Coherence attribute applications on seismic data in variousguises — Part 2

Satinder Chopra1 and Kurt J. Marfurt2

Abstract

We have previously discussed some alternative means of modifying the frequency spectrum of the inputseismic data to modify the resulting coherence image. The simplest method was to increase the high-frequencycontent by computing the first and second derivatives of the original seismic amplitudes. We also evaluatedmore sophisticated techniques, including the application of structure-oriented filtering to different spectralcomponents before spectral balancing, thin-bed reflectivity inversion, bandwidth extension, and the amplitudevolume technique. We further examine the value of coherence computed from individual spectral voice com-ponents, and alternative means of combining three or more such coherence images, providing a single volumefor interpretation.

IntroductionAlthough most seismic data are processed to maxi-

mize the bandwidth, some form of spectral balancing onthe seismic data prior to attribute computation almostalways helps in enhancing more subtle attribute anoma-lies. Most spectral-balancing algorithms assume theunderlying reflectivity to be random, such that balanc-ing removes the spectral contribution of the seismicwavelet, with resulting frequency anomalies moreclosely associated with tuned reflections that occurat layers exhibiting quarter-wavelength thickness. Par-tyka et al. (1999) and Marfurt and Kirlin (2001) use spec-tral decomposition to quantify such tuning effects on 3Dseismic data volumes. Partyka et al. (2005) show spec-tral magnitude components aðf Þ to be effective in map-ping lateral changes in vertical thickness, and theyshow spectral phase components φðf Þ to be effectivein mapping faults and stratigraphic edges. Spectralvoice components, vðf Þ ≡mðf Þ exp½iφðf Þ�, are less com-monly used by interpreters, but they often provide addi-tional insight into subsurface features (Fahmy et al.,2008; Chopra and Marfurt, 2016). Going one step fur-ther, coherence computed from such spectral voicecomponents can highlight discontinuities that are pref-erentially imaged by a given spectral component.Although the analysis of multiple spectral componentsis common when restricted to a specific geologic target,the generation of 10–20 coherence volumes computedfrom a suite of spectral components proscribes simpleanalysis tools such as animation and interactive coren-dering for a large 3D seismic volume as a whole. Our

goals therefore are to (1) determine what additionalinformation is provided by coherence volumes com-puted from narrowband spectra and (2) evaluate alter-native ways to combine such multiple images into asingle volume. Because different spectral componentsare sensitive to different scales of discontinuities, thechallenge is to analyze these volumes effectively. Alter-native methods that can be used for this purpose in-clude using color, principal component analysis (PCA),self-organizing maps (SOMs), and multispectral coher-ence. We discuss three of these methods in this paper,leaving the SOM method for discussion in anotherpaper.

Integration of coherence and spectraldecompositionSpectral decomposition

In its simplest implementation, one can computespectral components through the application of a suiteof band-pass filters (often called filter banks) to theoriginal seismic amplitude data. The interpretationvalue of a given spectral component is a function ofthe tuning thickness of a given geologic target and bythe signal-to-noise ratio at that frequency. However,phase is also important, as demonstrated by Libak et al.(2017), who show that the lack of a coherence anomalyalong a clearly discernable fault is often due to theunfortunate alignment of peaks and troughs of differentreflectors across the fault. Such phase-alignmentchanges with frequency allow for improved fault imag-ing. Smaller, vertically localized faults are often best

1TGS, Calgary, Alberta, Canada. E-mail: satinder.chopra@tgs.com.2The University of Oklahoma, Norman, Oklahoma, USA. E-mail: kmarfurt@ou.edu.Manuscript received by the Editor 5 January 2018; published ahead of production 24 March 2018; published online 29 June 2018; Repaginated

version published online 6 August 2018. This paper appears in Interpretation, Vol. 6, No. 3 (August 2018); p. T531–T541, 8 FIGS.http://dx.doi.org/10.1190/INT-2018-0007.1. © 2018 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved.

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Technical papers

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examined at the reflector tuning frequency, whereaslarger, through-going faults are commonly seen throughby a broad range of frequency components. There areseveral spectral decomposition algorithms available tothe seismic interpreter, each with its advantages anddisadvantages. For a comparison, we refer the readerto Leppard et al. (2010), who find matching pursuit al-gorithms to provide improved vertical resolution overthe computationally more efficient continuous wavelettransform, S-transform, and simple discrete Fouriertransform algorithms. Puryear et al. (2012) constrainedleast-squares algorithm provides further spectral reso-lution; however, this improved resolution results inabrupt changes from finite-valued to zero-valued spec-tral components on neighboring traces, which result inunwanted coherence artifacts.

