R(n)]-1 (5) where S is an estimate of statistical variations in the Th,U,K concentration estimates, Q is an estimate of the relevant geological noise and R is an estimate of the statistical variations in the energy window measurements.

In a third embodiment, where environmental effects are present, expression (1a) is modified to take into account the borehole size effect as well as the effect due to the presence of absorbers (e.g. barite) and radioactive emitters (e.g. KCI) in the borehole fluid. In a non-limiting example, where only barite and KCI are present in the borehole fluid, and where the borehole size effect has been modeled according to expression 8 below, expression (1a) is modified as follows: W=H(x)X+e (6) where H(x) is a corrected sensitivity matrix function of the borehole absorption coefficient x. In turn, x = p (r - rsonde) (7) where p is the density of the mud, r is the diameter of the borehole (measured from a caliper log) and rsonde is the diameter of the sonde.The functional dependence on x of the (i,j)-th element [i= 1, 2..., 5; j= 1, 2, 3] of the matrix H is given by Hjj(x) = (a - pixie -kijx)Hij (8) where Hi is the (i,j)-th element of the standard matrix (1 b), &alpha;ij, ssij and k11 are calibration constants which can be found empirically.

The influence of barite and KCI has been modeled by D. Ellis, as noted above. With KCI denoting the concentration of KCI in the mud and B denoting the barite coefficient (acting as a gamma ray absorber for the first window only), the tool response equation can be written as:

W1 Th f1 (x) e1 W2 f2(x) W3 = He (X) # U + f3(x) KCl + E3 (9) W4 0 W5 K 0 #5 where HB(X)=

BH11(x) BHr2(x) BH13(x) H21(x) H22(X) H23(x) H31(x) H32(x) H33(x) H41 (x) H42(x) H43(x) #H51(x) H52(X) H53(x) # and where fj(x) denotes the influence of 1% of KCI in the mud on the i-th window (there being no influence on windows 4 and 5). The functional dependence of fi(x) on xis given by fj(x) = a; (1 -e -bix) as seen by relationship (3) and its following discussion.

Those skilled in the art will recognize that the third embodiment method for correcting for environmental effects is just a suitable modification of the method of the second embodiment of the invention. Instead of estimating only X = (Th,U,K), the potassium-chloride (KCI) and barite (B) concentrations must also be estimated at each depth. If, for simplicity, it is assumed that KCI and B are constant along the selected borehole interval (the case where KCI and B are slowly varying quantities being but a straightforward variation), and Y is defined as the vector of the (Th,U,K,KCI and B) concentrations, the estimation of Y is performed using the extended Kalman filtering technique, which is well-known by those skilled in the art.

The estimate Y(n) of Y at depth n is given by Y(n) = Y(n-1) + K(n) [W(n) - G(n)Y(n-1)] (10) where G(n) is the following matrix:

B(n-1 )H11(x) B(n-1 )H12(x) B(n-1)H13(x) fl(x,) b H21 (Xn) H22(xn) H23(xn) f2(x) O H31(xn) H32(xn) H33(Xn) f3(x) (11) H42(Xn) H42(Xn) H43(xn) 0 0 H5a(xn) H52(X,) H53(Xn) 0 0 with B(n-1) being the estimate of B at depth n-1, xn being defined for depth n as the borehole absorption coefficient of relationship (7), and b = Hll(x,) Th (n-1) + Hl2(xn) U(n-1) + Hq3(xn) K(n-1) [Th(n-1), U(n-1) and K(n-1) being the (Th,U,K) estimates at depth (n-1)].

The gain K(n) is now seen to be a (5X5) matrix given by Kn=[S(n-1) + Q(n-1)] G'(n) [G(n)[S(n-1)+Q(n-1)]G' (n) + R(n)]-1 (12) where S is a (5X5) matrix which represents the covariance of the statistical variations in the Th,U,K,KCI and B estimates; 0 is assumed to be of the following form

Qt O 0 0 0 O Qu O 0 0 0= 0 0 Ok 0 0 (13) O O O O O 0 0 0 0 0 where Ot, Qu and Ok are the variances of the geological noises in Th,U,K; and R is an estimate of the statistical variations in the energy window measurements.

In both the second and third embodiments, the log made up of samples X(n) or Y(n) estimated through use of the filter gain referred to in connection with expressions (5) or (12) can be further filtered, in a fixed lag-filter process which takes into account borehole depth levels subsequent to the one currently being processed.

