GB2032105A

GB2032105A - Improved multifold cross- correlation for borehole signals

Info

Publication number: GB2032105A
Application number: GB7931115A
Authority: GB
Original assignee: Schlumberger NV
Current assignee: Schlumberger NV
Priority date: 1978-09-29
Filing date: 1979-09-07
Publication date: 1980-04-30
Also published as: AU532692B2; AU4919879A; DE2933340A1; MY8500181A; FR2437631B1; NL7906204A; FR2437631A1; NO792827L; GB2032105B; CA1151280A

Abstract

Methods and apparatus are described for improving the cross correlation of three or more signals (e.g. acoustic logging signals) derived in an investigation of a borehole. The technique involves the testing of signs of samples employed in forming a cross-product during a cross- correlation. Sign conditions representative of a good match are so recognized and the resulting cross- product modified (by weighting) if needed for constructive contribution to the cross-correlation. Sign conditions indicative of a lack of correspondence between samples can also be detected so that cross- products from such samples can be prevented from adding to correlation peaks when an even number of negative samples are present.

Description

SPECIFICATION Improved multifold cross-correlation for borehole signals This invention generally relates to an improvement in the processing of a plurality of geophysical signals derived from an investigation of a borehole penetrating an earth formation.

More specifically, this invention relates to an improved multifold correlation method and apparatus for deriving a parameter from combinable geophysical signals obtained from a borehole investigation.

Multifold correlation techniques for processing geophysical signals have been published. In one such technique as described in a publication entitled "Acoustic Logging For Mining Applications" by James H. Scott and Joe Sena, presented at the SPWLA fifteenth Annual Logging Symposium of June 2-5, 1974, a two-fold cross-correlation technique is described for use in an acoustic investigation of a borehole. An acoustic transmitter is used to send an acoustic pulse into the formation. Receivers sense acoustic energy after its passage through the borehole and adjacent formation and generate waveform signals indicative of the sensed acoustic energy.

The Scott et al article describes a digital technique with which one can derive parameters such as the interval travel times of compressional and shear waves from the waveforms by combining a pair of these in a two-fold crosscorrelation signal process.

Another multifold correlation technique is described in an application entitled "Method and Apparatus For Determining Acoustic Wave Parameters In Well Logging", originally filed by John D. Ingram on May 27, 1975 in the United States Patent and Trademark Office, currently bearing Serial No. 928,389. In accordance with one of the techniques described in the Ingram application, parameters such as the compressional and shear wave interval travel times are obtained by forming a four-foid cross correlation with signals from four receivers spaced along an acoustic investigation tool.

The two-fold correlation technique described in the Scott et al article is useful in generating a correlation peak from which an approximate determination of such parameters as the compressional and shear wave interval travel times can be made. The correlation peaks, however, normally tend to be poorly defined making it difficult to determine accurate interval travel times. The interval travel time is particularly difficult to derive automatically for purposes such as making accurate well logs on which these parameters are plotted as a function of depth.

When a four-fold correlation technique such as described by Ingram is employed, the correlation peaks are substantially sharpened, thus enabling automatic determination of parameters such as interval travel times. The four-fold correlation is obtained by sampling four receiver waveforms and forming cross-products between corresponding samples located in windows shifted along the four waveforms. The cross-products are summed for each window position to define a single correlation point of a correlogram. The window position can be related to a parameter such as the interval travel time of an acoustic wave so that, for a range of window positions, a correlogram is formed. The correlogram for a four-fold correlation may have a sharp peak which represents at that peak an accurate measurement of the interval travel time for the acoustic wave.

The described four-fold cross-correlation technique is normally highly effective for measuring the correspondence between geophysical waveforms obtained from a borehole investigation. Yet, at times, significant side lobes (other peaks) and deteriorations of the peak sharpness are observed in the correlogram. Such side lobes and peak degeneration reduce the accuracy of acoustic correlation techniques for measuring parameters in the receiver waveforms.

It is, therefore, an object of the invention to provide a method and apparatus for improving tfie cross-correlation of waveforms derived from a borehole investigation.

