NOISE SUBTRACTION FILTER

Abstract: A filter (36) for use in filtering noise from cyclical signals have a data component and a noise component in which a predetermined number of the cyclical signals are averaged to produce an average signature signal (76). The average signature signal (76) is updated each cycle (74) to produce a current updated average signature signal, and the current cyclical signals and the current updated average signals are substracted (68) from one another to remove the noise component and produce a residual signal (72) which contains the data component. The time frames of the current cyclical signals and the current updated average signals are adjusted (78) to be equal so as to enable point by point subtraction. As an additional feature, the updating of the average signature combines a portion of the last average pump signature with a portion of the last residual signal (74).

Description: NOISE SUBTRACTION FILTER Field of the Invention This invention relates to methods and apparatus for filtering noise signals that occur on a periodic basis. The invention is particularly suitable for use in filtering pump noise in telemetry systems in whicn data is transmitted in the form of pressure pulses through the fluid that is employed in drilling a well. In well drilling the oscillating component of the pump pressure signal that is generated by the pump or pumps is often much larger than the pulses that are telemetered through the well drilling fluid, and hence it is essential that the pump noise be removed so that the telemetered pulses can be recognized and detected. The Prior Art The prior art arrangements for filtering pump noise include frequency responsive electric networks, and subtraction circuitry in v/hich pump noise- is largely cancelled out by subtracting a preceding pump noise signal from a current pump noise signal. In order for a frequency responsive electric network to function satisfactorily the frequencies of the pump noise signals must be significantly different -ψJi E __ OMPI W V IPO " SUBSTITUTE: SHEET ^ATIO from the frequencies of the telemetered pulse signals. Hence, such filters are satisfactory only when the frequency characteristics of the telemetered data pulse signals are different from the frequency characteristics of the pump noise signals. Subtraction circuitry in which a preceding pump noise signal is subtracted from a current pump noise signal has been limited to the use of a single pump because the noise signals of plural pumps interact and beat with one another to produce combined signals which change with time. Summary of the Invention The aforesaid difficulties are overcome in the present invention by continuously developing and up¬ dating an "average pump signature" over a certain number of pump cycles so that the average pump signature is representative of the pressure signals that are produced by the pump during a predetermined interval of time, e.g. one pump cycle. The time scale of the average pump sig¬ nature is continuously compared witn the time scale of the current pump noise signal, and if necessary, the average pump signature s compressed or expanded in time by linear interpolation to correspond with the time scal of the current pump noise signal. The resultant average pump signature is then subtracted from the current pres¬ sure noise signal to leave a "residual" signal which contains the telemetered data pulses. The updating of the average pump signature combines a portion of the last average pump signature witn a portion of the last residual signal. The data pulses have little effect upon the average pump signature since that signature is obtained by averaging over several pum cycles and hence the probability of several data pulses occurring in synchronism with the pump pressure signals is very low. This method and apparatus functions satis¬ factorily when plural pumps (such as three) are used simultaneously because the pump noise signals are repre¬ sented by a sum of the average pump signatures. The invention may be carried out by programming a computer or by circuit hardware. Brief Description of the Drawings Fig. 1 illustrates one form of a pulse code for producing pressure pulses that may be employed in tele¬ metering data from the interior of a well to the surface; Fig. 2 illustrates " how encoded pressure pulses may be processed at the surface to provide a read-out of tne parameters that are measured downnole; Fig. 3 illustrates four of the signals that are produced by the apparatus of this invention; Fig. 4 illustrates the sequence of operations during data acquisition while operating with one pump; Fig. 5 illustrates the sequence of operations during the subtraction procedure while operating with one pump; Fig. 6 illustrates the sequence of operations during data acquisition while operating with multiple pumps; Fig. 7 illustrates the sequence of operations during the subtraction procedure while operating with multiple pumps; Fig. 8 shows circuit nardware that may be employed to carry out the steps of Figs. 4 and 5 with a single ump; and Fig. 9 snows circuit hardware that may be employed to carry out the steps of Figs. 6 and 7 with multiple pumps. Q\*.