US 3457499 A Description (OCR text may contain errors) v5.1* "uhu QTY QR 344579499 July 22, 1969 D. R. TANGUY 3,457,499 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION 0F WELL LOGGING MEASUREMENTS Filed June 5, 1967 8 Sheets-Sheet l /56 /5e Y A A en/J f?. fav/yay INVENTOR IHM. ATTORNEY July 22, 1969 D. R. TANGUY 3,457,499 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF WELL LOGGING MEASUREMENTS fc5/7 OR C); en/J f?. Taf/'yay Lc/C INI/ENTOR BYmWZ W .TTORNE Y July 22, 1969 D. R. TANGUY 3,457,499 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF WELL LOGGING MEASUREMENTS BYQQQWQ AYTORNE Y .Fuy 22, 1969 D. R. TANGUY 3,457,499 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF WELL LOGGING MEASUREMENTS A Filed June 5, 1967 8 Sheets-Sheet 4 JITI'ORNEY July 22, 1969 o. R. TANGUY 3,457,499 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF g WELL LOGGING MEASUREMENTS Filed June 5, 1967 8 Sheets-Sheet 5 ATTORNEY `uly 22, 1969 D. R. TANGUY METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF WELL LOGGING MEASUREMENTS 8 Sheets-Sheet 6 Filed June 5, 1967 N/ENTOR Byw Y? 7e/WJ Tanguy ATTORNEY `uly 22, 1969 D. R. TANGUY WELL LOGGING MEASUREMENTS Filed June 5, 1967 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF 8 SheetsSheet 'f INI/ENTOR ATTORNEY July 22, 1969 D. n. TANGUY 3,457,499 METHODS AND APPARATUS FOR IMPROVING THE RESOLUTION OF WELL LOGGING MEASUREMENTS Filed June 5, 1967 8 Sheets-Sheet 8 en/J R Tanguy [NI/EN TOR Bygwmr. y United States Patent O METHODS AND APPARATUS FOR IMPROV- ING THE RESOLUTION F WELL LOGGING MEASUREMENTS Denis R. Tanguy, Houston, Tex., assignor to Schlumberger Technology Corporation, Houston, Tex., a corporation of Texas Filed June 5, 1967, Ser. No. 643,581 Int. Cl. G01v 3/00, 3/18 U.S. Cl. 324-1 30 Claims ABSTRACT OF THE DISCLOSURE This disclosure describes techniques for processing derived well logging signals indicative of an investigated subsurface characteristic to arrive at improved indications of the subsurface characteristic. This is accomplished, in one manner, by a computational process wherein each derived signal is combined with a computed signal representing an infinite series of `weighted derived signals to produce a new infinite series computed signal for subsequent combination with a later derived signal. Each infinite series computed signal is also combined with at least one derived signal to produce computed output signals for recording the computed value of the subsurface characteristic. Other disclosed manners of obtaining improved indications are to utilize the computed output signals to produce the inliinite series computed signals, or to produce a plurality of infinite series computed signals having different parameters, or some combination of the above. This invention relates to signal processing methods and apparatus for processing well logging measurement signals for providing improved indications of subsurface conditions or characteristics. In the logging of subsurface earth formations surrounding a borehole drilled into the earth, investigating apparatus is moved through the borehole and investigates the surrounding earth formations to provide an output signal which varies in accordance with variations of the investigated -characteristics of the adjoining earth formations. In electrical logging for example, the output signal varies in accordance with the electrical resistivity or conductivity of the subsurface earth formations. In any case, it is often desirable that the investigating apparatus respond to only a relatively limited portion of the formation material which is adjacent the apparatus at any given instant. For example, it is frequently desired that the vertical resolution of the investigating apparatus be sensitive to only a limited vertical interval of the adjoining earth formations. In this manner, earth formation beds can be more accurately investigated even under severe borehole conditions. When speaking of vertical resolution of an investigating apparatus, the vertical geometrical factor (hereinafter called V.F.G.) is frequently utilized to more accurately describe this vertical resolution. The V.G.F. of an electrical logging type investigating apparatus for example, can be defined as the relative response of the investigating apparatus as a function of relative borehole depth as the investigating apparatus passes from -oo to |oo through a thin conductive bed extending radially outward from the borehole to infinity and surrounded by beds of zero conductivity. To make it easier to use, the V.G.F. is usually normalized to 1. Thus +00 f Xda ice is made equal to l where X is the relative response and dz is a depth increment along the borehole axis. This same procedure can be used to find the V.G.F. if other formation characteristics than conductivity or its reciprocal resistivity are being investigated, i.e., if other than 1electrical logging type investigating apparatus is being utiized. However, many investigating apparatus respond to a greater vertical region than desired (i.e., they do not have the most desirable V.G.F.). One technique for correcting this is to provide additional transducer elements in the downhole investigating apparatus to compenstae for or to cancel the undesired portion of the response so that the effective vertical resolution of the apparatus is substantially improved. For example, in logging by electromagnetic principles, which is referred to as induction logging, socalled focusing coils are added to the downhole investigating apparatus to can-cel to a large extent the response of the apparatus to the so-called shoulder regions lying immediately above and below the desired vertical region of response of the investigating apparatus. However, other problems arise whenever additional transducer elements are added. One such problem is that more apparatus must be placed in the downhole investigating apparatus thus making the downhole investigating apparatus more complex and usually more expensive. Other problems concerning the quality of the measurement may also occur. For example, in induction logging as more coils are added to improve the vertical focusing, the depth of investigation of the apparatus in a horizontal or radial direction tends to decrease. Additionally, as more coils are added, the efficiency of the downhole investigating apparatus decreases, i.e. there is less received signal strength, thus increasing the problems of noise. Another way of improving the effective vertical resolution of the downhole investigating apparatus is by utilizing the signal processing or computing techniques set forth in U.S. Patent No. 3,166,709 granted to H. G. Doll on I an. 19, 1965. This Doll patent teaches the principle of temporarily storing or memorizing well logging signals obtained at various vertically spaced depth levels in the borehole. These stored signals are then combined in an appropriate manner to produce a resultant signal corresponding to the signal that would have been obtained with an investigating apparatus having better vertical resolution. This process is sometimes referred to as computed focusing. The resultant signal is a computed signal and the relative depth levels corresponding to the stored signals which are being combined at any given instant are called computing stations. These computing stations are defined relative to the investigating apparatus and therefore effectively move through the borehole as the investigating apparatus moves through the borehole. The relative depth level to which the resultant signal is referenced is called the center point or recording point of the investigating system. In following the teachings of the above-named Doll patent, it would sometimes be desirable to provide computing stations at a large number of measurement levels in the borehole such as in those cases where the total signal received by the investigating apparatus is made up of contributions from a relative great distance from the center point or recording point of the downhole investigating apparatus. For example, in some types of nduction logging investigating apparatus, the V.G.F. never quite reaches zero response for an appreciable distance in the downhole direction from the apparatus center or recording point. However to provide such computing stations, a relatively large capacity memory would be required to store the necessary number of well logging measurement signal samples. Another way of improving the Vertical resolution by signal processing techniques is the technique shown in copending application Ser. No. 605,424 by Nick A. Schuster, filed on Dec. 28, 1966. Among other things, this technique enables the use of a much larger number of computing stations for a memory system of given capacity. In a more general sense, it enables more sophisticated forms of signal processing to be performed with a relatively small memory system of convenient size for use at the well site. The present application describes another technique of a different nature to obtain further improvements in certain situations. It is an object of the invention therefore, to provide new and improved methods and apparatus for processing well logging measurement signals wherein more accurate measurements can be obtained. It is another object of the invention to provide new and improved well logging signal processing methods and apparatus for providing more accurate well logging measurements utilizing relatively simple and inexpensive signal processing apparatus. It is still another object of the present invention to provide new and improved well logging signal processing methods and apparatus for providing improved measurements of downhole earth formation characteristics with relatively small and inexpensive memory and computing devices. In accordance with one feature of the present invention apparatus for processing well logging signals comprises means for deriving signals representative of a characteristic of earth formations surrounding a borehole at different depth levels in the borehole and first combining means for combining each derived signal with at least one -other signal to provide first computed signals correlated in depth with the derived