Damage zonesAccurate imaging of fault damage zones has become

increasingly important in seismic exploration, particu-larly in shale resource plays, where such faults can sig-nificantly increase permeability but also introducedifficulties in geosteering. Depending on the play, suchdamage zones may connect to nearby aquifers and pro-duce water, produce high-sulfur gas from nearby saltlayers, or produce large volumes of gas from more dis-tant, more mature parts of the play. Liao et al. (2017) usea reprocessed megamerge survey composed of multiplelegacy 3D seismic surveys tomap the damage zone abouta large strike-slip fault associated with the Oklahoma Au-lacogen. Using 3D seismic attributes, they image not onlythe main strike-slip faults, but also the Riedel shears andrhombochasms.

Figure 1. Stratal slices just above the top Hunton limestone (base Woodford shale) through spectral magnitude componentsgenerated at approximately (a) 20, (b) 30, (c) 40, (d) 50, (e) 60, and (f) 70 Hz. Lineaments corresponding to major strike-slipfaults are well delineated at lower frequencies (yellow arrows), whereas finer lineaments corresponding to Riedel shears arebetter delineated at higher frequencies (white arrows). The white ellipses indicate two rhombochasms that will be seen in laterfigures (data courtesy of TGS, Houston).

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In this paper, we examine a different portion of thisstrike-slip fault system imaged by a modern wide-azimuth survey acquired by TGS in 2015. In Figures 1and 2, we show an equivalent suite of time slicesthrough corresponding spectral magnitude and phasevolumes, respectively. These spectral magnitude dis-plays indicate an abundance of lineaments, althoughtheir definitions may not be very clear for all of them.Figure 3 shows the coherence attribute computed onthe spectral magnitude volumes. Each of the displaysexhibits abundance discontinuity detail, including twomajor strike-slip faults (yellow arrows), Riedel shears(cyan arrows), and two rhombochasms (red ellipses).However, many areas of these images appear defocused(green ellipses).

Voice componentsIn Figure 4, we show a suite of time slices through the

real voice component volumes ranging from 20 to 70 Hzcorresponding to the magnitude components shown inFigure 1. In addition to the spectral and phase compo-nents, Goupillaud et al. (1984) describe the voice compo-nent, which is a simple function of spectral magnitudeam and phase ϕm, at each time-frequency sample fortrace m and is given by

amðt; f Þ ¼ amðt; f Þ cos½ϕmðt; f Þ�: (1)

Our implementation of energy-ratio coherence is basedon the analytic trace, such that the Hilbert transform ofequation 1 is also used:

Figure 2. Stratal slices just above the top Hunton limestone (base Woodford shale) through spectral phase components generatedat approximately (a) 20, (b) 30, (c) 40, (d) 50, (e) 60, and (f) 70 Hz. Lineaments corresponding to major strike-slip faults are well-delineated at lower frequencies (yellow arrows), whereas finer lineaments corresponding to Riedel shears are better delineated athigher frequencies (white arrows). The black ellipses indicate two rhombochasms that will be seen in later figures (data courtesyof TGS, Houston).

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aHmðt; f Þ ¼ amðt; f Þ sin½ϕmðt; f Þ�: (2)

The real part of the sum over all frequencies f of allthese voice components reconstructs the original trace.Figure 5 shows a stratal slice through the energy-ratiocoherence computed from the spectral components.Comparing the 20 Hz component of Figures 3 and 5,we notice considerably more detail in Figure 3a, but withsome of these features mimicking the rugose topographyof the top Hunton limestone. In contrast, Figure 4a seemsto delineate only the major fault and several of the largerRiedel shears. Examining coherence computed from the50 Hz component shown in Figures 3d and 5d, we noticethe improved lateral resolution of the image computed

from the spectral real and Hilbert transform of the spec-tral voices, where the discontinuities are consistent withour strike-slip deformationmodel described by Liao et al.(2017) using clay models and a nearby seismic data vol-ume. By ignoring the phase component of the seismicdata, coherence computed from the spectral magnitudesappears to introduce “structural leakage” or othermixingartifacts into the image (the green ellipses in Figure 3eand 3f) that do not appear in the coherence imagescomputed from the voice components (Figure 5e and 5f).Figure 3g shows the stratal slice though coherencecomputed from the original (broadband) seismic datavolume. Careful comparison shows increased structuraldetail in the coherence images computed from spectralvoices in the areas indicated by the green ellipses, which

Figure 3. Stratal slices just above the top Hunton limestone (base Woodford shale) through coherence volumes computedfrom the spectral magnitude components shown in Figure 1 at (a) 20, (b) 30, (c) 40, (d) 50, (e) 60, and (f) 70 Hz as well as from(g) the original broadband seismic data. Although many more discontinuities have been illuminated by coherence computed fromthe spectral magnitude components, the results are not as crisp as those computed from the broadband data in (g) indicated bythe green ellipses. The arrows and red ellipses indicate the same features shown in the previous figures (data courtesy of TGS,Houston).