The invention will now be described, by way of example only, with reference to the accompanying drawings, of which: Figure 1 illustrates an exemplary embodiment of a system in accordance with the invention; Figure 2 illustrates characteristic spectra of thorium, uranium and potassium and the five energy windows of an exemplary logging tool; Figure 3 is a flowchart illustrating a process in accordance with a first, simple embodiment of the invention; Figure 4 is a flowchart illustrating a process in accordance with a second, more exacting embodiment of the invention; Figure 5 is a flowchart relating to the second embodiment of the invention; Figure 6 is a flowchart illustrating a process in accordance with a third embodiment of the invention which accounts for environmental effects of the borehole size and borehole fluid;; Figure 7a illustrates an assumed subsurface distribution of Th,U,K; Figure 7b illustrates a filtered Th,U,K log produced by a process in accordance with the first exemplary embodiment of the invention from an energy windows log produced by applying a tool sensitivity matrix to the Th,U,K distribution of Figure 7a and adding noise; Figure 7c illustrates a filtered Th,U,K log produced by a process in accordance with a second exemplary embodiment of the invention from the same energy windows log; and Figure 7d illustrates a Th,U,K log produced by a prior art process from the same energy windows log.

Figures 8a and 8b illustrate filtered Th,U,K logs produced in accordance with said first and second exemplary embodiments, respectively, from the same energy windows logs derived in an actual borehole; and Figures 9a and 9b respectively illustrate filtered Th,U,K logs produced in accordance with the second exemplary embodiment, and produced in accordance with the third (environmental correction) embodiment which also includes additional borehole B and KCI logs; wherein both sets of logs are derived from the same energy windows logs gained in an actual borehole.

Figure 1 shows a logging tool 10 in a borehole 11 for investigating subsurface earth formations 12 by deriving a log thereof. In a particular embodiment, tool 10 logs the gamma radiation detected thereby in each of several energy windows, for example five. A particular example of such a tool is designated NGT-A and is described in U.S. Patent No. 3,976,878. Tool 10 is supported in borehole 11 by a cable 13 which passes over a sheave wheel 14 and is secured to a drum-and-winch mechanism 15. Mechanism 15 includes a suitable brush and slipring arrangement 16 for providing electrical connection between conductors within cable 13 and a unit 17 labelled CSU which controls the supply of power and electrical signals to and from tool 10 via a cable 13 and readies signals from the tool for application to storage 18.Either or both of units 17 and 18 can include equipment for converting analog signals received from tool 10 into digital signals associated with the respective depth levels n in borehole 11 at which the analog signals have been derived by tool 10, as indicated by wheel 19 which engages cable 13 and is linked with a depth recorder 20, which in turn is linked with either or both of units 17 and 18. Either or both of unit 17 and storage 18 can include additional equipment for preprocessing of logs to prepare them for use in the invented process. Unit 18 can store logs derived by separate measuring devices carried by the same tool 10 in one or more passes through borehole 11, logs derived from separate passes of different tools 10 through borehole 11, and/or logs derived from passes of tool 10 or other similar tools through different boreholes in the same or similar subsurface formations.A surface controller 21 controls the speed and position of tool 10 in borehole 11. The exemplary tool designated NGT-A includes a scintillation detector schematically indicated at 1 Oa which comprises a 12-inch long and 1-3/4 inch diameter sodium iodide crystal optically coupled to a photomultiplier, and includes electronic circuitry schematically illustrated at 10b which takes the photomultiplier output and determines the amount of gamma rays in each of five energy windows and sends corresponding electrical signals to the surface via conductors in cable 13.

One example of the energy range in the energy windows is illustrated in Figure 2, where the five windows are designated W1, W2, W3, W4, and W5 and the MeV boundries thereof are indicated. The vertical scale is the probability of emission of gamma ray photons, the leftmost curve indicates the spectrum of the total gamma radiation to which the tool is exposed and similarly the appropriately labelled three other curves indicate the potassium, uranium and thorium gamma rays to which the tool is exposed. Of course Figure 2 is for an idealized setting and does not take into account factors such as interaction of the emitted gamma rays with the formation surrounding the borehole, the borehole itself and the logging tool, nor does it take into account factors such as the influence of adjacent borehole depth levels on the one of interest at the time.

Referring to Figure 1, the tool electronics indicated at 10b receive the output of the photomultiplier in the scintillation detector indicated at 1 0a and perform known pulse amplitude analysis to divide it into the five energy windows indicated in Figure 2. In principle, the output of the scintillation detector for the time interval, e.g. six inches, is accumulated in each of the five energy windows, and the result is an energy windows log sample or component for the depth level n identifying the short depth interval. A sample or component of the energy windows log thus comprises five measurements, one for each respective one of the energy windows. Thus, sample W comprises measurements [W1,W2,W3,W4,W5]. The sequence of such measurements W, each for a respective successive borehole depth level, makes up the energy windows log.

The sample or component of the energy log for a particular depth level n in the borehole is designated W(n).