signals. The apparatus further comprises memory means for storing the first computed signals and means for reading out the first computed signals from the memory means at later times and supplying selected first computed signals to the first combining means to provide said at least one other signal. The apparatus further coinprises second combining means for combining each derived signal with at least a selected signal read out from the memory means to provide second computed signals representative of the characteristics of the surrounding earth formations. By so doing, a selected formation response portion (i.e., a selected portion of the V.G.F.) of each derived signal is cancelled out to leave sharp resolution second computed signals. In accordance with another feature of the present invention, apparatus for processing well logging signals comprises means for deriving signals representative of a characteristic of earth formations surrounding a borehole at different depth levels in the borehole and first combining means for combining each derived signal with at least one other signal to provide first computed signals which are more accurate representations of the characteristic of the surrounding earth formations. The apparatus further comprises second combining means for combining each rst computed signal with at least one other signal to provide second computed signals and memory means for storing the second computed signals. The apparatus further comprises means for reading out the second computed signals from the memory means and supplying selected ones of the second computed signals to the first and second combining means. Again, high resolution signals are produced `by this apparatus. In accordance with still another feature of the present invention, a method of processing well logging signals comprises deriving signals, having a given vertical geometrical factor, representative of a characteristic of earth formations surrounding a borehole at different depth levels in the borehole and combining each derived signal with at least one -other signal to provide first computed signals correlated in depth with the derived signals. The method further comprises storing the first computed signals and reading out the tirst computed signals at later times to be combined with each derived signal as said at least one other signal. The method further comprises combining each derived signal with at least a selected read out first computed signal having a given vertical geometrical factor (i.e., the tool which produces the signal has a given geometrical factor which, in effect, imparts this geometrical factor to the signal) to provide second computed signals, the vertical geometrical factor of said selected read out first computed signal cancelling an undesired portion of the derived signal vertical geometrical factor to provide each second computed signal with an improved vertical geometrical factor of improved vertical resolu'ion, and recording the second computed signals as a function of depth to provide a computed log of the formation characteristic. In accordance with yet another feature of the present invention, a method of processing well logging signals comprises deriving signals, having a given vertical geometrical factor, representative of a characteristic of earth formations surrounding a bore hole at different depth levels in the borehole and combining each derived signal with at least one other signal to provide first computed signals. The method further comprises combining each first computed signal `with at least one other singal to provide second computed signals having a given vertical geometrical factor, and storing the second computed signals. The method further comprises reading out the second computed signals at later times and using selected second computed signals for combination with each derived signal and each first computed signal to produce the first and second computed signals, the vertical geometrical factor of the second computed signals cancelling undesired portions of the vertical geometrical factor of the derived signals to provide the first computed signals with an improved vertical geometrical factor of improved vertical resolution, and recording the first computed signals as a function of depth to provide a computed log of the investigated characteristic. For a better understanding of the present invention, together with other and further objects thereof, reference is had to the following description taken in connection with the accompanying drawings, the scope of the invention being pointed out in the appended claims. Referring to the drawings: FIGURE 1 shows a downhole investigating apparatus disposed at different depth levels in a borehole with a graphical representation of the investigating apparatus V.G.F. at a plurality of the depth levels along with a schematic representation of signal processing apparatus, for purposes of explaining the background of the present invention; FIGURES 2a, 2b, 2c, 2d and 2e show graphical representations of V.G.F.s useful in understanding the theory of the present invention; FIGURE 3 shows an induction logging type investigating apparatus along with signal processing apparatus for performing the operation depicted in FIGURES 2a, 2b, 2c, 2d and 2e; FIGURES 4a and 4b show other V.G.F.s useful in explaining other features of the present invention; FIGURE 5 shows apparatus for performing the operation depicted in FIGURES 4a and 4b; FIGURES 6a and 6b show still other V.G,F.s useful in understanding other features of the present invention; FIGURE 7 shows apparatus for performing the operation depicted in FIGURES 6a and 6b; FIGURES 8a, 8b and 8c show still other V.G.F.s useful in understanding other features of the present invention; FIGURE 9 shows apparatus for performing the operation depicted in FIGURES 8a, 8b and 8c along with other embodiments of the present invention; and FIGURE shows another embodiment of the present invention. Referring to FIGURE 1, there is shown a downhole investigating apparatus 11 having a center or recording point O, located at a plurality of various depth positions in a borehole 12, designated P1, P2, P3, P4 PZ where the subscript z refers to the rst apparatus position from which a signal was derived. The depth levels or measure points corresponding to the positions P1, P2, etc. of the downhole investigating apparatus 11 are designated M1, M2, M3, M4 MZ respectively. The depth interval between measure points M1 and M2 is designated d1 and the depth interval between each successive measure point thereafter is designated d2. To the right of the borehole 12 there are shown the V.G.F's G1, G2, G3, G1 G2 corresponding to each of the apparatus positions P1, P2, P3, etc. The derived signals corresponding to each of the V.G.F.s G1, G2, etc. are designated S11, 81H11, Sn (d1+d2), Sn (d1+2112) Sn (dl+md2) respectively. The derived signals from the downhole investigating apparatus 11 are supplied to the surface of the earth through a conductor pair 13 which passes through an armored multiconductor cable (not shown) which also supports the downhole investigating apparatus 11 in the borehole `12. These derived signals are supplied to an amplifier 14 which provides the ground reference potential for the uphole signal processing apparatus. Amplier 14 could, for example, be a diterential amplier. The output signal Sn from amplifier 14 is written into a memory 15, which is considered to be an infinite memory moving to the right, at write-in contact 15a. The subscript n refers to the signal being presently derived, n-d, refers to the signal derived an interval d1 downhole, etc. Memory 15 has a plurality of read-out contacts designated 15b, 15e, 15d, 15e, 15f 15z. The memory 15 is driven by a shaft 16 in accordance with the movement of the cable in and out of the borehole by suitable means (not shown). Thus, the values written into the memory 15 at writein Contact 15a will move to the right in accordance with the movement of the downhole investigating apparatus 11 through the borehole. Located the interval d1 (corresponding to depth interval d1) from write-in contact 15a is a read-out contact 15b and located the interval d2 from read-out contact 15b is a read-out contact 15e. The remainder of the read-out contacts 15e, 15d, 15e, 151C, etc. are located at intervals of d2 from each other. All of these readout contacts are connected to a weighted adding network 17 to which also is supplied the derived signal Sn from the output of amplier 14. The output signal from weighted adding network 17, designated Cn, is supplied to a recorder 18 which is driven by the shaft 16 so as to provide a log of Cn versus depth. It can be seen that the signal derived when the investigating apparatus was in position P5 at measure point M5 has moved to read-out contact 15e when the investigating apparatus is in position P1, the signal derived at measure point M4 has moved to read-out contact 15d, etc. Thus, the signals supplied to weighted adding network 17 from the rea-out contacts 15a, 15b 15z are de- Signa-ted Sn, Sn-dla Sn-(d1+d2)a Sn(d1+2d2)s Sn-(d1+3d2) Sn (d1+ m+1)d2), respectively. It is the purpose of the FIGURE 1 apparatus to substantially improve the V.G.F. of the downhole investigating apparatus 11, i.e., to substantially improve the vertical resolution of the system. Looking now at FIGURE 2a, there is shown the V.G.F. G1 of the FIGURE 1 investigating apparatus 11. This V.G.F. G1 has an area A. FIGURE 2d shows the V.G.F. resulting from the computing process of FIGURE 1 corresponding to the computed signal Cn. That is, the computing signal Cn is deemed to represent the well logging measurements as if the downhole investigating apparatus had the V.G.F. of FIGURE 2d. Before proceeding with the discussion of how the FIG- URE 1 apparatus converted the V.G.F. G1 of FIGURE 2a to the V.G.F. of FIGURE 2d, it would be helpful to first discuss what a V.G.F. is. As defined earlier, the V.G.F. is the relative response of the investigating apparatus to a thin conductive bed extending radially to infinity and surrounded by nonconductive shoulder beds, as the investigating apparatus passes from -oo to +00 across the