Π A. wniirrue Description of the Preferred Embodiments Pulse Encoding Copending application Serial No. 405,063 discloses and claims methods and apparatus .for encoding and synchronizing data in a pulse telemetry system. Fig. 1 illustrates one of the encoding arrangements that is disclosed in that application. A pulse is con¬ sidered to be a drop in pressure for a fixed period of time (e.g. 0.5 second) followed by one second of normal pressure. Synchronization pulses are produced at the beginning of each synchronization interval. The time intervals between the successive data pulses (Dl, D2, D3) in a sync interval provides an analog measurement of the data parameters that are to be telemetered to the surface, and three data words may be produced during each synchronization interval. Redundant pulses (Rl, R2) are provided midway in time betweeen adjacent pairs of data pulses. The redun¬ dant pulses provide a means for discriminating between data pulses and noise pulses. Thus, data pulses can be considered to be data pulses (Dl, D2, D3) oni ' y if a redundant pulse exists midway in time between adjacent pairs of data pulses. Each sync interval is a sub-frame of information, and a selected number of sub-frames (e.g. 11) comprise a frame which constitutes one complete set of data. During certain sub-frames a particular pattern of frame identification pulses is produced and telemetered to the surface to enable the apparatus at the surface to identify the sequence of data transmission. Processing the Encoded Data Fig. 2 illustrates one arrangement for processing the encoded data. The drilling rig includes the usual rotary table 10, kelly 12, swivel 14, traveling block 16, mud pumps 18, mud pit 20, and a drill string made up of drill pipe sections 22 secured to the lower end of the kelly 12 and to the upper end of a drill collar 24 and terminating in the drill bit 26. The downhole pulse encoding apparatus and a valve for producing negative pressure pulses in the drilling fluid may be located in a drill collar 28 locate above the drill bit 26. A pressure transducer 30 is coupled to the conduit for the drilling fluid and it senses the negative pres¬ sure pulses that are produced downhole. The mud pumps 18 produce pressure signals that have certain characteristics which constitute noise with respect to the data pulses. A strobe generator 32 produces strobe signals that represent the time required for each cycle of each mud pump. The signals from tne pressure transducer 30 and tne strobe generator 32 are applied to an input module 34 where the pressure signals are passed througn a low-pass filter and then are averaged in pairs and the average is stored 50 or 100 times per second in a ouffer until required by the filter module 36. The filter module 36 is the subject of this inventio It serves to remove or reduce the noise signals produced by the mud pumps 18. The output of the filter 36 is applied to a detector 38 which employs a matched fiiter to enhance the detecta- bility of the encoded pulses. The pulse signature used in the matched filter is a first order approximation to a rectangular pulse v/hich h been high-pass filtered at a frequency corresponding to l/(4*pulse width) hz. The use of a high-pass filter allows a simple level detector to be used for pulse identification. "Ideal" mud pulse: t = υulse width Actual matched filter pulse signature: Output from matched filter: The lowest sharp peak to the best match between actual psi- pulse and filter signature. seconds A high speed FFT convolution technique is used to implement the matched filter convolution. In operation, the convolution is performed approximately once every 20 seconds whenever data is made available by the filter module 36. The output of the matched filter is stored in a "Detection Buffer" which can hold data for more than one complete sub-frame. (If the sub-frame is 60 seconds long, tne buffer is set up to- hold data for a 64-second interval. ) A simple level detection scheme is performed on tne (overlapping) 64-second intervals. (The detection level TE SHEET is a user-controlled parameter.) Pulse position (time) is assigned at the pulse minimum; pulse height and width are also determined. The decoded pulses are stored in a "Pulse Table" for use by the decoder module 40. If pulse width does not fit witnin certain predefined limits, then the pulse is considered to be "noise" and discarded. Sub-frame sync pulses are found by a search of invar iant pulses of one-minute periods over the last three minutes. When these pulses are found, the detection buffer is shifted in time to ensure that the start of the sub-frame will be located at the start of the buffer. The time of the sync pulse is recorded for use by tne decoder module 40. The first time a downhole Tool starts up downhole, a search for frame ident pulses is enabled within the detector module 38 before the sub-frame sync pulses are identified. This enables the apparatus to synchronize on the first sub-frame that is transmitted from downhole. The output of the detector 38 is applied to a decode 4ϋ which identifies tne pulses and calculates the values. This module operates once every sub-frame. Every time