The energy windows log W for the borehole interval of interest is stored in storage 22, and is used in the remainder of Figure 1 for conversion into a log of selected gamma radiation emitting materials, such as thorium, uranium and potassium. The storage 22 may also be used to store tool response information and other geological information for the further conversion of energy windows log W into logs of the gamma ray emitters and absorbers in the borehole fluid. The conversion of the energy window log W into selected gamma radiation emitting formation materials logs and borehole fluid gamma ray absorber and emitter logs can be in real time in which case units 17, 18, and 22 serve only as buffer storage.Alternately, the conversion can be done by first storing the logs for the entire borehole depth interval of interest, or for a part of it, in one or more units 17, 18 and 22, and thereafter transmitting the log to another location for conversion into a materials, a borehole emitter, and a borehole absorber log. The filter generated at unit 24 for the given borehole depth level is supplied to a unit 26, which also receives the energy windows log and the tool response information from unit 22 and generates from its input a log of the formation materials of interest e.g. a Th,U,K concentrations log, and a log of the borehole fluid emitter and absorbers e.g. KCI and B, which affect the readings of energy windows log. A tangible representation of the logs can be temporarily stored in buffer storage 28 and more permanently in a unit 30.Unit 30 can include recording devices such as paper or film log recorders for producing log traces of the Th,U,K,KCI,B log. Filter updating unit 24 generates a respective filter for each depth level in the borehole on the basis of the energy windows log supplied to it from unit 22 and the material concentrations log and borehole fluid gamma ray absorber and emitter concentrations log generated in unit 26, and can additionally use previously generated log samples from buffer storage 28.

In a nonlimiting example of the first, simpler embodiment of the invention, the filter gain found in unit 24 for a given borehole depth n is the matrix M discussed in connection with expressions (2a) and (2b) weighted by a scalar k(n) which varies between zero and unity and is determined for a given borehole depth level n by the manner in which the total detected gamma radiation y changes from one depth level to another in the vicinity of level n. The exact manner in which w controls the filter in this example has been chosen on the basis of discoveries relating to the nature of the logging process, and an example which has been found to produce satisfactory results in practice is to base the weighting scalar k(n) for a particular depth level n on a factor designated C(n), which in turn is based on the following relationship between total gamma radiation y(n) detected at depth level n, total gamma radiation w(n- 1) detected at the preceding depth level n- 1, the factor C(n- 1) for the preceding depth level n- 1, and the constants a and g:

If, g is taken as 3, and the term in the absolute brackets when multiplied by 9 is greater than C(n-1), then a is given a value of .8. Otherwise, a = .125.

The weighting scalar k(n) can then be set as follows; k(n) = C(n) if.05 C(n) .6 k(n) = .05 if C(n) < 0.5 (15) k(n) = .6 if C(n) > .6 In this example of the first, simplified embodiment of the invention, in which K(n) = k(n)M and the product of the matrices M and H is unity, the filtering described in connection with expression (4) above can now be characterized by:: X(n) = [1 - k(n)] X(n-1) + k(n)MW(n) (16) It should be appreciated from the discussion in connection with expressions (14), (15), and (16), that at one extreme, when the total detected gamma radiation is stable or changes very slowly in the vicinity of the depth level of interest and thereby indicates a homogeneous zone in the borehole, the weighting scalar k(n) is at its low value of 0.05 and the new filtered estimate of the Th,U,K concentrations is based almost entirely on the filtered estimate for the previous borehole depth level.At the other extreme, when the total detected gamma radiation is changing rapidly in the vicinity of the borehole depth level of interest at the time, the weighting scalar k(n) is at its high value of 0.6 and the previous filtered estimate for the Th,U,K concentrations is de-emphasized in favor of the estimate based entirely on the current measurements of radiation in the five energy windows. In the intermediate range, the balance between the relative weights accorded to the previous filtered estimate of the Th,U,K concentrations and the radiation detected in the five energy windows shifts in favor of the latter with increasing change in the total detected gamma radiation in the vicinity of the borehole depth level of interest.

An exemplary process embodying the above example of the first, simpler embodiment of the invention is illustrated in Figure 3, and commences with steps 30 and 32 which sequentially provide the depth level samples of the five windows log samples W(n) and the total detected gamma radiation log samples ey(n), respectively. At step 34 a pointer n is set to the depth level of the bottom end of the borehole depth interval of interest, so as to start the process with the appropriate sample of the W(n) log, and at step 36 the depth index is set to the same level to extract the appropriate sample of the y(n) log.At step 38 the process finds the current value of the factor C(n), in accordance with the procedure discussed in connection with expression (14) above, using as an input the sample of the r(n) log pointed to by the current value of n and using, in this case, a value of one for the factor C(n-1). The factor C(n) output from step 38 is stored in step 40 as the factor C(n- 1) to be supplied back to step 38 for use in producing the next factor C(n). It is also supplied to step 42, where the weighting scalar k(n) is generated in accordance with the process discussed in connection with expression (15) above.The output of step 42 is supplied to step 44, which also receives the sample of the W(n) log pointed to by the current pointer n, and produces a filtered estimate of the Th,U,K concentrations for the depth level n in accordance with the process discussed in connection with expression (16) above. For this first run through steps 44, the process uses for X(n-1) an estimate for the Th,U,K concentrations for the depth level n(min) which is derived by applying the matrix M to the windows log sample for the depth level n(min). The output of step 44 is the filtered estimate for the Th,U,K concentrations for depth level n, and it is stored in step 46 for use in the next run through step 44.The output of step 44 also is stored, recorded and/or plotted in step 48, which can also receive and store, record and/or plot the estimates of the total detected gamma radiation w(n), which can be simply the sum of the five windows of the W(n) log, and the weighting scalar k(n). A test is made at step 50 to determine if the current depth level n is within the borehole depth interval of interest and, if that is the case, the index n is incremented at step 52, and the process returns to steps 44 and 38. Of course, this time in step 38 the factor C(n-1) provided by step 40 to step 38 is the previous output of step 38 and, similarly, the previous filtered estimate X(n- 1) which step 46 supplies to step 44 this time is the previous filtered estimate provided to step 46 by step 44.When step 50 indicates that the top of the borehole depth interval of interest has been reached, the process ends.