conductive bed. The resulting curve obtained represents the signal that would be indicated on a meter as the investigating apparatus transgresses the conductive bed. This meter reading plotted versus depth gives the V.G.F. curve. This V.G.F. has a vertical point which is designated the center or recording point and in this application, the center or recording point for any given V.G.F. will be designated by an arrow with the corresponding signal which that particular V.G.F. produces (e.g. Sn, 81H11, ctc.) The V.G.F. is fixed with respect to the downhole investigating apparatus and thus, in effect, moves through the borehole with the investigating apparatus. For normalization, the area under the V.G.F. curve must be equal to 1. Another point to be noted about V.G.F.s is that, if a signal is increased or reduced in magnitude, the V.G.F. which produced that signal can also be considered to be increased or reduced in magnitude by the same proportion. Turning now to FIGURE 2b, assume that the V.G.F. G2 corresponding to the signal 81H11 is reduced in magnitude from its original area A to an area B. (Note that the V.G.F.s derived from the downhole investigating apparatus for each depth level will have the shape of G1 and area A.) The new V.G.F. is represented in FIG- URE 2b by the V.G.F. G2, having an area B. This V.G.F. G2' is subtracted from V.F.G. G1 but is shown in an upright position to more clearly show how it subtracts from V.G.F. G1. The weighted signal corresponding to V.G.F. G2 is designated Sn d1. The V.G.F. resulting from the subtraction of the V.G.F. G2 from V.G.F. G1 is shown in FIGURE 2b as the dotted in V.G.F. Gs, having two component V.G.F.s G61 and Gc2 of area C and D respectively (D is the hatched line area). Looking at FIGURE 2c, this V.G.F. Gs is represented by the solid line V.G.F. Gs. The component V.G.F. GC2, of area D, of V.G.F. Gs is made-up of an infinite series of V.G.F.s G'3, G21, G5 Gz having areas E, F, G Z respectively, only V.G.F.s Gg, G21, and G'5 being shown. The V.G.F. G21 is shown as a dotted line curve to help distinguish it from V.G.F.s G3 and G5. These V.G.F.s G3, G21, etc. represent weighted versions of the V.G.F.s G3, G4, etc. respectively, which V.G.F.s G3, G4, etc. correspond to the stored derived well logging signals S (d1+d2), S1, (.11+2d2), 811411113112), etc. respectively. The signals corresponding to these weighted V.F.G.s are designated S (,d1+d2 S'n (dl+2d2), S11 (d1+3d2), etc. The/Se V.G.F.s Gg, G21, G5, etc. which are subtracted from the portion of V.G.F. Gs of area D, are also shown in an upright position to more clearly shown how they combine to subtract the V.G.F. GS. The resulting V.G.F., after subtracting G2, G3, etc. from the V.G.F. Gs, is shown in FIGURE 2d. The area A of V.G.F. G1 is made-up of the component areas B, C, and D. Thus, Since each of the V.G.F.s G1, G2, etc., were of area A, when the respective signals S11, 81H11, etc. were derived, it is clear that the amount each V.G.F. is reduced, is the ratio of its new area -to its original area A. Thus, as stated earlier, since 'a reduction of a signal produces an equal reduction in the V.G.F., each derived signal must be Weighted by the ratio of its new area to its original area A to provide the particular V.G.F.s desired. Thus, Writing Equation 3 for V.G.F. areas in terms of signals, is the signal that would result from the V.G.F. component, having an area C, of V.G.F. GS. This V.G.F. of area C is the one that remains after subtracting the V.G.F.s G2, G'3, etc. from V.G.F.-G1 and is the shape of the computed V.G.F. of the computed signal Cn. Likewise, since the V.G.F. of area D is made-up of the areas E+F+ -l-Z, Equation 4 can be written as: C A B where Equation 6 thus defines Co as the signal produced from a V.G.F. having the salme shape as the V.G.F. component G62, but having an area of magnitude A. (This will be explained in more detail later.) Since the area D is made-up of an innite series of V.G.F.s, Co will hereinafter be called an innite series computed signal. NOW, for normalization, the area of this computed V.G.F. must be equal in magnitude to the area A of the original V.G.F. G1. As stated earlier, the area A is normalized to one, i.e. 'fX dz=1. Thus, to normalize the computed signal to one, both sides of Equation 4 are divided by C. The A in Equation 4 can be dropped since it is equal to one Thus, the normalized Equation 4 can be written as: and the normalized Equation can be written as: Looking now at FIGURE 2e, there is shown the V.G.F.s of FIGURES 2a-2d after normalization. The original apparatus V.G.F. G1, now designated G1, has an area of l/C. The original V.G.F.s G2, G3, G4 GZ, now designated G2, G3, G4 G"Z, have areas of -B/C, -E/C, -F/C, -G/C Z/C respectively. The area of V.G.F. Gc2 (the hatched line portion) is -D/C. The final computed V.G.F., designated Gcb now has an area of A, A being equal to 1. (Le. it is now normalized to 1.) The signals corresponding to these V.G.F.s G'l, Gng, GIa, GIC. Of FIGURE 2e are The signals corresponding to the V.G.F.s Gcl and Gcg are Cn and respectively. Now, concerning how Equation 7 is solved by the FIGURE 1 apparatus, the signals Sn, Sn dl, etc. of Equation 7 `are supplied to weighted adding network 17 to be weighted by the respective Weights l/C, -B/C, -E/ C, etc. of Equation 7 to provide the new computed signal Cn for recordation by recorder 18. It can thus be seen that the computed V.G.F. of FIGURE 2d can be produced from the original apparatus V.G.F. of FIG- URE 2a by providing an infinite memory having an infinite number of read-out contacts for supplying an infinite number of signals to `an infinite number of weighting function circuits. Now referring to FIGURE 3, there is shown apparatus for solving Equation 7 with much less apparatus. In FIGURE 3, there is shown a downhole investigating apparatus 20 which comprises a central support member (not shown) which supports a coil array 21 `and a fiuid-tight housing 22 which contains the downhole electrical circuitry. The central support member is supported by a cable 23 which passes to the surface of the earth through the borehole 12. The coil array 21 comprises, in order from top to bottom, a first receiver coil Rh a second receiver coil -l-RZ, a third receiver coil -R3, and a transmitter coil -l-T. Suitably, the distance between R1 and -i-RZ could be approximately 30 inches, -l-R2 to R3 could be approximately 18 inches and R3 to T could be approximately 22 inches, for example. The number of turns for the coils -R1, +R2, R3 and T could be turns, 100 turns, 16 turns, and 100 turns respectively, for example. This coil array would approximately give the V.G.F. shown to the right of the coil array in FIGURE 3. It is to be understood that this coil array is only exemplary and any suitable coil array could be utilized. Furthermore, the present invention is not limited to induction logging tools and any well logging tool could be utilized, as for example, sonic or nuclear logging tools. Within `the fluid-tight housing 22, an oscillator 24 supplies a constant current to a transmitter coil T through a low value resistor 25. The signal received by the receiver coils are supplied to a phase-sensitive circuit 26 to which also is supplied the phase-reference signal taken across resistor 25. The phase-sensitive circuit 26 supplies the derived well logging signals to the surface of the earth via la conductor pair 27 which passes through the armored cable 23. These derived signals comprise a varying DC signal proportional to that portion of the signal induced into the receiver coils which is in-phase with the phasereference signal taken across resistor 25. These signals are therefore proportional to the conductivity of the adjoining earth formations. At the surface of the earth, the conductor pair 27 is supplied to the input of an amplifier 2S which supplies the ground reference potential for thel uphole circuitry. Amplifier 28 could thus be a differential amplifier, for example. The output signal Sn of amplifier 28 is supplied to the input of a weighting function circuit 34a having a weight of 1/C, of a weighted adding network 34, and to the input of a write amplifier 33, the output of which is supplied to a write-in contact 29a of a rotating memory 29. Rotating memory 29 could comprise any suitable memory device, such as for example, the magnetic memory shown in the above-mentioned Doll patent, or the capacitor memory shown in U.S. Patent No. 3,230,445 granted to W. J. Sloughter et al. on Jan. 18, 1966. In this application, the memories can be considered to be capacitor memories, and thus the write ampliers will have low output impedances to quickly charge or dischargeI the capacitors to the proper voltage. The read-out amplitiers will have high input impedances so as to not disturb the charge on the capacitors for later read out, if desired. Rotating memory 29 is considered to rotate in a counter-clockwise direction in accordance with the depth of the downhole investigating apparatus 20. This movement of the downhole investigating apparatus 20 is supplied to the rotating memory 29 by means of a rotating wheel 30 which rotates in accordance with the movement of cable 23. The wheel 30 transfers motion to a shaft 31 which causes the rotation of rotating memory 29, through a differential gear 43, and the recording medium of the recorder 32 in accordance with the movement of the downhole investigating apparatus 20. A shaft 43a is supplied to the other input of the differential gear 43. Located a counterclockwise interval d1 from write-1n contact 29a is a read-out contact 29b which is connected to the input of a read-out amplifier 36, whose output signal Smm is su-pplied to a weighted function circuit 34b having a weight of -B/C of weighted adding network 34. The output signal Sn dl from read-out amplifier 36 is also supplied to the input of a weighting function circuit 37 having a weight of p, of Weighted adding network 37. The output of weighted adding network 37, taken across a low value resistor 37C, is supplied through a single-throw switch 38 to a write amplifier 39, whose loutput designated COM., is supplied to a write-in contact 29C of memory 29. Write-in