the detection buffer is filled, the decoder module 40 uses the information within the Pulse Table set-up by the detector module 38 to identify pulse types. Sync pulses are first identified by their position in time. Frame ident pulses are then searched for, agai at predefined time positions. All pulses are allowed a small error in time setup as a user setpoint called "Pulse Position Variance" (typically 0.1 second). All remaining pulses are searcned ' to identify the "groups of three equally spaced pulses" which identify data -and redundant pulses. Once the pulses are identified sub-frame numbers and data values can be calculated and supplied to tne output buffer 42 via the Decoder Buffer. The output buffer 42 transmits tne data within the decoder 40 to a computer 46 or a printer 44 for setting forth the data parameters that are transmitted to the surface. The Pump Noise Subtraction Filter Fig. 3A illustrates the pump strobe signals when on pump is operating. Each strobe signal is produced at th time of one pump cycle. Fig. 3B illustrates the pump pressure signals when one pump is operating. These signals are much larger than -the data pulses, and hence the pump noise signals must be removed or reduced in order to recognize and detect the data pulses. Fig. 3C illustrates an "average pump signature" 50 that is obtained over a certain number of pump cycles. It .is shown inverted with respect to tne pressure signal of Fig. 3B to illustrate the subtraction process. The currently updated average pump signature of Fig. 3C is subtracted from eacn cycle of the pump pressure signals of Fig. 3B to expose a residual signal constituti the data signals, as illustrated in Fig. 3D. There are two processes running simultaneously durin tne pump noise filter operation. The first is tne data - acquisition, shown m Figure 4 (this is the i.nput module 34 of Figure 2); the second is the subtraction process, snown in Figure 5 (this is trie filter module 36 of Figure 2). In a computer base-d process the acquisition process will typically operate on "interrupts" generated by an external clock, with the subtraction process being the "main line" program. Fig. 4 shows pressure data sampled at 100 times per second being stored into a. input buffer. The current pressure data is transferred periodically to the current pressure buffer. Every time the leading edge of a Pump Strobe signal is recognized an entry is made in the Strobe Table. The pump noise subtraction process of Fig. 5 starts every time a new Pump Strobe entry is made in the Pump Strobe Table. Since the pump speed can vary with time, the period of one cycle will change and therefore the total number of samples in one cycle will change. The current pump signature 50 may require to be compressed or expanded to match the latest pump period. The pump signature 52 illustrates the circumstance where the current pump signature is expanded so that the time base 54 is equal to the time of the current pump cycle. After this process there will be the same number of samples in the Pump Signature as there are in the current pump cycle. The output of the pump noise subtraction filter is the "residual" 56 which is the difference between the pump pressure signals of the latest pump cycle and the current average pump signature. The Pump Signature is -updated by adding a rraction of the residual (known as the Weighting factor) to a fraction of the current signature. (Typically i/15 and 14/15 respectively. ) This produces a new average pump signature 58. As the portions of the fractions are cnanged the filter can be made to distribute -its "weight" over many cycles (and reduce the effect of any noise, including data pulses, on the signature) or fewer cycles, to make the signature more responsive' to changes in pump signature. The Strobe Table and Pressure Buffer are next reset to maJe space for new data. When the filter is started (from scratch) the averag Pump Signature is assumed to be zero for all points in th cycle. Normal operation of the filter will cause the signature to gradually take on the characteristics of the • 5 actual pump signature. .For a weighting factor of W (0 < W < 1) the Calcu¬ lated Pulse Signature will be the following if the last Dump cycle was cycle "i" : 10 Signature= (Residual of Pump Cycle(i))+ ^(Residual of Cycle(i-l)) +W 3 (Residual of Cycle (i-2))+... ' Figs. 6 and 7 show the changes required to operate 15 the model using multiple pumps (simultaneously). Fig. 6 shows that the Pump Strobe Table must now identify the pump number as well as the time of arrival of the Pump Strobe signal. Fig. 7 shows that the subtraction process must wait 20 until a pump strobe signal has been obtained from each operating mud pump. The "predicted" pressure is the sum of all the signatures of the operating pumps, taking into account the relative pnase position of each pump. The residual pressure is now the difference between 5 the current pressure data and the predicted pressure. As before, the residual pressure is the desired output from the filter. The signatures are updated as before except that only i/(total pumps operating) of the residual is assigned 0 to each signature. • The Strobe Table