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we interpret to be associated with smaller, vertically lim-ited Riedel shear zones.

Principal component analysisPCA is a useful statistical technique that has found

many applications, including image compression andpattern recognition in data exhibiting high dimensional-ity. Interpreters are familiar with the usual statisticalmeasures, such as mean, standard deviation, and vari-ance, which are essentially 1D. Such measures are cal-culated one attribute at a time with the assumption thateach attribute is independent of the others. In reality,many of our attributes are coupled through the under-lying geology, such that a fault may give rise to lateralchanges in waveform, dip, peak frequency, and ampli-

tude. Less desirably, many of our attributes are coupledmathematically, such as alternative measures of coher-ence (Barnes, 2007) or of a suite of closely spaced spec-tral components. The amount of attribute redundancy ismeasured by the covariance matrix. The first step inmultiattribute analysis is to subtract the mean of eachattribute from the corresponding attribute volume. Ifthe attributes have radically different units of measure,such as frequency measured in Hertz, envelope mea-sured in milliVolts, and coherence without dimension,a Z-score normalization is required. The element Cmnof anN byN covariance matrix is then simply the cross-correlation between the mth and nth scaled attributeover the volume of interest. Mathematically, the num-ber of linearly independent attributes is defined by thevalue of eigenvalues and eigenvectors of the covariance

Figure 4. Stratal slices just above the top Hunton limestone (base Woodford shale) through spectral voice components generatedat approximately (a) 20, (b) 30, (c) 40, (d) 50, (e) 60, and (f) 70 Hz. Lineaments corresponding to major strike-slip faults are well-delineated at lower frequencies (yellow arrows), whereas finer lineaments corresponding to Riedel shears are better delineated athigher frequencies (cyan arrows). The purple ellipses indicate two rhombochasms that will be seen in later figures (data courtesyof TGS, Houston).

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matrix. The first eigenvector is a linear combinationthat represents the most variability in the scaled attrib-utes. The corresponding first eigenvalue represents theamount of variability represented. Commonly, eacheigenvalue is normalized by the sum of all the eigenval-ues, resulting in a percentage of the variability repre-sented.

Although the computation of multiattribute eigen-vectors and eigenvalues does not provide the samephysical insight into the data as multiattribute display,it does reduce the number of attributes used for sub-sequent analysis. For this reason, PCA is the first stepin “fancier” clustering techniques such as SOMs, gener-ative topographic maps, and support vector machineanalysis. Dewett and Henza (2016) use SOM to combinemultispectral images of coherence into a single volume.

We will apply similar clustering workflows to this datavolume in a future paper.

By convention, the first step is to order the eigen-values from the highest to the lowest. The eigenvectorwith the highest eigenvalue is the principal componentof the data set (PC1); it represents the vector withmaximum variance in the data and also representsthe bulk of the information that would be commonin the attributes used. The eigenvector with the sec-ond-highest eigenvalue, called the second principalcomponent, exhibits lower variance and is orthogonalto PC1. PC1 and PC2 will lie in the plane that repre-sents the plane of the data points. Similarly, the thirdprincipal component (PC3) will lie in a plane orthogo-nal to the plane of the first two principal components.In the case of N truly random attributes, each eigen-

Figure 5. Stratal slices just above the top Hunton limestone (base Woodford shale) through coherence volumes computed fromthe spectral voice components shown in Figure 2 at (a) 20, (b) 30, (c) 40, (d) 50, (e) 60, and (f) 70 Hz. Note the improvement in faultdelineation in the areas indicated by the green ellipses. The arrows and red ellipses indicate the same features shown in theprevious figures (data courtesy of TGS, Houston).

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value would be identical and equal to 1∕N . Becauseseismic attributes are correlated through the underly-ing geology and the band limitations of the sourcewavelet, the first two or three principal componentswill almost always represent the vast majority of thedata variability.

Saleh and de Bruin (2000) demonstrate the extrac-tion of amplitude-variation-with-offset (AVO) attributesfrom distorted offset-dependent amplitudes, and theygo on to show that these attributes were more robustdisplaying improved ability to identify fluid effects.Tingdahl and Hemstra (2003) discuss the estimationof fault orientation using PCA on seismic attributessuch as dip, azimuth, coherence, or meta-attributes de-rived from the others. All the considered attributes havea common property in that they have high values at theposition of the faults and exhibit low values elsewhere.Singh (2007) discusses the application of PCA on AVO-derived attributes for lithofacies discrimination andfluid detection.