In a nonlimiting example of the second, more exacting embodiment of the invention, the filtering is again accomplished through the process discussed in connection with expression (4) above, but the filter for a particular depth level is derived through the more complex process discussed in connection with expression (5) above. The filter is different depending on whether the current depth level of interest is found to be in a homogeneous or a transition zone in the borehole, and the filtered X(n) estimates can be further filtered by fixed-lag smoothing.

An exemplary process in accordance with this second embodiment of the invention is illustrated in flowchart form in Figure 4, and commences at step 54 which sequentially provides the five energy windows log W(n), starting with the sample for the lowermost depth level n = 1 for the borehole interval of interest.

Step 54 further provides a starting value S(O) for the 3X3 matrix S, a sensitivity matrix H and starting values for the estimate X(O) for the filtered Th,U,K concentrations at depth level zero. Said starting values can be as follows:

104 0 0 s(o) = [1; o 104 0 0 0 104 X(O) = # 0 # At step 56 a vector A(0) is evaluated by a least-squares fit according to the relationship: W(k) = H A(0) y(k) + R(k) (17) fork=1,2 6 where A(O) is a vector of the form::

#1 #2 A3 W(k) designates the five-windows log samples for depth levels one through six, y(k) designates the total detected gamma radiation for depth levels one through six and R(k) designates an estimate of statistical variations in W(k) for depth levels one through six and is defined, for a given depth level n, by::

(W1)/2 0 0 0 0 0 (W2)/2 0 0 0 R= O O (W3)/2 0 0 (18) 0 O O (W4)/2 0 0 0 0 0 (W5)/2 where W1, W2, etc. are the measurements in the respective energy windows for the relevent depth level. To avoid divergence of the filter, the diagonal elements are all bounded below by some positive constant (e.g. 1).

At step 58 in Figure 4, the estimate Q(O) of the variances of the relevant geological noises found is a function of the total detected gamma radiation y(l ) for depth level one and the vector elements of the X(O) found at step 56, in accordance with the relationship:

#1 0 0 Q(0) = [y(1)]2 0 A22 o = [y(1)]2A(0) (19) 0 0 where the elements X1, A2 and #3 of the vector A(0) are for the 3X3 matrix A(O). At step, 60 the adaptive filter gain K(n) is found for the current depth level of interest as a function of the matrices S and Q for the previous depth level, the matrix R for the current depth level and the logging tool sensitivity matrix H and its transpose H', in accordance with the relationship discussed in connection with expression (5) above. For the first run through step 60, when n = 1, the matrix S is the starting value provided from step 54, the matrix 0 is provided by step 58 and the matrix R is derived as discussed in connection with expression (18) from the windows log sample for depth level one.At step 62 a filtered estimate X(n) is derived for the Th,U,K concentrations at the current depth level n as a function of the filtered estimate X(n -1) at the previous depth level, the adaptive filter gain K(n) found at step 60 for the same level n, the windows log sample W(n) for the same depth level, and the logging tool sensitivity matrix H, through a process of the type discussed in connection with expression (4) above. For the first run through step 62, when n = 1, the filtered estimate for X(O) drops out and X(n) is a function only of K(n) and W(n). The X(n) estimate from step 62 is stored at 64, for use as the X(n-1) filtered estimate in the next run through step 62.At step 66 an estimate is derived of the matrix S(n) as a function of the identity matrix I, the filter gain K(n) found at step 60, the logging tool sensitivity matrix H and the estimates for the matrices Sand Found for the previous depth level n-1, the relationship therebetween being: S(n) = [I - K(n)H] [S(n-1) + 0(n-1)] (20) For the first run through step 66, where n = 1, the estimate for the matrix S for the previous depth level is provided from step 54 and the estimate for the matrix Q for the previous depth level is provided from step 58.