contact 29C is located a short counterclockwise interval from read-out contact 29C. Located a counterclockwise interval d2 from write-in contact 29C is another read-out contact 29d which is supplied to the input of a read-out amplifier 40, which supplies the output signal C0 to a weighting function circuit 34C having a weight -D/ C, of weighted adding network 34, and to a weighting function circuit 37b having a weight q, of weighted adding network 37. The output from weighted adding network 34, which comprises the outputs of weighting function circuits 34a, 34b, and 34e, taken across a low value resistorA 34d, issupplied to the input of a function forming circuit 41 which corrects for electrical skin effect phenomena. This function forming circuit 41 could be constructed in accordance with the teachings of U.S. Patent No. 3,226,633 granted to W. P. Schneider on Dec. 28, 1965. Alternatively, the skin effect correction scheme shown in U.S. Patent No. 3,230,445 granted to W. I. Sloughter on Jan. 18, 1966, could be utilized. The output signal from function forming circuit 41 is supplied through a single-throw switch 42 to the recorder 32 for recordation as a function of depth. While the details of Weighted adding networks 34 nd 37 have not been shown, it will be appreciated that they could comprise standardweighting circuits. For example, each weighting function'circuit could comprise'a suitable amplifier of the proper polarity and a high value resistor of desired weight'. By this means,the currents produced by each of the Weighting function circuits will be proportional to the respective weighted input signal, and these currents will sum across the low resistance resistor to produce a voltage proportional to the weighted input signals. Concerning how the FIGURE 3 apparatusperforms the operation depicted in FIGURES 2a-2e, the derived sig- `nal Sn applied to weighting function circuit 34a and written into memory 29 corresponds to the V.G.F. G1 in FIGURES 2a and 2b. After weighting, this derived signal Sn corresponds to the V.G.F.v G1 of FIGURE 2e, i.e. CSD- d1 The infinite series computed signal Co read out at read-out contact 29a', after weighting, corresponds to the V.G.F. Gc2 Of FIGURE 2e, i.e. The recording point for this V.G.F. Gc2, shown as the arrow C'., in FIGURE 2b or the arrow in FIGURE 2e, is located a depth interval d2 in the downhole direction from the recording point Sn d1 of V.G.F. G2. In FIGURE 3, it can be seen that the read-out derived signal Sn d1 is combined with the read-out computed signal C0 to produce the new computed signal Co+d2, which is immediately written into memory 29. (Note-After the write-in signal CUN, is stored -for a depth interval idg, this same signal is designated Co+d2 d2 or C0 the depth interval d2 later.) Thus, since the signal C0+d2 is written into memory 29 at, for all practical purposes, the same instant of time as the read-out derived signal S dl which, in part, produced it, the read-out computed signal Co is located the depth interval d2 from the read-Out derived signal SIHH. Thus, it can be seen that the computed signal Cn recorded in recorder 32 is equal to the sum of the signals Sn, Sn d and Co weighted by the weighting factors 1/C, -B/C, and -D/C respectively 0f weighted adding network 34 in accordance with Equation 8, In V.G.F. terms, this is saying that V.G.F. Gcg and G"2 are subtracted from V.G.F. G'1 to leave V.G.F. G'cl in FIGURE 2e. To start the FIGURE 3 apparatus at the. bottom of the borehole, it is necessary to first store signals in'all positions of the memory. To accomplish this, the investigating apparatus 20 is held stationary at the bottom of the borehole while supplying signals to the surfaceI of the earth. Memory 29 is rotated by turning shaft 43a by hand while reading the derived signal Sn into all positions of the memory 29. Switches 38 and 42 are opened during this initial operation. In this manner, the derived signal Sn is stored in all positions of the memory. (Remember that the signals stored in all positions of memory during the-operation discussed above are' normalized to l.) For memory 29 to have accurate readings in all positions of memory at this time, the assumption must be made that the earth formations at the bottom of the borehole are substantially homogeneous for the depth interval that the originalapparatus V.G.F. response is somewhat greater than zero. However, in the event that this condition does not exist, any error will be quickly eliminated. This can be seen by noting in FIGURE' 2b or 2e that the V.G.F.s diminish in area as the downhole investigating apparatus moves uphole, thus diminishing any error also. Now, to .initiate the logging operation, the switches 38 and 42 are closed, shaft 43a is no longer rotated, and the downhole investigating apparatus 20 begins moving uphole, To better understand how the infinite series computed signal Co is obtained, it would be desirable to follow several signals derived at several depth levels in the borehole through the apparatus of FIGURE 3 to see how the operation depicted in FIGURES 2b and 2c is performed. Thus, looking at FIGURES 1, 2e and 3, in conjunction, the signal derived at measure point M3 in FIGURE 1 was written into memory 29 .at write-in contact 29a of memory 29 and read out at read-out contact 29h for computation. (Each derived signal is, of course, combined with the read-out signals Sn d1 and Co as stated earlier, and this facet of the operation need not be repeated over again below.) When the investigating apparatus is at depth level or measure point M2, the signal derived at measure point M3 is read out yat read-out contact 291;, multiplied by the weighting factor p, and written back into memory 29. (Each signal read out at read-out point 29b is combined with the signals Sn and Co and this facet of the operation need not be repeated again below.) After the downhole investigating apparatus has moved an interval d2 to the measure point M1, the signal which was derived at measure point M3 (now called Sn(d1+d2) since the investigating apparatus has moved a depth interval drt-d2 uphole from the measure point M3) is read out at read-out contact 29d as a component pSn (d1+d2) of the infinite series computed signal C0. The V.G.F. G3 of FIGURE 2e corresponds to this component signal pS (d1+d2), after weighting in weighted adding net work 34 of FIGURE 3. When the investigating apparatus is at measure point M1, the signal derived at measure point M4, now designated Sn (d1+2d2) has been read out of memory 29 at read-out contact 29h, multiplied times p, written back into memory 29 at write-in contact 29e, read out at readout contact 29d as a portion of the infinite series computed signal CU, multiplied times q in weighted adding network 37 and written back into memory 29 at write-in contact point 29e. This signal is then, after a depth interval d2, read out again at read-out point 29e as the component pqSn (d1+2d2) of the innite series computed signal C0. This signal pqSn (d1+2d2), after weighting in weighted adding network 34, corresponds to the V.G.F. G4 of FIGURE 2e. The signal derived at measure point M5, tracing its past history, has been read out of memory 29 at readi +Pqm 1Sn-(d1+md2) (9) Now, setting p=E/D and q'=F /E and substituting these values for p and q into Equation 9, the new relationship yfor CD is: Now substituting Equation 10 into Equation 7, the expanded relationship -for Cn in terms of V.G.F. areas can be written as: Now comparing the weighting factors in Equation ll with the weighting factors in Equation 7, it can be seen that the weighting factors applied to the signals Sn, Sn d1, S (d1+d2), and Sn (d1+2d2) are exactly equal to the desired weighting factors in Equation 7. For the weights to be applied to the remainder of the signals S11-(dum), S11-(dimora) sn-rdlJfmd), Comparing the 12 weighting factors for these signals in Equation ll with the weighting factors in Equation 7, it is clear that: In terms of q, Equation 12 can be written as: G=Fq, H=Fq2 Z=Fqm2 (13) Now it can be seen that the areas G, H, etc, can be determined from Equation l2. In practice, in selecting the circuit parameters, a trial and error method may be utilized to substantially cancel undesired portions of the original apparatus V.G.F., including providing a plurality of noninnite series computed signals. It should be noted here that the weighting functions for Co must equal l ffor normalization. That is, in terms of p and q from Equation 9, must equal 1. By utilizing the V.G.F. areas given above for p and q, i.e. p==E/D and q=F/E, p and q will automatically be normalized. From the preceding, a general technique can be formulated for determining the values of the weighting functions and the location of read-out contacts from memory with respect to the Write-in contacts. To determine these factors, in connection with the innite series computed signal, it is necessary to first graphically locate the infinite series of V.G.F.s at the desired positions, spaced an equal distance apart, and with desired weights to cancel out the undesired portion of the original apparatus V.GLF. The interval between the recording points of these infinite series V.G.F.s determines the depth interval between the Write-in yand read-out contacts for the infinite series computed signals. (Le. 29C and 29d in FIGURE 3.) The depth interval between the recording point of the original apparatus V.G.F. and the recording point o'f the first V.G.F. (closest to the original apparatus V.G.F.) determines the depth interval between the write-in contact where the derived signal Sn is read into memory (if Sn is supplied directly to weighted adding network 34), 4and the read-out contact where the infinite series computed signal is read out of memory. The weight of the infinite series weighting function circuit to which the read-out derived signal (S11411 in FIGURE 3) is applied, is equal to the ratio of the area of the first V.G.F. of the infinite series to the total area of all of the V.G.F.s of the intinite series. The Weight of the weighting function circuit to which the read-out infinite series computed signal CD is applied, is equal to the ratio of the area of the second