and Pressure Buffer are reset to end the process. The algorithm for tne pump noise subtraction filter described above is set forth in detail in Appendix I 5 hereto. SUBSTITUTE SHE BAD Fig. 8 illustrates how the input module 34 and filter 36 for removing pump noise can be implemented for one pump with circuit hardware. Signals from the pressure transducer 30 are applied through a bandpass filter 60 to an analog-to-digital converter 62 where the pressure signals are sampled at 100 cycles per second. The pressure signals are averaged in pairs and the average is stored 50 times a second in a current pressure buffer 64. The current pressure buffer 64 accepts data from the analog-to-digital converter 62 during the interval of time between successive pump strobe signals (Fig. 3A). A certain number of memory locations for data words in the current pressure buffer 64 are filled with the digital data when the pump strobe signals are one second apart. However, the pump speed can vary with time, and tne period of one pump cycle will change. Therefore the number of samples in one pump cycle will change. The current pressure buffer 64 will accept up to five seconds of digital data, so as to encompass all practical pump speeds. The pump strobe signals of Fig. 3A are produced by the strobe generator 32 and applied to a strobe table register 66 whicn enters the successive strobe times. The register '66 is coupled to a microprocessor 67 which controls the sequence of operations. The microprocessor 67 controls the transfer of data from the buffer 64 and the transfer of signatures from buffers 74 and 76. One subtraction process- is initiated each time that a new entry is made in tne strobe table register 66. Upon the occurrence of a new entry in the strobe table- register 66, the data in the current pressure buffer 64 and the current average pump signature are shifted to the subtractor circuit 68 wnich subtracts one from tne other to produce at its output 70 the residual signal of Fig. 3D. The residual signal is stored in a residual buffer 72 until it is called for by the detector 38. The average pump signature is obtained by averaging tne pressure signals that are produced over a selected number of the current pump cycles in an update pump signa ture averaging buffer 74. Preferably, the average pump signature is also updated periodically by the addition of a fraction of the current residual signal in the residual buffer 72 to a fraction of the current average pump signature. The fraction of the current residual signal that is added to the current average pump signature is called the "weighti factor". The proportions of the fractions can.be cnanged to acnieve particular results. For example, a large number of pump cycles may be employed in developing a signature wherein the effect of any noise, including mud pulses, is reduced. If fewer pump cycles are employed in developing the signature, the average pump signature is more responsive to changes in the pump signature. Typical operating parameters for producing an update average pump signature employ 14/15 of the old average pump signature plus 1/15 of the current residual signal. The averaging of the pressure signals that are pro¬ duced during a predetermined number of pump cycles and the addition of a fractional part (e.g. 14/15) to a fractional part (e.g. 1/15) of the residual signal is performed by the update pump signature averaging buffer 74. The current residual signal .from the residual buffer 72 is shifted into the averaging buffer during each pump cycle where the 14/15 and 1/15 addition is effected. The resultant current average pump signature is snifted into the average pump signature buffer 76. 1 A compressor/expander 78 serves to compress or expand the time scale of the current average pump signa¬ ture in buffer 76 so that it corresponds to tne time scale of the current pressure in buffer 64. 5 Subtraction occurs on a data word by data word basis Thus tne appropriate word from the pump signature buffer is subtracted from the current word in the data buffer. The word selected from the average pump signature buffer 76 is selected by the compressor/expander 78 under 10 the control of microprocessor 67 according to the followi formula: = s i where m is the index of the word selected from the pump 15 signature buffer, s is the total number of words in the pump signature buffer, i is the index of tne current word m tne data buffer 64 and n is the length, in words of tne pressure data stored in tne data buffer 64. When the filter operation commences the average pump 20 signature is zero for all points in the cycle. As the initial current pressure cycles are stored in the buffer 64, tney are shifted through the subtractor 68 and the residual buffer 72 into tne buffer 74 wnere tne pump sig¬ nature gradually takes on the characteristics of the 25 actual average pump signature. The average pump signatur is continually updated by the Duffer 74 and the current average pump signature is stored in the buffer 76. The proper data points in the buffer 76 are selected by tne compressor/expander 73 and shifted into the subtractor 30 68 where the current average pump signature and the current pump pressure are subtracted from one another to produce the residual signal that is shifted into the buffer 72. 