At step 68 the output of step 66 is stored as the estimate S(n-1) for use in the next run through steps 60 and 66, and the process is now initialized to run sequentially through the remainder of the depth levels in the borehole depth interval of interest. The depth level index n is therefore incremented at step 70 and, if a test at step 72 determines that the new depth level is still within the borehole depth interval of interest, and step 74 determines that the investigated lithology zone is not homogeneous, step 76 finds the vector A(n) by evaluating the following relationship (21) for the vector A(n) by a least-squares fit method at the current value of the depth level index n and each of the values one through six for the index k:: W(n+k) - Hx(n) = HA(n) [y(n + k) - y(n)] + R(n+k) (21) fork= = where y(n) is the sum of the components of W(n) = HX(n). At step 76, the matrix O(n) is found for the current depth level n as a function of the elements of the vector y(n) found at step 76 and the difference between the total detected gamma radiation at depth levels n and n+1 in accordance with the relationship::

#1 0 0 Q(n) = [y(n i- 1) + 1)y(n)]2 O A22 0 # =(&gamma;(n + 1) - y(n))2 A(n) (22) 0 0 #3 where Al, A2 and A3 are the components of A(n), and the output of step 78 is stored at step 80 as the matrix 0(n-1 ) to be used in the next evaluation in step 60.Of course, those skilled in the art will appreciate that in order to avoid filter divergence the diagonal elements of Q(n) must all be bounded below by some positive constant. The process then starts again at step 60 and cycles until the test at step 72 determines that the top end of the borehole depth interval of interest has been reached, at which time the process can end. If, during a cycle, it is determined at step 74 that the zone of interest is homogeneous, steps 76,78 and 80 are bypassed, and step 75 sets the matrix O(n) for the next level equal to a given small predetermined matrix 0 used to track slow (Th,U,K) variations. Matrix O is then stored at step 80 as the matrix Q(n- 1) to be used in the next evaluation in step 60.

In accordance with the invention, the materials log samples X(n) can be further improved by fixed lag smoothing in which the estimate X(n) for the concentrations of Th,U,K at a given level n in the borehole becomes a further filtered sample X(n/n+N) which is determined by the sample X(n) and the samples X(n) for the next several feet of the borehole, e.g., for the next ten feet when samples are taken every six inches and N is 20.The relationship between a further filtered sample X(n/n+N) and the factors which determine it can be represented as:

# N k-1 # X(n/n+N) = X(n)+[S(n-1)+Q(n-1] # # # [I-K(n+j)H]' (23) k=1 j=O where N equals 30 has been found to produce satisfactory results in practicing one example of this aspect of the invention and where the quantity (E(n+k) is evaluated for each required depth level n in accordance with:: E(n) = H' [H S(n) H' + R(n)]- [W(n) - H X(n-1)] (24) In the further filtering process described in connection with expressions (23) and (24) above, the filtered sample X(n) is produced through a process such as at step 62 in Figure 4, the matrix S(n) is produced as in step 66 in Figure 4, 1 is the identity matrix, K(n+j) is produced for a given depth level n in accordance with a process as in step 60 in Figure 4, H is the logging tool sensitivity matrix and H' is its transpose, W(n) are the energy windows measurements for the depth level n, e.g. from step 54 in Figure 4, R(n) is the noise estimate produced by a process as discussed in connection with expression (18) a bove and X(n-l) is the filtered Th,U,K estimate for the depth level previous to depth level n.

As described above, the process connected with Figure 4 can be simplified where the estimate X(n) being evaluated is for a depth level which happens to be in a homogeneous portion of the borehole, in which the concentrations Th,U,K are stable or do not change rapidly. In a homogeneous zone, it can be expected that the geological noise Q(n) estimated in steps 76 and 78 in Figure 4 is very low. Indeed, it has been found that the invented process produces satisfactory result when Q(n) is set to Q in homogeneous portions of the borehole.Therefore, in accordance with another aspect of the invention, a test is made first to determine if the depth level of interest is likely to be in a homogeneous zone or in a transient zone, and subsequent processing as described in Figure 4 uses Q(n) = Q for all levels within a homogeneous zone and otherwise derives O(n) as discussed in connection with steps 74 and 76. A test to determine whether a depth level is in a homogeneous or in a transient zone, which has been found to produce satisfactory results in practicing this invention, is to check the manner in which the total detected gamma radiation y changes in the vicinity of the depth level n of interest.For example, a depth level n can be considered to be in a homogeneous zone if either of the following inequalities (26) is satisfied, where T1 is a threshold, e.g. 13, and T2 is another threshold, e.g. 4: 5 [(n + k) - k) - y(n - 1)2 / (n - 1)1 < T1 (25) k=O [y(n) - 4(n - 1)2/jl(n - 1) < T2 where y(n - 1) is the reconstruction of the gamma ray at level (n - 1) given by the filter.

The overall process using the second, more exacting embodiment of the invention, is illustrated in Figure 5, and commences with step 54 which provides sequentially the energy windows log samples W(n). Step 74 determines whether the current depth level n is in a homogeneous zone, by a test such as discussed in connection with expression (25) above. If the current depth level is not in a homogeneous zone, but in a transient one, step 84 finds the matrices Q(n- 1), R(n) and S(n- 1) in the manner discussed in connection with Figure 4. If the current depth level is in a homogeneous zone, step 86 finds the matrices R(n) and S(n) as discussed in connection with Figure 4, but assuming that the geological noise matrix Q(n- 1) is zero.The results of steps 84 and 86 are supplied to step 88, where the adaptive filter gain K(n) for the current depth level is found in the manner discussed in Figure 2. At step 90 the filter is applied as discussed in connection with Figure 4 to produce the filtered estimate X(n) for the current depth level, which is supplied to steps 84 and 86 to be used therein to find the next set of matrices. Fixed-lag smoothing estimates are produced in step 92, in a process as discussed in connection with expressions (23) and (24). At step 94, the process results are stored, recorded and/or plotted, e.g. by producing a tangible representation of the Th,U,K concentrations on the basis of the further filtered estimates X(n/n + N) and/or other process results such as the estimates log X(n), etc.