In accordance with this and other objects, one aspect of the invention is directed to a method for automatically forming cross-correlations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, characterized by the steps of determining the degree of sign coherence between waveform samples employed in a set used to form a cross-product for a crosscorrelation; and modifying the cross-product formed between the samples in the set in conformance with the determined degree of sign coherence to provide a constructive contribution of the cross-product to the cross-correlation.

Another aspect of the invention is directed to an apparatus for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation, characterized by means for measuring the degree of sign coherence between waveform samples employed in a set used to form a cross-product for a cross-correlation; means for generating a cross-product of the samples in the set; and means for modifying the cross-product in accordance with the measured degree of sign coherence to enable a constructive contribution of the cross-product to the cross-correlation.

The improvement is based upon the discovery that negative samples can affect the contribution made by cross-products to the correlation technique in a destructive manner. For example, in a four-fold cross-correlation technique, the crossproduct of four samples, two of which are positive and two are negative, is positive. The crossproduct is thus added to the correlation as if the four samples correspond, yet in fact the situation actually involves the worst possible mismatch.

When one seeks to form a cross-correlation between an odd number of, say three, waveforms, the presence of one negative sample in a cross product causes the latter to be negative, an excessive influence of the negative sample since the other two positive samples appear in correspondence. In fact, when all three samples are negative, which is evidence of a high degree of correspondence, the cross-product is negative to thus decrease the correlation instead of increasing it.

It is significant to note that when a crosscorrelation is made between a pair of waveforms, such as described in the aforementioned Scott et al article, the effect of the negative sample corresponds with the physical situation. Thus, the cross-product between a pair of negative samples is properly positive and the effect of a single negative sample yields a correct negative crossproduct. This advantage does not apply to situations where more than two receiver waveforms are to be cross-correlated.

With a technique for improving a multifold cross-correlation in accordance with the invention, cross-product contributions to a correlation are made as a function of the sign coherence between the samples employed to form the cross-product.

As described herewith with respect to one embodiment in accordance with the invention, a cross-correlation of a plurality of at least more than two waveforms, involves testing of the signs of the samples to determine whether crossproducts should be formed and used in the correlation. If an equal number of samples are positive and negative, the cross-product can be formed, but its result is weighted in such manner as to reduce the correlation to reflect the mismatch. If there are more samples of one sign than the other, then the cross-product can be weighted in accordance with the apparent correspondence of the majority of samples. If an odd number of samples are in the set used to form the cross-product and all samples have a negative sign, then the cross-product is weighted positive to reflect an apparent match.

A variety of sign tests and weighting techniques can be employed to assure that the cross products contribute in a constructive manner to the correlation of the waveforms. As a result, correlogram side lobes (other undesired peaks) are reduced and the sharpness of the correlation peak for the parameter of interest is improved.

A particular advantage of this invention is its effect upon tool configurations. For example, the aforementioned Scott et al article shows an acoustic investigation tool employing an odd number of receivers, namely three. With such tool a cross-correlation between a pair of waveforms can be made as described. If a cross-correlation between all three receiver waveforms would be attempted, then the result would yield many side lobes and poorly defined peaks in the correlation.

With a sign testing technique in accordance with the invention, however, the cross-correlation between three waveforms can yield useful results.

The invention thus has the effect of expanding the utility of a borehole investigation tool having an odd number of at least three or more receivers, because the powerful analysis of a multifold crosscorrelation technique can be applied with accurate and reliable results.

The impact of the invention, however, also improves the effectiveness of a tool having an even number of at least four receivers. For example, as described herein for one technique in accordance with the invention, a test of the signs of the samples is made for a four receiver tool. If the majority of samples agree in sign, then the cross-product of those is used and the odd sample is effectively discarded. Again, the result is an improved correlogram with fewer side lobes and a sharper correlation peak for the parameter of interest.

In another feature of the invention, the contribution to a correlation from cross-products of samples near the ends of windows is reduced.

This desensitizes the correlation to large sample variations at the window edges. The technique involves applying a weighting furction to those samples or their cross-products located near the window edges. An advantage of this technique resides in an improved sharpness of the peak in the correlation for the parameter of interest.