35 O PI Fig. 9 illustrates how the filter 36 for removing pump noise can be implemented for two or more pumps with circuit hardware. The current pressure data input circuitry is the same as that shown on Fig. 8. An average pump signature is obtained for eacn pump, with the circuitry for the respective pumps being identi¬ fied by the letters A and B. Tne outputs of the compressor/expanders 78A and 78B are applied to an adder " 80 which produces the sura of all of tne signatures ot tne operating pumps, taking into account the relative phase position of each pump. The signatures are updated as before except that only l/( umber of pumps operating) of the residual is assigned to each signature. The residual pressure is then tne difference between the current pressure data in buffer 64 and the predicted pressure signature in adder 80. It will be apparent that the noise subtraction fil- ter 3 ύ may be expanded to function with any desired number of pumps. BAD ORIGINAL O PI_ SUBSTITUTE SHEET ' 1 APPENDIX 1 Detailed Description of the Filter Section Algorithm The filtering algorithm employed in this section is the ' 5 pump phase partition model, and the assumptions upon which this model is based have been stated in the descrip¬ tion of the pump noise subtraction filter. The implemen¬ tation details are described in the following: SYMBOL DEFINITIONS 10 P.in(i) = Input pressure data at the i-th sample. S(j,i) = Input strobe data at i-th sample from pump j (l j 3) 15 Is(j,k) = Sample index for -th strobe from pump j P.ρred(ι) = Predicted pressure for the i-th sample 20 P.sig(j,m) = Pump j*s AC pressure profile at its m-th stroke phase position. 0 < ra Signa¬ ture size - 1. The signature size is 123. 25 P.mean(i) = Predicted mean pressure for the i-th sample. P.res(i) = Residual pressure ctt the i-th sample = P.m(i) - P.ρred(i). This is tne filter 30 sections output to the detector. P.ave(j) = Pump j's average signature value. P.ran(i) = Computer generated random pressure data. 35 " * = Pump j ' s signature update weight ; Q <ϋ Update weight l imit . The filter, section receives pressure data, P.in(i), and pump strobe indices, -Is (j ,k) ,- from the input section. Strobe data, S(j,i), has been evaluated for strobe sample index (strobe occurrence time) by the Input Section. The kth index has been assigned for pump j at data sample i Is(j ,k) = i whenever S (j , i )+S ( j , i-i +S (j , i- ) -S(j , i-3) -S (j , 1-4)-S( j , i -5) > (3/4) * Strobe height (j) and Minimum (S(j,i),3(j,i-l),S(j,i-2) ) > Maximum (S( j , i-3 ) ,S ( j , i-4) ,S (j , i-5) ) (Tne strode height is a user controlled parameter. ) This particular algorithm searcnes for tne leading edge of a strooe, and it is ≤omewnat noise tolerant due to the two tescs described above. The q-th pump's contribution to the pressure for tne i-th sample is referenced in its pump signature table, P.sig, by linearly interpolating tne index, ra(q), for the sample index bracketed by the indices of two nearest strobes. That is, m(q) = Signature size * (i-Is (q,kq-l ) )/(Is (q , q)-Is (q,kq-l) ) where kq is selected on tne oasis . that Is(q,kq) > i > Is (q,kq-l) BAD ORIGINAL 1 This linear interpolation of the index estimates the phase of the pump. Tne predicted pressure for the i-th sample is 5 computed by summing the individual pump pressure contribu¬ tions of each pump that is "in operation" to the mean pressure, P.mean(i), P.predd )=P.mean (ι)-t-[sum q over ail umps in 10 operation: P.sig(q,m(q) ) ] The * j-th pump is considered "in operation" if its last strobe occurred less cnan five seconds from tne 15 current input sample, i.e., f at the i-tn sample and for last strobe index, Is(j,k), i-Is(j,k) < 5U0 (= 5 seconds) 20 If the pump is considered "orf", its signature and update weight are initili ed to zero. The difference- etween the predicted pressure, P.pred, and tne pressure input, P. in, composes the residu pressure. 25 P.res(i) = P.in(i) - P.predd) * which is passed to the detector section. 30 35 ss OMFI < ">. WKQ I p ump signatures , P . s ig (q , m (q ) ) , are updated at every sample point by the relation P . sig ( q ,m ( q ) ) = 5 (P.sig(q,m(q) )*U(q)+P.res(i) )/(number of pumps in operation) Maximum (i,U(q)+l) 0 After a pump stroke is complete, i.e., i=Is(q,kq), the predicted mean pressure is updated by P.mean(i)=(P.mean(i)+P.ave(q) )/2 5 wnere P.ave(q) is the mean value of the pump signature for q-th pump. After the predicted mean pressure is updated, this 0 average signature value is subtracted from tne elements of the pump's signature table. Also, the signature update weight is incremented until its maximum is reached, 5 U(q)=Mιnimum(ϋ(q)τl,Signature Update Weight Limit) Whenever there are no pumps m operation and for five seconds after this conαitions ceases to exist, the filter algorithm generated random pressure data for the residual Q pressure so that sample timing can be maintained,- P.res(i)= .ran(i) . 5 BAD ORIGINAL _ o?.τ? *