V.G.F. of the infinite series of V.G.F.s to the area of the first V.G.F. thereof. Thus, it can be seen that these rst two V.G.F.s of the infinite series determine the areas of the remainder of the infinite series V.G.F.s, as well as the depth interval between each successive V.G.F. For this reason, it may at times be desirable to utilize read-out derived signals not connected with the infinite series computed signal, like Sn d1 in FIGURE 3, for combination with the derived Signal Si, and the read-out iniinite series computed signal Co to produce the final computed signal Cn. As many of these nonininite series signals as desired may be used. Finally, the weighting functions of the weighted adding network 34 which produces the final computed signal Cn are determined in the same manner discussed in connection with Equation 8. Looking now at FIGURE 4a, there is shown a graphical example of cancelling out undesired portions of an original apparatus V.G.F. G6 by utilizing an intinite series cancellation without a noninfinite series computing station. The arrow designated Sn represents the recording point of the original apparatus V.G.F. G6 which produces the derived signal Sn. Located at intervals d3 apart in the downhole direction from the arrow designated Sn, are a plurality of V.G.F.s designated G7, G8, G9, etc. extending to infinity. The signal designation Snnd, Sn 2d3, S 3d3 Sn md3 correspond to the weighted signals corresponding to these V.G.F.s G7, G8, etc. The areas D, E, F Z are represented by the hatched line portion of the V.G.F. G6 and have an area D. (The designations A, B, C, etc. are the same in FIGURE 4a as in some of the other figures, but this does not necessarily means that they are equal thereto.) After subtracting the hatched line portion of area D from the original V.G.F. G6, the V.G.F. GCS having an area C remains. This final computed V.G.F. is shown in FIGURE 4b. (Note-The subtracted V.G.F.s G7, G8, etc. are reversed in polarity in FIGURE 4a to more clearly show how they subtract from the V.G.F. G6.) Now looking at FIGURE 5, there is shown apparatus for performing the operation depicted in FIGURES 4a and 4b. The derived signal from the surface amplifier (like amplifier 28 of FIGURE 3) is ASupplied to a Weighting function circuit 49b having a weight of l/C, of a weighted adding network 49 and to a weighting function circuit 45a having a weight j, of a weighted adding network 45. The output from weighted adding network 45, taken across a low value resistor 45e, is supplied through a suitable write amplifier 46 to a write in contact 47a of a suitable memory 47, similar to the memory 29 of FIGURE 3. Memory 47 is considered to rotate in a clockwise direction in accordance with depth, which depth function is supplied from a shaft 48 as in the FIGURE 3 apparatus. Located a clockwise interval d3 from write in contact 47a is a read-out contact 47b which supplies the read-out computed signal C to a weighting function circuit 45b having a weight k, of weighted adding network 45, and to a weighting function circuit 49a having a weight -B/ C, of weighted adding network 49. The output signal Cn from weighted adding network 49 is supplied to a suitable recorder 50 driven by shaft 51 in accordance with depth as in the FIGURE 3 apparatus. To determine the parameters of the FIGURE 5 apparatus, the procedure set forth above can be utilized. Since there is no readout derived signals to be combined with Sn and Co to produce Cn in FIGURES 4a and 4b, the derived signal Sn need not be stored in memory. Thus, the derived signal Sn is combined with the read-out infinite series computed signal Co to produce the new infinite series computed signal CONS. Thus, in accordance with the technique discussed earlier, the interval d3 between the recording points of the original apparatus V.G.F. G6 and the first infinite series V .G.F. determines the interval between the write in and read-out contacts 47a and 47b. To obtain the values of the weighting functions for the infinite series computed signal of FIGURES 4a, 4b and 5, the same procedure discussed above is utilized. The weight to be applied to the derived signal Sn is determined bythe ratio of the area of the first infinite series V.G.F. G, to the areaof all of the infinite series of V.G.F.s. Thus, j=B/D. The weight to be applied to the read-out computed signal C(J is the ratio of the area E of and 3. That is, the ,weight to be applied to the infinite 'l The equation for the computed signal Cn for the FIG- URE 5 apparatus is: 14) where The values for j and k could be inserted in Equation 15 to write Equation 15 in terms of V.G.F. areas. Again must equal one for normalization which automatically occurs by using the above technique for selecting the infinite series weights j and k. The FIGURE 5 apparatus is started at the bottom of the borehole in the same manner as the FIGURE 3 apparatus. Now referring to FIGURES 6a and 6b, there is shown another feature of the present invention. It may happen that the infinite series cancellation of undesired portions of the original apparatus V.G.F., or infinite series cancellation in combination with noninfinite series cancellation, as shown above, will not completely cancel all undesired portions of the original apparatus V.G.F. Such a case is shown in FIGURES 6a and 6b where the desired final computed V.G.F. is shown in FIGURE 6b. The solid line V.G.F. of FIGURE 6a represents the final computed V.G.F. produced from the infinite series cancellation or infinite series plus noninfinite series cancellation discussed above. The signal corresponding to this solid line V.G.F. of FIGURE 6a is the term designated C, its recording point being the location of the arrow designated Cn. This solid line V.G.F. of FIGURE 6a has two component V.G.F.s G03 and Gc.; of areas C and B respectively. To provide the final computed V.G.F. of FIGURE 6b, it can be seen that the component V.G.F. Gc.; must be cancelled out. In accordance with the teachings of the above mentioned copending Schuster application, the signal Cn corresponding to the nal computed V.G.F. of FIGURE 6b is stored in memory and subsequently read out to cancel the undesired component V.G.F. GM. This read-out final computed V.G.F. is represented by the dotted line V.G.F. G05 in FIGURE 6a, which is shown in its proper polarity (positive). The signal corresponding to this V.G.F. G is designated Cn1 d4, its recording point being a depth interval d4 from the arrow Cn in FIGURE 6a. Now referring to FIGURE 7, there is shown apparatus for performing the operation depicted in FIGURES 6a and 6b. In FIGURE 7, the derived signal SIl from the downhole investigating apparatus (not shown) is supplied via the conductor pair 53 to an amplifier 54, which supplies the ground reference potential inthe same manner as amplifier 27 in FIGURE 3. The output of amplifier 54 supplies the referenced derived signal Sn to a computing circuit 55 which is constructed similar to the computing circuit enclosed by the dotted line box 55 in FIGURE 3. The output signal Cn from this computing circuit, corresponding to the solid line V.G.F. of FIG URE 6a, is supplied to a weighting function circuit 56a having a weight l/ C, of a weighted adding network 56. The output signal Cm from weighted adding network 56, taken across a low value resistor 56C, is supplied through a write amplifier 58 to a write in contact 57a of a rotating memory 57 which rotates in a counterclockwise direction. The signal Cm is also supplied to a suitable recorder (not shown) for a recordation as a function of depth, in the same manner as in the FIGURE 3 apparatus. Located a counterclockwise interval d4 from the write in point 57a is a read-out point 57b which'supplies the read-out computed signal Cm d4 through a suitable read-out amplifier 59 to a weighting function circuit 56b having a weight of -l-B/C of weighted adding network 56. Looking at FIGURES 6a, 6b and 7 in conjunction, the solid line V.G.F. of FIGURE 6a corresponds to the output signal Cn from computing circuit 55. The output signal C111 from weighted adding network 56 corresponds to the final computed V.G.F. in FIGURE 6b. This signal C111 is written into memory 57 at write-in point 57a, and read out an interval d4 later at read-out point 57b to be combined with the signal Cn in weighted adding net- Work 56 so as to cancel out the undesired V.G.F. portion G64 of the V.G.F. corresponding to the signal Cn, thus leaving the V.G.F. of FIGURE 6b. This computed signal C111 is recorded in recorder 32 in the same manner as before. Assuming that the computed signal Cn is already normalized to 1 (i.e. B+C=1), the weights to be applied to the signals C11 and C111 114 are -1-1/ C and +B/C respectively. It is to be understood that other computed signals could be read out of memory 57 at other read-out contacts (other depth levels) if required. The Weighting functions for these additional signals would be iD/C, iE/C, etc. where D, E, etc. are the areas of the V.G.F.s corresponding to the other read-out computed signals. Referring now to FIGURES 8a, 8b and 8c, there are shown graphical representations of other V.G.F.s in accordance with other features of the present invention. In FIGURE 8a, there is shown an original apparatus V.G.F. G11 having an area A (the letter symbols used in connection with this embodiment do not necessarily have the same magnitudes as those used in other embodiments). There is also Shown in FIGURE 8a a noninfinite series V.G.F. G12 of area B and an infinite series of V.G.Fs G13, G14, G15, etc. having areas of E, F, H, etc. respectively. All of these V.G.F.s G12, G13, G11, G15, etc. have the same shape but not magnitude. The combined areas of all of these V.G.F.s of the infinite series are represented by the hatched line area D. Considering the center point of each of these V.G.F.s G12, G13, etc. to be the peak thereof, the arrows emanating from the peaks of each of these V.G.F.s designate the recording points thereof. The signal designations C11 11S, C11 (d8+651, Cn (68+265) @114118+61651 represents the signals produced by each of these V.G.F.s. (Again, the prime designates the fact that these are weighted signals corresponding to the