These and othe advantages and objects of the invention can be understood from the following description of several embodiments which are described in conjunction with the drawings.

FIG. 1 is a block diagram and schematic representation of a tool employing a sample test technique in accordance with the invention.

FIG. 2 is an illustration of representative receiver waveforms derived from a borehole investigation.

FIG. 3 is a block diagram representation of a portion of a tool employing another form of the invention.

FIG. 3A is a curve illustrative of a weighting function useful in reducing correlation window end effects in accordance with the invention.

FIG. 4 is a logic and block diagram of one form of an apparatus and method for sign testing of samples in accordance with the invention for use in a cross-correlation.

FIG. 5 is a logic and block diagram of another apparatus and method for weighting of samples for use in a cross-correlation of waveforms derived from a borehole investigation.

FIG. 6 is a detailed logic block diagram of a sample selection network used in the embodiment of FIG. 5.

With reference to Figs. 1 and 2 a tool 10 for investigating a borehole 12 in an earth formation is shown suspended from a cable 14. A control system 1 6 is located on the surface to provide tool 10 with suitable electrical power and control signals in a manner well known in the art. A depth signal is generated on line 18 to indicate the location of tool 10.

The tool 10 may be of various different types depending upon the particular investigation to be made. For the embodiment of Fig. 1, tool 10 is of the acoustic investigation type such as, for example, described with greater detail in said aforementioned U. S. patent application to Ingram.

Tool 10 may thus include an acoustic pulse transmitter 20 which is spaced from a plurality of four spaced sonic receivers 22.1-22.4.

The sonic receivers 22 detect acoustic energy after its passage through portions of the borehole to produce signal waveforms 24 such as illustrated in Fig. 2. The waveforms 24 are processed to derive various parameters from which an evaluation of the borehole or the formation around the borehole can be made.

The parameters derived from the waveforms 24 may be compressional and shear wave interval travel times obtained in a manner as, for example, described in the aforementioned Ingram patent application. Thus, waveforms 24 from receivers 22 are digitized with an analog to digital converter 26 and the resulting samples stored in a memory 28 of a signal processor 30. The conversion of waveforms 24 to samples preferably is done down hole in tool 10 though a surface located A/D converter could be used. Similarly, storage of samples and their processing can be done down hole or after transmission along cable 14 with a surface located signal processor 30.

One particularly effective technique for deriving a parameter from a plurality of waveforms 24 involves formation of a cross-correlation between the waveforms 24 as a function of such parameter. The value of the parameter for which the correlation has a peak represents the best correspondence and thus the measured parameter value.

The aforementioned application of Ingram describes such cross-correlation technique.

Briefly, this involves forming and summing cross-products between samples of different waveforms. A group of samples from each waveform 24 is selected to form these crossproducts and the cross-products are accumulated to form one correlation point. A different group of samples is then selected, preferably as a function of the parameter of interest, and a new correlation point computed. Afte a number of these correlation points have been obtained over a portion of the waveforms 24, a peak in the correlation points signifies the value of the parameter.

For example, with reference to Fig. 2 the groups of samples to be initially cross-correlated are selected by figuratively locating a window such as 32 according to relationships described in the aforementioned Ingram patent application for compressional or shear waves.

The cross-products for the cross-correlations are formed by multiplying correspondingly located samples. Thus, samples S", S2 3,1' and 4,1 define a set used to form a cross-product. When the windows 32.1-32.4 are so aligned that all the same have the same sign, such as when they are from the same cycle in the waveforms 24, then the cross-product is positive and properly added as part of the correlation to other crossproducts of corresponding samples in the windows 32.

In practice, the waveforms 24 are not precisely alike and the windows 32 are shifted so that samples of different cycles and thus different signs are likely to be part of a set used in forming a cross-product. For example, windows 32 may have been shifted in the correlation technique so that sample i,i' S2 1 are positive and samples S3 , S,, are negative, reflecting a mismatch. Yet their cross-product is positive resulting in an erroneous or destructive contribution to the correlation point to be computed for the window position.