From the nonlimiting example of the third embodiment which is represented by the flowchart of Figure 6, those skilled in the art will recognize that the "environmental corrections" third embodiment of the invention is similar to the second exemplary embodiment. The important difference between the embodiments is that the third embodiment corrects the Th, U and K logs by accounting for the environmental effects of gamma ray emitters and absorbers in the borehole fluid, and the size of the borehole. Thus, instead of estimating a vector of dimension 3 (Th,U,K), a vector of at least dimension 5 (e.g. Th,U,KCI,B) must be estimated if at least one gamma ray emitter (in this case chosen as KCI) and at least one gamma ray absorber (in this case as barite (B)) are found in the borehole fluid. Additionally, the tool response (expression (9)), becomes a non-linear function of the unknowns. However, using the extended Kalman filtering principle, the estimation equation will be formally the same as for a standard linear Kalman filter such as that of the second embodiment. The only change is that the constant 5X3 matrix H must be replaced by a depth varying 5X5 matrix G(n). G(n) is defined as the matrix of partial derivatives of Hs(x)X + f(x)KCI with respect to Th,U,K,KCI and B evaluated at the preceding level by the filter as seen in expression (11), which accounts for the additional gamma ray emitter KCI in the mud as well as the gamma ray absorber.

Beyond supplying an estimated vector, (Y(n)) of dimension 5, and a depth varying sensitivity matrix (G(n)), the filter must be provided with a proper response equation model of the logging tool. Thus, as explained with reference to expressions 7 and 11, the borehole absorption coefficient x(n) which appears in G(n), is provided to account for the size of the borehole, while b, which also appears in G(n) accounts for the borehole fluid gamma ray absorber in the mud.

An exemplary process in accordance with this third embodiment of the invention is illustrated in flow-chart form in Figure 6. The process commences at step 154 which provides the same starting information as step 54 of the second embodiment of Figure 4 except that vector Y(O) of dimension 5 replaces X(O), S(O) is a 5X5 symmetric matrix which represents the knowledge about the first Th,U,K,KCi and B values prior to any measurement, and x(n) which is the borehole description coefficient is provided.Additionally, A(n), the 3X3 matrix defined in expression (22) is now the following 5X5 matrix:

A12 0 0 0 0 0 A22 0 0 0 0 0 A32 0 0 (13) 0 0 0 0 0 0 0 0 0 0 At step 156 the 3- vector A(O) is evaluated by a least squares fit according to a more complex relationship than that of step 56 of the second embodiment. Accordingly, the vector is a function the environmental effects which are introduced into the relationship by the f(x), KCI and HB(O) terms, and other terms which were discussed in conjunction with step 154 and the second embodiment.

Steps 158, 160, 162, et seq. parallel the steps of the second exemplary embodiment except that the 5X3 tool sensitivity matrix H and its transpose H' are replaced by a depth varying 5X5 matrix G(n) and its transpose G'(n). Likewise, the application of the smoothing steps of Figure 5 can be applied to the third exemplary embodiment, except that instead of finding the filtered estimate X(n) in step 90, the filtered estimate Y(n) of the five logs is found. Similarly in the fixed lag smoothing estimate step 92 and store/record/plot, Th,U,K estimate step 94, Y(n/n+N) is used so that the five variables (Th,U,K,B and KCI) will be smoothed and stored, recorded and plotted.

Those skilled in the art will appreciate that the third exemplary embodiment described above can be modified to account for different gamma ray emitters or absorbers in the borehole fluid. For example, if thorium is used in the borehole fluid, relationship (8) would be changed such that

f1(x) f2(x) f3(x) Th fluid f4(x) f5(x) would replace the potassium term. As a result, G(n) as seen in expression (11) would be changed. If thorium were used in addition to the potassium chloride in the borehole mud, and if barite was also in the mud, the provided method and system would suffice, except that G(n) would become a 5X6 matrix due to the six unknowns.Similarly, if one gamma ray emitter was in the mud, but the gamma ray absorber effected two of the energy windows instead of one, the six unknowns would require a 5X6 matrix. Clearly, the provided method and system can account for other combinations of gamma ray emitters and/or absorbers in the borehole mud and the inventor is not limited to those particularly cited.