weighted V.G.F.s of FIGURE 8a.) The depth interval between Sn and Cn 118 is d8 and between each of the V.G.F.s of the infinite series of V.G.F.s IS d5. As inthe preceding embodiments, the arrow emanating from the center point of the first V.G.F. G13 of the infinite series of V.G.F.s also designates the recording point of the infinite series computed signal corresponding to the hatched line area D, and is designated Coz. After subtracting this hatched line area D and the V.G.F. G12 of area B from the area A of the original V.G.F. G11, the resulting V.G.F. is shown in FIGURE 8b as the solid line V.G.F. having an uphole portion G65 of area C and a downhole portion G66 of area R. Since this solid line V.G.F. is produced by the subtraction of the areas B and D from the area A in FIGURE 8a, corresponding to the subtraction of Co2 and C 8 from S11, the signal designation for this solid line V.G.F. of FIGURE 8b is Sn-(C'62-i-C'n 8), whose recording point will be the same as that of the derived signal Sn. Since the V.G.F. portion G65 is the desired final computed V.G.F. shape, the portion G66 must be cancelled out. To accomplish this, another infinite series of V.G.F.s, different from the series represented by the area D in FIGURE 8a, is utilized. This second infinite series of V.G.F.s are the dotted line V.G.F.s G16, G11, G13 whose recording points are a depth interval d6 apart, having weights of j, k, l, etc., in FIGURE 8b. The hatched line portion of the V.G.F. portion G66 of area R represents the total area of this second infinite series of V.G.F.s The depth interval between the recording point of the original apparatus V.G.F. G11(Sn) and the recording point of the first V.G.F. G16(C11 117) of this second infinite series of V.G.F.s is d1. The signals corresponding to each of these V.G.F.s of the second infinite series of V.G.F.s are designated The recording point of the rst V.G.F. G16 of the second infinite series of V.G.F.s also designates the recording point of the hatched line V.G.F. portion of area R corresponding to the signal designated C63. After subtracting out the hatched line V.G.F. portion of area R, the V.G.F. of FIGURE Sc remains. This is the final computed V.G.F. whose recording point is designated by the arrow emanating from the peak thereof. The signal produced from this final computed V.G.F. is designated Cn. Now, in retrospect,.it can be seen that the V.G.F.s in the noninfinite series V.G.F. and both of the infinite series of V.G.F.s that were utilized to cancel out the undesired portions of the original apparatus V.G.F. G11, are made up of individual V.G.F.s having the same shape -and vertical borehole axis extent, though not necessarily magnitude, as the final computed V.G.F. of FIGURE 8c. Thus, as in the FIGURE 1 situation, the computed signals Cn could be stored in a memory of infinite extent or length and read out and weighted in accordance with the weights and intervalsbetween readout stations as represented in FIGURES 8a and 8b. Again, the V.G.F. which subtract from original V.G.F. G11 are shown of opposite polarity to more clearly show how they subtract from G11. Now referring to FIGURE 9, there is shown apparatus for performing the operation depicted in FIGURES 8a-8c wherein relatively short memories and a minimum of apparatus need be utilized in accordance with the present invention. The derived signal Sn from amplifier 28 is supplied to a weighting function circuit 60a of a weighted adding network 60. The output signal Cn from weighted adding network 60, taken across a low value resistor 60a, is supplied through a suitable write amplifier 61 to a write in contract 62a of a suitable memory 62 and to a suitable recorder (not shown) for recordation as a function of depth. Memory 62 is driven in a counterclockwise direction by a shaft 63a which is coupled through a suitable gear 63 from a differential gear (not shown) like the one in FIGURE 3. Located a counterclockwise interval l1-d6 from write-in contact 62a is a read-out contact 62b which supplies the read-out computed signal Cn 6,+66 representative of the investigated characteristic an interval d1-d6 downhole from the present depth position of the downhole investigating apparatus, through a suitable read-out amplifier 65 to a weighting function circuit 66a of weight w of a weighted adding network 66. The output from weighted adding network 66, taken across a low value resistor 66e, is supplied through a suitable write amplifier 67 and single-throw switch 67a to a write-in contact 62C, of memory 62, located a short clockwise interval from read-out contact 62h. Located a clockwise interval d6 from write-in contact 62C is a read-out contact 62d, which supplies the read-out infinite series computed signal C03 to a weighting function circuit 66b of weight v, of weighted adding network 66 and to a weighting function circuit 60b, having a weight of -R/C, of the weighted adding network 60. The output signal Cn from weighted adding network 60 is also supplied through a write amplifier 72 to a write-in contact a of a rotating memory 70, which is driven in a counterclockwise direction by a shaft 63b from a suitable differential gear. Located a counterclockwise interval d6 from Write-in contact 70a is a read-out contact 70b which supplies the read-out computed signal C 68 to a weighting function circuit 60d, of weight nB/ C, of weighted adding network 60, and to a weighting function circuit 69a, of weight x, of a weighted adding network 69. The output signal C62165 of weighted adding network 69, taken across a low value resistor 69e, is written in to writein contact 70C of memory 70 via a read-in amplifier 71 and single-throw switch 71a. Located a counterclockwise interval d from write-in contact 70e is a read-out contact 70a' which reads out the infinite's'eries computed signal Co2 to a read-out amplifier 72. The output of read-out amplifier 72 is supplied to a weighting function circuit 60e, of weight -D/G; of weighted adding network 60, and to a weighting function circuit 69b of weight y, of Weighted adding network 69. Before proceeding with the operation of the apparatus of FIGURE 9, it would be desirable to first determine the values of the various weighting function circuits of FIG- URE 9 by looking at the V.G.F.s of FIGURES Sai-8c. First, taking the weighting functions of the weighted adding network 60 which provides the final computed signal C11, it is first noted that the area R of the hatched line portion of FIGURE 8b is the same in area asthe. nonhatched line portion of the original apparatus V.G.F. G11 from the peak of V.G.F. G11 to infinity in the downhole direction. Thus, since the area A is equal to the sum of p the areas B-l-C-l-D-i-R, it can be seen that :A -B-D -R Since the V.G.F. G11 is considered to be normalized, i.e., A=1, this relationship becomes C=1B-D-R. Now, for normalization of the final computed V.G.F., the above relationship is divided by C to give the weights l/ C, -B/ C, -D/C, and -R/ C to be applied to the signals Sn, Cn ds, Co2, and C03 to which these areas A, B, D, and R correspond. Now, to determine the weights x and y in accordance with the previously discussed procedure, the ratio of the area E of the first V.G.F. G13 of the first infinite series to 1 the total area D of all of the V.G.F.s of this first infinite series gives the weight for the weighting function x to termined in accordance with the prior procedure by the 1 ratio of the area I of the first V.G.F. G16 of the second infinite seriesl to the total area R of all of the V.G.F.s `of the second infinite series (i.e., u=]/R). 'The value of the weighting function v to which the read-out signal C03 is weighted by, is determined in accordance with the prior 1 procedure by vtaking the ratio vof the area K of the second V.G.F. G17 to the area I of the first V.G.F. G16 of the second infinite series, i.e., v=K/]. y' f Now, concerning how the apparatus of FIGURE 9 performs the operation depicted in FIGURES SLL-8c, the derived signal S,n which is supplied to the weighting -function circuit 60a corresponds to the V.G.F. YG11 of area A in FIGURE 8a. Concerning the discussion of the v'remainder of the operation of the FIGURE 9A apparatus in connection with the FIGURES 8a-8c V.G.F.s, it is to `be 'understood that the signals stored in memories 6 2 and '70 are normalized signals, that is, weighted adding networks 60, 66'and 69 provide normalized computed signals.' The original appa-ratus yV.G.F. G11 in FIGURE 8a is' nor- The final computed signal C11, having the V.G.F. shape of FIGURE 8c is stored in memory 70 until the downhole investigating apparatus has moved an interval d8, at which time it is read out `as the computed signal C2148 to be combined with the read-out infinite series computed signal C02 in weighted adding network 69 to produce the new infinite series computed signal C01+115 which is .stored in memory 70. After a depth interval d5, the read-out innite series computed signal Co2 (Note.- After the interval d5, the write-in signal C02 d5 becomes C2+d5 115 or C02) is combined with the new derived signal Sn, the second infinite series computed signal C03, and the read-out computed signal C1148 in weighted adding network 60 to produce the new computed4 signal Cn. This first infinite series computed signal C02 proportionally corresponds to the hatched line V.G.F. of area D in FIGURE 8a. Concerning the second infinite series computed signal C03, the final computed signal Cn is stored in memory 62 until the downhole investigating 'apparatus has traveled a depth interval (1T-d6, 'at which time it is read out and combined with the read-Out second infinite series computed signal CO3 to producek the new second infinite series computed signal C3+d6. This new signal is then written back into memory 62 until the downhole investigating apparatus has moved uphole a depth interval d6, at which time it is read out as the Lsecond infinite series computed signal CO3 'and combined in weighted adding network 60 with Sn, 01H18 and CO2 to produce the new computed signal Cn.