As part of the correlation technique is in an initial step, the signs of samples are evaluated for their degree of coherence. In tool 10 this involves selecting the set of samples to be used in forming a cross-product at 40 and evaluating the signs of the samples in evaluator 42. The sign evaluator 42 may apply a variety of criteria; for example, if there are four samples to be used in the cross-product, two of which have opposite signs from the others, then the final cross-product as formed in multiplier 44 is modified at 46 with a negative weight and added to the correlation accumulator 48 to thus reflect the mismatch by reducing the value of the correlation point. The result is a more accurate cross-correlation.

In Fig. 3 an additional feature of the invention for improving a cross-correlation is shown. In this case the cross-products formed by sets of samples near the edges 50, 52 of a window 32 are weighted in a function multiplier 54. The function may, for example, have an appearance as suggested by curve 56 in Fig. 3A. Curve 56 reduces sets of samples near window edges 50, 52 according to the straight slopes 58.1, 58.2 whereby the outer most cross-products are reduced to one-quarter of their value, the next cross-product to one-half and the third to threequarters its value. The remainder of the crossproducts remain at their computed value.

The technique for evaluating the coherence between the signs of samples used to form a cross-product may be carried out with logic circuits dedicated for this purpose or with firm ware involving a prewired program in a digital processor or with a programmable signal processor provided with suitable instructions.

When the cross-correlations are carried out downhole in tool 10, the use of circuits or firm ware may be preferred. However, it may be more advantageous to accumulate the samples in a suitable memory on the surface so that one may then practice the improved cross-correlation technique of this invention at a later time under less strenuous circumstances when tool 10 is no longer within borehole 12.

Whichever form appears most suitable for practicing the invention, the logic diagrams of Figs. 4 and 5 are illustrative of how one may implement the invention for a large number of waveforms. Thus with reference to Fig. 4, the sampled waveforms are construed available from a suitable memory for a number of n waveforms.

The value of n may be odd or even, but is at least greater than two.

The samples S" S2, Sn for each of the waveforms 24.1,24.2 and 24.n include an amplitude and sign and appear on separate lines 70.1,70.2 and 70.n coupled to sign sensors 72 and multipliers 74. The sign sensors 72 test the sign bit for each of the samples S and generate an output 76, 78 sign signals indicative that the sample is positive or negative.

The results of the sign sensor outputs 76, 78 are respectively accumulated in counters 80, 81.

Thus counter 80 determines how many samples are positive and counter 81 determines how many samples are negative.

Sign testers 82 and 84 are provided to evaluate on output lines 86, 88, respectively, whether all of the sample signs are positive so that line 86 becomes active, or whether all of the sample signs are negative so that line 88 becomes active.

In the event the samples are all negative, further sign evaluations are made with sign testers 90, 92 as to whether the number of negative samples is even when line 94 becomes active; or whether there is an odd number of negative samples when line 96 goes active.

Once the sign coherence evaluation is complete, the level on lines 86, 94 and 96 are combined by an OR function network 100 to activate multipliers 74.1 and 74.2. The latter form a cross-product of samples S,, S2 and Sn and apply the result on line 102 to a modifier network 46.

The cross-product modifier includes a multiplier 104 which combines a weighting function tithe cross-product as a function of the number of negative samples. Thus, when line 106 is representative of either all positive or an even number of all negative samples and thus is active, the weighting function of +1 from network 108 is permitted to pass through logic gate 110 to multiplier 104. The latter thus produces on line 112 a positive cross-product for addition to other cross-products in a cross-product accumulator 48.

In the event all of the negative samples are negtive and there is an odd number of such samples, line 96 becomes active. Since the sample signs are the same, there exists a good match and a weighting function of -1 from network 1 1'4 is permitted to pass through logic gate 11 6 for multiplication with the negative cross-product on line 102. The cross-product thus produced on line 112 adds constructively to those in accumulator 48.

Although the modification of the cross-product was described as obtained by multiplication, one can appreciate that when only the sign of the cross-product is to be changed, this can be also accomplished by changing the sign bit of the digital cross-product.