For test purposes, the above-discussed first and second exemplary embodiments of the invention were applied both to energy windows logs derived from assumed subsurface distributions of thorium, uranium and potassium and to energy windows logs derived in actual boreholes. As an example, Figure 7a illustrates an assumed subsurface distribution of Th,U,K where the vertical dimension is depth in the borehole in feet and the horizontal scale of Th and U are in parts per million while that of K is in percent. An energy windows log was derived from the Th,U,K distributions of Figure 7a by applying thereto a logging tool sensitivity matrix H in accordance with the relationship W-HX and adding noise to simulate actual logging conditions.

The Th,U,K log of Figure 7b is that end result of applying the first exemplary embodiment of the invention to said simulated energy windows log, and the Th,U,K log of Figure 7c is the result of applying the second exemplary embodiment to the same simulated energy windows log. For comparison with known prior art, Figure 7d illustrates a Th,U,K log derived from the same simulated energy windows log in accordance with the prior art relationship X = MW and using a prior art four-second RC filter.

When the exemplary embodiments of the invention were applied to an energy windows log derived in an actual borehole, results such as those illustrated in Figures 8a, 8b, 9a and 9b are produced. The Th,U,K log in Figure 8a is the result of using the first exemplary embodiment of the invention discussed above and that of Figure 8b is the result of using the second exemplary embodiment. The Th,U,K log in Figure 9a is also the result of using the second exemplary embodiment of the invention while the Th,U,K,B,KCl(k), log of Figure 9b is the result of the third exemplary embodiment which makes environmental corrections.

In comparing the logs produced in Figures 9a and 9b, a marked improvement in the true values of formation Th,U,K can be observed. It is seen that the effect of the borehole KCI and B, and the borehole size effect had acted to suppress the readings of formation uranium. Likewise, in comparing the K readigs, the environmental corrected filter is seen to have reduced the formation K reading and provided an additional log of KCI in the mud. Finally, close comparison of the Th log reveals that the Th readings which are environmentally corrected are slightly higher than the second embodiment readings of Figure 9a. This is due to the borehole size which is greater than 8" as seen by the caliper log.

The process illustrated in Figure 3 as well as those illustrated in Figures 4,5 and 6 can be computer-implemented by arranging and programming a general purpose digital computer of a suitable size and configuration, such as a commercially available machine under the designation PDP 11/34 to carry out the steps discussed above. In the alternative, the illustrated processes can be implemented by means of a special purpose hardwired and/or firm-wired machine carrying out the discussed steps. The processes of Figures 3,4,5 and 6 can be carried out substantially in real time. It is clearthatthe process of Figure 3 is simpler and requires less processing time and equipment than that of Figures 4,5 and 6.On the other hand, it is believed that the process of Figures 4 and 5 produces superior results while the process of Figure 6 in conjunction with Figure 5 superior is yet. Accordingly, all are preferred embodiments of the invention, and which one is chosen for a particular implementation depends on whether minimizing processing speed and equipment needs is preferable to optimizing preceived quality of results in a given set of circumstances.

The estimates of the vector A(n) produced in step 76 of the second exemplary embodiment and step 176 of the third exemplary embodiment which are measures of the geological noise which influence the end result of the invented process, can integrate important geological knowledge about the variation in the real concentrations of Th,U,K with borehole depth. For example, the vector A(n) for a particular borehole depth level should always be such that each of the Th,U,K estimates remain positive. An additional item of geological knowledge for use in the invented process is that the Th,U,K logs are usually not anti-correlated.

Yet, additional items of geological information which are less important than the requirement that the relative contributions of Th,U,K in the production of total detected gamma radiation, are continuous functions of borehole depth, that the sequence of ratios Th/K usually presents a continuity pattern, and that the two additional ratios Th/U and U/K can present continuity patterns, e.g. in the case of the same shale interrupted by non-radioactive sandstone beds (or in the case of washouts).As another improvement, the tool sensitivity matrix H discussed in connection with the process of Figures 4 and 5 need not be the same for each depth level but can vary to account for geological knowledge of the borehole and the formation surrounding it at a given depth level so as to bring the Th,U,K estimates produced by the invented process yet closer to the probable true distributions of Th,U,K in the subsurface formations. This depth-varying option is incorporated in part in the third exemplary embodiment, as the tool response equation (9) takes into account the borehole size which may be depth-varying.

For further background explanation, attention is directed to the text at page 9, line 28 through page 31, line 18 of the European Patent Application No. EPO 81401249.8 filed July31, 1981,and published under No.

0070943, incorporated herein by reference.