-The proportional V.G.F. corresponding to the second infinite series computed signal C03, after weighting, is the hatched line V.G.F. of `area R in FIGURE 8b. Thus, it can be seen how the V.G.F,s of areas B, D, and R cancel out undesired portions of the original apparatus V.G.F. G11 to produce the final computed V.G.F. of FIGURE 8c. The equation for the computed signal Cn is therefore: and Thr-,apparatus of FIGURE appreduces Ibother the infinite series computed signals C01y and C03 in the same lgeneral manner as the Aapparatus of FIGURE 3 provides generating each of the infinitelseries They final computed malized, but the remainder of the V.G.F.s shown in signals Cn and corresponding V.G.F.s forvjeachl'of the various depth levels couldlbe' traced in the same manner as in the FIGURES 12a-2a and 3, to show how both of the inrnite series ofpFIGURES Sa'and 8b are produced. Since this has already beendone in connection with FIG- URES 2`a-2eand 3, it need not be repeated in connection with FIGURES 8a-'-8c and'9'. Additionally, the FIGURE 9 'apparatus could be initiated at the bottom of the borehole in the same manner as in the FIGURE 3 apparatus, by opening switches 67a and 71a' and rotating the memories by hand while supplying Sn to the surface signal processing apparatus. It can thus be seen that in` 'accordance with the teachings of the present invention, there can be a plurality of 19 infinite series and noninfinite series computed signals utilized. Furthermore, these infinite series of V.G.F.s can be started at any depth interval from the present depth level of the downhole investigating apparatus. Additionally, any number of infinite series or noninnite series computed signals could be utilized, as desired. Additionally, a combination of infinite series computed signals derived from both computed signals and derived signals could be utilized (i.e. the combination of the principles of FIGURES 2x1-2e and 3 v'and FIGURES 8a- 8c and 9). This is represented by the dotted lines in FIGURE 9 coupling the derived signal Sn to the write amplifier 61 or to the write amplifier 72, the dotted xs indicating that the computed signal Qn would not be supplied to write amplifier 61 or write amplifier 72. It is also to be understood that a plurality of infinite series computed signals obtained from the derived signal Sn could be utilized. This could be carried out by supplying the derived signal Sn, instead of the computed signal Cn, to both write lamplifiers 61 and 72. Obviously, in these alternative situations, the circuit parameters would be different from those obtained in accordance with the V.G.F. of FIGURES Sai-8c, but nevertheless, these circuit parameters could be obtained in accordance with the teachings of the present invention. It may happen that the original apparatus V.G.F. does not have the most desirable original appartaus V.G.F. to which to apply the teachings of the present invention. In this event, the original 'apparatus V.G.F. could be prepared for the signal processing technique of the present invention. This preparing apparatus could utilize for example, the computing process disclosed in the abovenamed Dol-l patent, the computing process disclosed in the copending Schuster application, or any other signal processing technique. This may take the form of applying the derived signal Sn to the computing apparatus for preparing the original apparatus V.G.F. and then applying the normalized output signal from this preparing type computing apparatus to the apparatus constructed in accordance with the present invention. In addition to the above examples, there will occur to one of ordinary skill in the art many other possibilities of using infinite series computed signals to provide more desirable V.G.F.s. For example, a given V.G.F. may have Y an oscillatory Ifunction, having positive and negative excursions, and having reduced magnitudes approaching depth infinity (like a damping function). In accordance with the teachings of the present invention, an infinite series computed signal could be produced to substantially cancel this oscillatory V.G.F. Taking the FIGURE 3 apparatus as an example, the weighting function q would be negative and the weighting function p would be positive or negative depending on the polarity of the first V.G.F. portion of the oscillatory V.G.F. It is to be understood that the weighting factors of the various weighting function circuits could be shifted around in a desired manner to arrive at the same result. For example, the normalizing factor could be provided y y ,in the weightingv function network that provides the' final example, in the FIGURES 4 and 5 embodiment, if the l weighting function circuits 45a, 45h, 49b and 49a are assigned the weights 1, a, '(l-l-a), and -b, the equation for Cn can be written as: and combining Equations 19 and 20 and rearranging: (21) Equation 21 is satisfied only if: b "iwz (22) a could now be computed for a given depth interval d3. Additionally, the depth interval d3 and a could both be varied to arrive at the most desirable computed V.G.F. Considering the embodiment shown in FIGURES 8a- Sc and 9, it should also be pointed out that a single memory could be utilized in place of the two memories 62 and 70 shown in FIGURE 9. To illustrate this, refer to FIGURE 10 where there is shown a functional block diagram of this operation. In FIGURE 10, the derived signalSn is written into a rotating memory at a writein contact 80a. Memory 80 has read-out contacts 80b, 80e and 80d, and a write-in contact 80e, read-out contact 80b being located an interval d8 from write-in contact 80a, read-out contact 80C located an interval d8 from write-in contact 80e, and read-out contact 80d located an interval dg' from read-out contact 80e. The signals Sn ds, C04 and CO5 are supplied from read-out contacts 80b, 80e and 80d respectively to the weighting functions l, a, and respectively of an infinite series weighted adding network 81. The resulting computed signal C06 is written into memory 80 at write-in contact 80e and supplied to a weighted adding network 82, where it is weighted by the factor -b. The derived signal Sn is weighted by the factor (l-i-a) in weighted adding network 82 which provides the final computed signal Cn. The relationship for Cn is thus: l y Cn':(1'l-)Sn'bco6 (23) where Co6:Sn-dg"laCo4-i'co5 (24) Writing the equation for Cn in terms of derived signals in the same manner as done earlier: 'This infinite series of Equation 25 can mathematically be made to fit a given original apparatus V.G.F. to provide a final computed V.G.F. as in the earlier embodiments. Additionally, a or could be negative to produce yan infinite series of ardifferent nature. It is noted that the last term of Equation 25, i.e. the a and terms could be neglected for many cases since a times would usually be much less than one 1 Additionally, if a'capacitor type memory is utilized in the various embodiments, it may be desirable to read out thevderived signal Sn from memory for combination with theinfinite series computed signals to produce the final computed signal Cn rather than supplying Sn directly to the weighted adding network. This is because the signals read out from memory in this case (capacitor memory) are in the form of pulses and a continuous derived signal Sn applied to the weighted adding network may produce erroneous results.lThis,-of course, would cause a depth shift of the entire operation. l l While there have been described what are at present considered to be preferred embodiments of this invention, it will be obvious to those skilled in the art that various changes and modifications lmay be made therein without departing from the invention, and it is, therefore, intended to cover all such changes and modifications as fall within the true spirit and scope of the invention, What is claimed is: 1. Apparatus for processing well logging signals, com prising: (a) means for deriving signals representative of a characteristic of earth formations surrounding a borehole at different depth levels in the borehole, each of said derived signals being representative of the characteristic in a given portion of a formation; (b) rst combining means for combining each derived signal with at least one other signal to provide first computed signals correlated in depth with the derived signals; (c) nemory means for storing the first computed signa s; (d) means for reading out the first computed signals from the memory means at later times and supplying selected first computed signals to the first combining means to provide said at least one other signal, said selected first computed signals corresponding to previously investigated depth levels; and (e) second combining means for combining each derived signal with at least one signal read out from the memory means to provide second computed signals representative of the characteristic of the surrounding earth formations, said read-out signals operating to cancel a selected portion of the vertical formation response of each derived signal so that the second computed signals will have a sharper vertical formation response than do the derived signals. 2. The apparatus of claim 1 wherein the combining means for combining each derived signal Sn with the read-out first computed signal Cn to obtain the new first computed signal Co d, is combined in accordance with the relationship: where g and h are weighting functions of positive or negative polarity and Co represents an infinite series of weighted signals derived at depth levels extending back to the depth level at which a signal Was initially derived. 3. The apparatus of claim 2 wherein the infinite series of weighted signals is an infinite power series, Co being expressed by the relationship: Co=gS.n-d'l'ghSn-Zdl'gh2Sn-3dl +ghm 1Snmd where Sn d, Sn 2d, etc., are the signals derived at the different depth levels and Sn md is the first derived signal. 4. The apparatus of claim 3 wherein the means for providing second computed signals combines each derived signal Sn with the signal Co read out from the memory means to obtain each second computed signal C11 in accordance with the relationship: where X and Y are weighting functions of positive or negative polarity. 