Guo et al. (2009) compute 86 spectral componentsranging from 5 to 90 Hz using a matching pursuit tech-nique described by Liu and Marfurt (2007). Next, PCAwas performed on the 86 spectral components by formingan 86 × 86 covariance matrix. Thereafter, the covariancematrix is decomposed into 86 eigenvalue-eigenvectorpairs. They find that the first three components accountfor most of the spectral variance seen along the horizonof interest, with the remaining components accountingfor approximately 17% of the data variance. This way,

the dimensionality reduction was brought down from86 to 3.

We apply PCA to the generated voice component co-herence volumes at 20, 30, 40, 50 60, and 70 Hz, and weexamine the first principal component volume. A stratalslice display equivalent to the other displays shown inFigures 1–4 is shown in Figure 6. Note that the first PCAcomponent has captured most of the discontinuity de-tail in the individual voice components, although the lin-eaments do not show up as crisp as seen on some of theindividual voice component displays.

RGB color blendingColor blending of three data sets, one with red, an-

other with green, and the third with blue, is an effectiveway of integrating the information in the individual datasets for ease in comparison, viewing, and hence inter-pretation. Leppard et al. (2010) and Henderson et al.(2008) provide excellent examples of effective RGBcolor blending used to represent three spectral compo-nents. In contrast, Li and Lu (2014) and Honorio et al.(2017) compute coherence on different voice compo-nents and combine them using RGB color blending.In Figure 7, we show a color-blended image for threedifferent energy-ratio coherences on voice componentvolumes (40 Hz in red, 50 Hz in green, and 60 Hz inblue). On this display, if the coherence at a given voxel’sthree color channels is maximum, the blended colorwill be white, whereas if it is minimum, the blendedcolor will be black. If the highest frequency coherenceis lower than the others, there will be less blue in theimage, resulting in yellow. In contrast, if the lowestfrequency coherence image is lower, there will be less

Figure 6. Stratal slices just above the top Hunton limestone(base Woodford shale) through the first principal componentvolume computed from the six coherence images shown inFigure 4. The yellow arrows indicate strike-slip faults, bluearrows Riedel shears, and red ellipses rhombochasms. Thisimage captures most (though not all) of the features includedon the six input coherence images, allowing the interpreter towork with a single, improved discontinuity volume (data cour-tesy of TGS, Houston).

Figure 7. Corendered coherence computed from 40, 50, and60 Hz voice components shown previously as Figure 4c-4e. Highcoherence at all components appears as white, whereas low co-herence at all components appears as black. Because lower co-herence for a given component subtracts color, low coherenceat 40 Hz appears as cyan, at 50 Hz as magenta, and at 60 Hz asyellow, clearly showing the contribution of the different spectralcomponents (data courtesy of TGS, Houston).

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T538 Interpretation / August 2018

red, resulting in cyan. Careful examination of theblended images quantitatively confirms the observationmade in the previous figure — that different frequen-cies are more or less sensitive to different fault scales.Although effective, the limitation of this color displaytool is that one is limited to showing only three compo-nents at a given time.

Multispectral coherenceDewett and Henza (2016) address this limitation by

computing energy-ratio coherence on a suite of voicecomponents uðf Þ and combining the resulting imagesusing SOMs. They then sharpen their faults using a com-mercial swarm intelligence algorithm.

Sui et al. (2015) address the multispectral coherenceanalysis problem by constructing a covariance matrixfrom the spectral magnitudes am:

Cmn ¼XL

l¼1

XK

k¼−K½aðf l; tk; xm; ymÞaðf l; tk; xn; ynÞ�; (3)

where L is the number of spectral components. They findthe resulting coherence images to be of higher qualitythan those computed from the broadband data, includingmost of the details seen in coherence computed by con-structing covariance matrices from the individual magni-tude components. By ignoring the phase component,they also find that the algorithm is less sensitive to struc-tural dip, resulting in algorithmic simplification.