The procedure is repeated for all of the crossproducts to be formed between corresponding samples in windows 32 (see Fig. 2). Thus if a window 32 is formed of twenty samples, as many as 20 cross-products can be formed and summed in correlation accumulator 48. Timing signals used to complete the described sign evaluation logic may be derived from a suitable control network 118.

In practice, a number of sets of samples may not meet the required conditions of the sign evaluation prior to formation of the cross-product.

This is sensed by monitoring the outputs 82, 84 with an exclusive NOR network 1 20. The output 122 of this network goes active if neither one of the conditions tested by networks 82, 84 are satisfied. The active output on line 1 22 resets various networks and causes extraction of the next set of samples from memory and form a crossproduct if the desired sign coherence is present.

The rejection of sets of samples whose signs do not meet the desired degree of coherence, effectively constitutes a modification of the cross product, i.e. in this case to zero.

The waveforms 24 may be weak or noisy so that a more complex sign testing technique as shown in Fig. 5 may be preferred. The embodiment of Fig. 5 is similar to that illustrated in Fig.

4 as suggested by use of like identification numbers. The sign coherence evaluator of Fig. 5, however, tests the signs of samples such that cross-products are formed and used under a variety of sample sign conditions.

Thus, each of the sample lines 70 are connected to a sign sensor 72 and a select network 140. The latter operates under control by sign selection signals on lines 142, 144 to modify the cross-product by presenting either the sample on line 70 for the cross-product multiplications or a weighted value such as unity. With a selection network 140 one may elect to use those samples whose signs are in the majority.

For example, if there are four receiver waveforms and in a cross-correlation process three or four samples have the same sign, then these can be multiplied to form the cross-product.

In the embodiment of Fig. 5, all four samples are multiplied, but the odd sample is effectively removed by substituting + 1 for its value.

The sign coherence evaluation is obtained with a plurality of comparators. Comparator 146 generates an active signal on output line 148 when the number of positive samples exceed the number of negative samples. Comparator 1 50 generates an active output on line 152, whenever the number of positive and negative samples are equal. Comparator 1 56 produces an active output on line 1 56 whenever the number of negative samples exceed the number of positive samples.

If, for example, there are a greater number of positive samples, line 148 becomes active and through OR gate 1 62 line 142 is active. This causes all samples which are positive to be passed by selection networks 140 to multipliers 74 and unity to be substituted for the negative samples.

When there are an equal number of negative and positive samples, line 1 52 is activated and through OR gates 162,164 operates to activate both sign selection lines 142 and 144. This allows all samples to be passed onto multipliers 74 without substitution of weighting values. The effect of the recognition of this sign condition is to force the cross-product negative as evidence of a mismatch.

Ths is obtained by applying line 1 52 through an OR gate 166 to enable AND gate 116 and through an inverter 1 68 inhibit an AND gate 1 70 interposed in line 106.

If the number of negative samples are in the majority, then line 1 56 from comparator goes active and operates through OR gate 1 64 to enable sample select line 144 and thus allow only negative samples to be used in forming a crossproduct. Subsequent tests for an even or odd number of negative samples are also made in the manner as described with reference to Fig. 4.

Fig. 6 shows the logic circuits which can be used for modifying the cross-product by employing either the sample value or a substitute weighted value, W, stored in a network 180 and applied to an AND gate 1 82. The sign selection lines 142, 144 are coupled to AND gates 184, 1 86 respectively together with the sign value of the sample on line 70. If the sign is positive and the positive sign selection line 142 is active, AND gate 1 84 is enabled, causing AND gate 1 82 to be disabled by virtue of the effect of inverter 1 88. An AND gate 190, however, is enabled thus permitting the sample to be applied on output 1 92 to multiplier 74.If the opposite sign selection line 1 44 is active, the sample on line 70 is prevented from passing to output 1 92 and instead the value W is substituted. Since W normally is + 1, the network 140 operates to exclude, from the crossproduct, those samples whose signs have been found to be in the majority. One may appreciate that a selection network 140 can be implemented in a variety of ways following the description of the logic functions. The entire logic of network 140 can be advantageously carried out with a correspondingly programmed signal processor.