Claims: WHAT IS CLAIMED IS: I. A method of filtering noise from signals having a data component and a cyclical noise component comprising averaging a predetermined number of the cyclical signals to produce an average signature signal, updating the average signature signal each cycle to produce a current average signature signal, and subtractin the current cyclical signals and the current average 10 signature signals from one another to produce a residual signal which contains the data component. 2. A method ot noise suotraction for use in processing data that is telemetered oy pressure pulses 15 that are transmitted througn well drilling fluid tnat is circulated øy pumping in repetitive cycles, comprising producing composite signals that are representative of the pressure changes in the fluid having a data component that is representative of the telemetered uata and naving 20 a cyclical noise component tnat is produced by the pumpin of the fluid, producing an average signature signal that is representative of tne average of saic composite signal over a selected number or current pumping cycles, .mi subtracting the current composite signals and tne current 25 average signature signal from one another to cause tne cyclical noise components tnat rire produced PV pumping to cancel leaving a residual signal tnat contains tne data component. 30 3. The method of Claim __ wnerem tne time frame of the signals is adjusted so that tne ' omposite signals and the average signature signais nave tne same time frame witn respect to the pumping cycles. 35 C'P RIGINAL w Wl * ^ 4. The method of Claim 2 wnerein the average signature signal is produced by adding a portion of tne current pump signature to a portion of tne current residual signal. - 5. The m tnod of Claim 2 wnerein the average signature signal is produced by adding 14/15 or tne current pump signature to 1/15 of the current resiαuai signal . 0 δ. A noise subtraction filter comprising means for producing a repetitive signal having a data component and a noise component, means for continuously averaging a predetermined number of the current repetitive signals to 5 produce an average signature signal, means for updating the average signature signal periodically to produce a current average signature signal, and. means for subtractin the current repetitive signals and tne current average signature signal, whereby the noise component in the 0 current repetitive signal is substantially cancelled leaving a residual signal which contains the data component. 7. A noise subtraction filter for use in pro¬ 5 cessing data that is telemetered through well drilling fluid tnat is circulated υy pump means that operates n repetitive cycles, comprising means adapted to oe coupled to tne well drilling fluid for producing composite signals representative of pressure changes in the fluid having a data component that is representative of the data that is telemetered through tne well drilling -fluid and having a cyclical noise component that results from the changes in pressure that are produced by tne pump means, means for averaging a predetermined number υf said composite signals 0. PI BADO R K 3 »« ^ v. ■ during a predetermined number of pump cycles to produce an average signature signal, and means for subtracting the current composite signals and t e current average signature signal rrom one anotner to cause the cyclical noise components to cancel leaving a residual signal wnicn contains the data component. 8. A noise subtraction filter ror use in pro¬ cessing data that is telemetered through well drilling 10 fluid that is circulated by pump means that operates in repetitive cycles, comprising means coupled to tne well drilling fluid tor producing composite signals represen¬ tative of pressure changes in the fluid having a data component that is representative of the data tnat is 15 telemetered through the well drilling fluid and having a cyclical noise component that results from the cnanges in pressure that are produced by tne pump means, means tor producing an average pump signature signal that is representative of the average of said composite signals 20 during a predetermined number of pump cycles, and means for ?3ubtracting the current composite signals and the current average signature signal from one anotner to cause the cyclical noise components tnat are produced by the pump means to cancel leaving a residual signal at the 25 output of tne subtracting means that contains tne data component. 9. The apparatus of claim 3 wherein the means for subtracting tne current composite signals and. the 30 current average signature signals includes means for compressing or expanding tne time rame ot one of the signals to cause both of the signals to have the same time frame. 35 10. Tne apparatus of Claim 3 wnerein the averag OM V ΪP pump signature signai is produced by adding a portion of the current pump signature to a portion of tne current residual signal. 11. The apparatus of Claim 8 wherein the average pump signature signal is produced by adding 14/15 of the current pump signature to 1/15 of the current residual signal. π S P BAD ORIGINAL^ _CMH_ > Wi-PO

Inventors: UMEDA T, UMEDA, T.
Applicants: EXPLORATION LOGGING INC, EXPLORATION LOGGING, INC.
Application year: 1983
Main classification: G01V1
IPC codes: E21B47, G01V1, H03H21