Marfurt (2017) builds on these ideas, but constructs amultispectral covariance matrix oriented along thestructural dip using the analytic voice (equations 1and 2) and therefore twice as many sample vectors(i.e., spectral voice components and their Hilbert trans-forms):

Cmn ¼XL

l¼1

XK

k¼−K½uðtk; f l; xm; ymÞuðtk; f l; xn; ynÞ

þ uHðtk; f l; xm; ymÞuHðtk; f l; xn; ynÞ�: (4)

The corresponding energy-ratio coherence computedusing this equation is then referred to as multispectralcoherence. We demonstrate the application of this ap-proach on the same 3D seismic data from central Okla-homa, USA. In Figure 8, we show a comparison ofmultispectral coherence computed on different versionsof the data discussed in part 1 of this paper, with coher-ence computed from the original broadband seismicdata. We notice that multicoherence displays exhibitmore focused and distinct lineament detail in all the ver-sions of the data that we have shown.

ConclusionPositive and negative experiences in horizontal drill-

ing through the Eagle Ford shale of South Texas and theSTACK play of Central Oklahoma have resulted in anincreased interest in damage zones. In this paper, wehave evaluated alternative workflows to improve the

detail of a damage zone illuminated by a modernwide-azimuth survey acquired over the SCOOP playof Central Oklahoma. This survey images not only manyof the strike faults associated with the Oklahoma Aulac-ogen, but also the associated Riedel shears and rhom-bochasms. Stratal slices along the base Woodford Shaleshow that

1) Spectral magnitude displays enhance the disconti-nuities in the data. Coherence on spectral magni-tude highlights the discontinuities at differentfrequencies.

2) Coherence on voice components highlights the dis-continuities at different frequencies that show bet-ter definition than coherence on the spectralmagnitude, which can be helpful for their interpre-tation.

3) Combining different voice components using coloris an effective way of combining the attribute vol-umes, but it is limited to three colors only.

4) PCA is an effective way of reducing the dimension-ality in terms of the number of attributes we mayuse, and it is a useful option with the interpreter.

5) Multispectral coherence displays show crisper defini-tion of lineaments and thus, most useful.

AcknowledgmentsWe wish to thank Arcis Seismic Solutions, TGS,

Calgary for permission to present this work.

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Satinder Chopra has 34 years of ex-perience as a geophysicist specializ-ing in processing, reprocessing,special processing, and interactive in-terpretation of seismic data. He hasrich experience in processing varioustypes of data such as vertical seismicprofiling, well-log data, seismic data,etc., as well as having excellent com-

munication skills, as evidenced by the many presentationsand talks delivered and books, reports, and papers he haswritten. He has been the 2010–2011 CSEG distinguishedlecturer, the 2011–2012 AAPG/SEG distinguished lecturer,and the 2014–2015 EAGE e-distinguished lecturer. He haspublished eight books and more than 400 papers and ab-stracts and likes to make presentations at any beckoningopportunity. His work and presentations have won severalawards, the most notable ones being the EAGE HonoraryMembership (2017), CSEG Honorary Membership (2014)and Meritorious Service (2005) Awards, 2014 Associationof Professional Engineers and Geoscientists of Alberta(APEGA) Frank Spragins Award, the 2010 AAPG GeorgeMatson Award, and the 2013 AAPG Jules BraunsteinAward, SEG Best Poster Awards (2007, 2014), CSEG BestLuncheon Talk Award (2007), and several others. His re-search interests focus on techniques that are aimed atthe characterization of reservoirs. He is a member ofSEG, CSEG, CSPG, EAGE, AAPG, and APEGA.

Kurt J. Marfurt received a Ph.D.(1978) in applied geophysics fromColumbia University’s Henry KrumbSchool of Mines in New York, wherehe also taught as an assistant profes-sor for four years. He joined the Uni-versity of Oklahoma (OU) in 2007,where he serves as the Frank andHenrietta Schultz professor of geo-

physics within the ConocoPhillips School of Geology andGeophysics. He worked for 18 years in a wide range ofresearch projects at Amoco’s Tulsa Research Center, afterwhich he joined the University of Houston for eightyears as a professor of geophysics and the director ofthe Allied Geophysics Lab. He has received the followingrecognitions: SEG best paper (for coherence), SEG bestpresentation (for seismic modeling), as a coauthor withS. Chopra best SEG poster (for curvature) and best AAPGtechnical presentation, and as a coauthor with R. Perez-

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Altamar for best paper in Interpretation (on a resourceplay case study). He also served as the SEG/EAGE distin-guished short course instructor for 2006 (on seismic attrib-utes). In addition to teaching and research duties at OU, heleads short courses on attributes for SEG and AAPG. Hecurrently serves as the editor in chief of the SEG/AAPGpublication Interpretation. His primary research interest

is in the development and calibration of new seismic attrib-utes to aid in seismic processing, seismic interpretation,and reservoir characterization. His recent work has fo-cused on applying coherence, spectral decomposition,structure-oriented filtering, and volumetric curvature tomapping fractures and karst with a particular focus onresource plays.

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