5. The apparatus of claim 4 wherein the means for deriving signals includes: (l) downhole investigating means for investigating the surrounding earth formations and generating signals indicative of the investigated characteristic as the downhole investigating apparatus moves through the borehole; and y (2) means for supplying the signals to the surface of the earth. 6. The apparatus of claim 5 and further including recorder means having a recording medium driven in` accordance with the movement of the downhole investigating apparatus through the borehole and responsive to the second computed signals Cn for providing a log of the computed values of the investigated characteristic as a function of depth. 7. The apparatus of claim 1 and further including: (l) means for storing the derived signals; and (2) means for reading out the stored derived signals at later times and supplying said read-out derived signals to the secondcombining means to the second computed signals. 8. The apparatus of claim 7 wherein the means for providing the second computed signals combines each derived signal Sn with each yfirst computed signal Co and one read-out derived signal Sn e to produce each second computed signal Cn in accordance with the relationship: where X, Y, and Z are weighting functions of positive or negative polarity. 9. The apparatus of claim 7 wherein the means for providing the second computed signals combines each derived signal Sn with each first computed signal Co and a plurality of read out derived signals Sn e Sn e to produce each second computed signal Cn in accordance with the relationship: where X, Y, Z Z are weighting functions of positive or negative polarity. 10. The apparatus of claim 7 wherein the combining means for combining each derived signal Sn with the read-out rst computed signal Co to obtain the new first computed signal C d, combines these signals in accordance with the relationship: where g and h are weighing functions of positive or negative polarity and Co represents an infinite series of Weighted signals derived at depth levels extending back to the depth level at which the first signal was derived. 11. The apparatus of claim 10 wherein the infinite series of weighted signals is an infinite power series, Co being expressed by the power series: where Sn (d+d) S (d+md) are the signals derived at the different depth levels and S md represents the first derived signal. 12. The apparatus of claim 1 wherein at least two of the first computed signals are read out of the memory means to be combined with each derived signal. 13. Apparatus for processing Well logging signals, comprising: (a) means for deriving signals representative of a `characteristic of the earth formations surrounding a borehole at different depth levels in the borehole, each of said derived signals being representative of the characteristic in a given portion of a formation; (b) memory means for storing the derived signals; (c) means for reading out the stored derived signals at later times; (d) first combining means for combining each readout derived signal with at least one other signal to provide iirstcomputed signals correlated in depth with the derived signals; (e) means for writing each first computed signal back into the memory element of the memory means from which the particular read-out derived signal which produced said first computed signal -Was stored; (f) means for reading out the first computed signals from the memory means and supplying selected first produce computed signals to the first combining means as 14. Apparatus for processing well logging signals, com `prising: (a) means for deriving signals representative of a characteristic of earth formations surrounding a borehole at different depth levels in the borehole, each of said derived signals being representative of the characteristic in a given portion of a formation; (b) iirst combining means for combining each derived signal with at least one other signal to provide rst computed signals correlated in depth with the derived signals and which rst computed signals are representative of the characteristic of the surrounding earth formations; (c) second combining means for combining each first computed signal with at least one other signal to provide second computed signals correlated in depth with the derived signals; (d) memory means for storing the second computed signals; and (e) means for reading out the second computed signals from the memory means and supplying selected ones of the second computed signals to the first and second combining means whereby the read-out cornputed signals supplied to the iirst combining means will operate to cancel out a selected portion of the formation response of the derived signals. 15. The apparatus of claim 14 and further including means responsive to the first computed signals for recording the first computed signals to provide a log of the computed characteristic of the surrounding earth formations. 16. The apparatus of claim 15 wherein the first combining means combines each derived signal Sn with a read-out second computed signal C to obtain each first Computed signal Cn in accordance with the relationship: where g and hare weighting functions of positive or negative polarity and Co is an infinite series of weighted first computed signals representing the formation characteristic at depth levels extending back to the rst investigated depth level. 17. The apparatus of claim 16 wherein the second combining means combines each lirst computed signal with a selected read-out second computed signal Co to produce each new second computed signal Co d in accordance with the relationship: where s and t are weighting functions of positive or negative polarity. 18. The apparatus of claim 17 wherein the innite series of weighted rst computed signals is an infinite power series, Co being expressed by the power series: where Cn d, Cn 2d Cn md are the rst computed signals representing the computed formation characteristic at depth levels extending back to the rst investigated depth level. 19. The apparatus of claim 1 and further including: (1) third combining means for combining each derived signal with at least one other signal to produce third computed signals correlated in depth with the derived signals; (2) means for storing the third computed signals; and (3) means for reading out the third computed signals at later times for supplying one of said at least one other signals to the second and third combining means. 20. The apparatus of claim 14 and further including: 1) third combining means for combining each first computed signal with at least one other signal to produce third computed signals correlated in depth with the derived signals; (3) means for reading out the third computed signals 24 at later times for supplying one of said at least one other signals to the rst and third combining means. 21. The apparatus of claim 1 and further including: (l) third combining means for combining each second computed signal With at least one other signal t0 produce third computed signals correlated in depth with the derived signals; (2) means for storing the third computed signals; and (3) means for reading out the third computed signals at later times for supplying one of Said at least one other signals to the second and third combining means. 22. The apparatus of claim 14 wherein at least two second computed signals are read out of the memory means and supplied to the second combining means for combination with each first computed signal. 23. A method of processing well logging signals, comprising: (a) deriving signals from an exploring device having a given vertical geometrical factor, said derived signals being representative of a characteristic of earth formations surrounding a borehole at dilferent depth levels in the borehole; (b) combining each derived signal with at least one other signal to provide first computed signals correlated in depth with the derived signals; (c) storing the rst computed signals; (d) reading out the rst computed signals at later times for combination with each derived signal as said at least one other signal, said read-out first computed signals corresponding to previously investigated depth levels; (e) combining each derived signal with at least a selected read-out first computed signal corresponding to a given vertical geometrical factor to provide second computed signals, the vertical geometrical factor corresponding to said selected read-out first computed signal cancelling an undesired portion of the derived signal vertical geometrical factor to provide each second computed signal with a corresponding improved vertical geometrical factor of improved vertical resolution; and (f) recording the second computed signals as a function or depth to provide a computed log of the formation characteristic. 24. The method of claim 23 and further including: (l) combining each derived signal with at least one other signal to' provide third computed signals which correspond to a given vertical geometrical factor and which are correlated in depth with the derived signals; (2) storing the third computed signals; and (3) reading out the third computed signals at later times for use as said at least one other signal which is combined with each derived signal to produce the third computed signals, and using said read-out third computed signals for combination with the derived signals and the first computed signals to produce the second computed signals, the vertical geometrical factors corresponding to the first and third computed signals cancelling undesired portioins of the vertical geometrical factor correspondnig to the derived signals to provide each second computed signal with a corresponding improved vertical geometrical factor of improved vertical resolution. 25. The method of claim 23 and further including: (l) combining each second computed signal with at least one other signal to produce third computed signals corresponding to a given vertical geometrical factor and which are correlated in depth with the derived signals; (2) storing the third computed signals; and (3) reading out the third computed signals at later times for use as said at least one other signal which 1s combined with each second computed signal to Patent Citations
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