The sign testing technique af Fig. 5 can be modified by varying the conditions applicable to testing networks such as 146, 1 50 and 1 54. For example, instead of a simple majority, one may require that there exist a greater difference between the number of positive and negative samples before the samples having the dominant sign are used to form a cross-product.

The window end effect correction as described with respect to Figs. 3 and 3A can be conveniently applied to an embodiment such as shown in Fig. 5.

In such case line 102 is coupled to a multiplier 200 for multiplication of the cross-product by a weight function produced on line 102 from a weight function generator 202. The latter generates a function on line 204 with the shape as depicted in Fig. 3A and as a function of a sample number. The latter is applied on line 206 to indicate the window location of the set of samples being used to generate the cross-product.

Having thus described several embodiments in accordance with the invention for improving a cross-correlation technique by testing the signs of samples used in the correlation, the advantages can be appreciated. Variations may be implements by one skilled in the art, without departing from the scope of the invention. For example, the order in which operations occur can be changed without altering the result. For example, cross-products can be formed between samples and then modified in accordance with and after a sample sign coherence evaluation is made.

Claims

1. A method for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, characterized by the steps of determining the degree of sign coherence between waveform samples employed in a set used to form a cross-product for a crosscorrelation; and modifying the cross-product formed between the samples in the set in conformance with the determined degree of sign coherence to provide a constructive contribution of the cross-product to th.e cross-correlation.

2. The method as set forth in claim 1, characterized in that the sign coherence determining step includes determining the number of negative and positive samples in the set; and comparing the numbers of negative and positive samples to establish which sign is predominant in a set of samples.

3. The method as set forth in claim 1 or 2, further characterized by the step of: reducing the magnitude of cross-products as a function of the proximity of the set of samples to the edges of a window range of samples employed in the cross-correlation.

4. An apparatus for automatically forming cross-correlations of a plurality of waveform signals derived from an investigation in an earth formation, characterized by means for measuring the degree of sign coherence between waveform samples employed in a set used to form a cross-product for a crosscorrelation; means for generating a cross-product of the samples in the set; and means for modifying the cross-product in accordance with the measured degree of sign coherence to enable a constructive contribution of the cross-product to the cross-correlation.

5. The apparatus as set forth in claim 4, further characterized in that said means for measuring sign coherence includes: means for counting the number of positive and the number of negative samples in a set; and means for comparing said numbers of positive and negative samples to generate a signal representative of the degree of sign coherence between the samples in the set.

6. The apparatus as set forth in claim 4 or 5, further characterized by means for reducing cross-products as a function of their proximity to ends of a window range of samples used to form the cross correlation.

7. A method for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, the method being substantially as herein described with reference to Figures 1 and 2 of the accompanying drawings.

8. A method for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, the method being substantially as herein described with reference to Figures 1 and 2, as modified by Figures 3 and 3A, of the accompanying drawings.

9. A method for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, the method being substantially as herein described with reference to Figures 1,2 and 4 of the accompanying drawings.

10. A method for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, the method being substantially as herein described with reference to Figures 1, 2 and 5 of the accompanying drawings.

11. A method for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation with a plurality of receivers, the method being substantially as herein described with reference to Figures 1,2, 5 and 6 of the accompanying drawings.

1 2. Apparatus for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation, the apparatus being substantially as herein described with reference to Figures 1 and 2 of the accompanying drawings.

1 3. Apparatus for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation, the apparatus being substantially as herein described with reference to Figures 1 and 2, as modified by Figures 3 and 3A, of the accompanying drawings.

14. Apparatus for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation, the apparatus being substantially as herein described with reference to Figures 1,2 and 4 of the accompanying drawings.

1 5. Apparatus for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation, the apparatus being substantially as herein described with reference to Figures 1,2 and 5 of the accompanying drawings.

16. Apparatus for automatically forming crosscorrelations of a plurality of waveform signals derived from an investigation of a borehole in an earth formation, the apparatus being substantially as herein described with reference to Figures 1, 2, 5 and 6 of the accompanying drawings.