Thus, in accordance with the invention, a log such as W(n) is derived of gamma radiation detected in selected energy windows by a logging tool, such as 10, passed through a selected borehole depth interval which extends through subsurface earth formations, and this energy windows log is converted into a log, such as X(n) or Y(n), of selected subsurface gamma radiation emitting materials such as Th,U,K, or both selected subsurface gamma radiation emitting materials and borehole gamma ray emitters and absorbers such as Th,U,K,B and KCI. The materials log is filtered by an adaptive filter, such as one discussed in connection with K(n), which is allowed to vary with borehole depth in accordance with selected changes with depth in detected gamma radiation and in a manner consistent with geological constraints.One nonlimiting example of such an adaptive filter was discussed in connection with Figure 3 and varies with changes with depth in the total detected gamma radiation and in a manner consistent with geological constraints as reflected in the choise of the filter characteristics, e.g. the choice of the filter gain k(n) characteristics, including the parameters on which the component C(n) is based and the manner in which previous estimates of Th,U,K are used in determining the current one of interest.In other nonlimiting examples, the filter is allowed to vary as discussed in connection with Figures 4,5 and 6 by taking into account an estimate, such as R(n), of the statistical variations in the windows log measurements, an estimate such as Q(n) of the geological noise and an estimate such as S(n) of the fluctuations in estimates of the materials log for previous borehole depth intervals. Additionally, the filter discussed in connection with Figure 6 is provided with a model which accounts for the true borehole size, and for the gamma ray emitters and absorbers in the borehole fluid. Moreover, the latter examples of filtering are also consistent with geological constraints, as reflected in the manner in which the estimates of statistical variations in the windows log measurements, geological noise and previous Th,U,K or, Th,U,K,B and KCI estimates are derived and as reflected in the manner in which previous filtered estimates of the Th,U,K or Th,U,K,B and KCI logs are used. In the second and third embodiments of a filter, a further smoothing based on a fixed lag, e.g. as discussed in connection with expressions (23) and (24), can be used to further improve the materials log. A tangible representation of the filtered logs of the subsurface materials is produced, and nonlimiting examples thereof are discussed in connection with Figures 7a, 7b, 8a, 8b and 9a and 9b.

While the invention has been described above with respect to particular preferred embodiments, it will be recognized by those skilled in the artthatthe invention is not limited to those particular embodiments but includes any variation or other embodiment thereof which is within the scope of the appended claims.

Claims (13)

1. Awell logging method comprising: deriving a log of gamma radiation detected in selected energy windows by a logging tool passed through a selected borehole depth interval containing borehole fluid having at least one of a gamma ray emitting substance and a substance which is a strong absorber of gamma rays, said borehole depth interval extending through subsurface earth formations; converting the energy windows log, by means of an adaptive filter based on a model of selected subsurface gamma radiation emitting materials, and said borehole fluid, said model being allowed to vary with respect to borehole depth in accordance with selected changes and with geological constraints, into a corrected log of the concentrations of said selected subsurface gamma radiation emitting materials along the selected borehole depth interval; and producing a representation of the filtered corrected log of said selected subsurface materials.

2. Awell logging method as in claim, further comprising: additionally converting said energy windows log by means of said adaptive filter into a log of the concentration of said borehole fluid gamma ray absorber; and producing a representation of the filtered log of said borehole fluid gamma ray absorber.

3. A well logging method as in claim 1, further comprising: additionally converting said energy window log by means of said adaptive filter into a log of the concentration of said borehole fluid gamma ray emitter; and producing a representation of the filtered log of said borehole fluid gamma ray emitter.

4. A well logging method as in claim 2, further comprising: additionally converting said energy window log by means of said adaptive filter into a log of the concentration of said borehole fluid gamma ray emitter; and producing a representation of the filtered log of said borehole fluid gamma ray emitter.

5. Awell logging method as in one of claims 1 to 4, wherein: said borehole fluid gamma ray emitter material contains at least one of the same materials of said selected subsurface gamma radiation emitting materials.

6. Awell logging method as in claim 5, wherein: said borehole fluid gamma ray absorbing material comprises at least barite.

7. Awell logging method as in any one of claims 1 to 14, wherein: said selected subsurface gamma radiation emitting materials include at least one of thorium, uranium, and potassium.

8. A well logging method as in claim 3, wherein: said selected subsurface gamma radiation emitting materials include at least one of thorium, uranium, and potassium.

9. A well logging method as in any one of claims 1 to 4, wherein: said selected energy windows comprises at least five energy windows.

10. A well logging method as in any one of claims 1 to 4, wherein: said adaptive filter which converts said energy windows log accounts for the effect of the size of the borehole on the derived log of gamma radiation.

11. Awell logging system comprising: means for deriving a log of gamma radiation detected in selected energy windows by a logging tool passed through a selected borehole interval containing borehole fluid having at least one of a gamma ray emitting substance and a substance which is a strong absorber of gamma rays, said borehole interval extending through subsurface earth formations; means for converting said energy windows log, by means of an adaptive filter based on a model of selected subsurface gamma radiation emitting materials, and borehole fluid, said model being allowed to vary with respect to borehole depth in accordance with selected changes and with geological constraints, into a corrected log of the concentrations of said selected subsurface gamma radiation emitting materials along the selected borehole interval; and means for producing representation of the filtered corrected log of said selected subsurface materials.

12. A well logging system as in claim 11, further comprising: additional means for converting said energy windows log, by means of said adaptive filter, into logs of the concentrations of said gamma ray emitting substance and said absorber of gamma rays.

13. Awell logging system as in claim 11 or 12, wherein: said adaptive model of said means for converting said energy windows log accounts for the effects of borehole size on said means for deriving a log of gamma radiation.