Seismic fault attribute estimation using a local fault model

Yihuai Lou1, Bo Zhang1, Ruiqi Wang2, Tengfei Lin3, and Danping Cao4

ABSTRACT

Faults in the subsurface can be an avenue of, or a barrierto, hydrocarbon flow and pressure communication. Manualinterpretation of discontinuities on 3D seismic amplitude vol-ume is the most common way to define faults within a res-ervoir. Unfortunately, 3D seismic fault interpretation can be atime-consuming and tedious task. Seismic attributes suchas coherence help define faults, but suffer from “staircase”artifacts and nonfault-related stratigraphic discontinuities.We assume that each sample of the seismic data is locatedat a potential fault plane. The hypothesized fault dividesthe seismic data centered at the analysis sample into two sub-windows. We then compute the coherence for the two sub-windows and full analysis window. We repeat the process byrotating the hypothesized fault plane along a set of user-defined discrete fault dip and azimuth. We obtain almostthe same coherence values for the subwindows and the fullwindow if the analysis point is not located at a fault plane.The “best” fault plane results in maximum coherence forthe subwindows and minimum coherence for the full windowif the analysis point is located at a fault plane. To improve thecontinuity of the fault attributes, we finally smooth the faultprobability attribute along the estimated fault plane. We illus-trate the effectiveness of our workflow by applying it to asynthetic and two real seismic data. The results indicate thatour workflow successfully produces a continuous fault attrib-ute without staircase artifacts and stratigraphic discontinuities.

INTRODUCTION

Identification and mapping of faults is the first step in seismicstructure interpretation in conventional and unconventional plays.

The identification of major and subtle faults is critical to identifypotential drilling hazards and understand the orientation and inten-sity of potential natural fractures. For large data sets, handpickingfaults is time consuming, such that any means to accelerate the proc-ess is attractive. Major faults are easily seen and picked by expe-rienced interpreters in areas of the seismic volume exhibiting arelatively good signal-to-noise ratio; however, in other areas, moresubtle faults are masked by noise. Twenty years after the introduc-tion of coherence, developing an accurate and sensitive fault attrib-ute remains an ongoing challenge.Coherence measurements that detect structural discontinuities are

normally used to assist fault interpretation in the 3D seismic survey.Fault detection algorithms fall into two categories. The first cat-egory selects the sampling window without considering the volu-metric dip and azimuth. Barnes (1996) and Luo et al. (1996) usecomplex trace analysis to detect faults and stratigraphic boundariesin 3D seismic data. The gradient structure tensor (GST) is proposedto detect discontinuities by using the eigenvector that correspondsto the largest eigenvalue (Bakker et al., 1999; Fehmers and Höcker,2003). Wu (2017) improves the fault detection performance ofGST-based coherence by using the directional structure tensors.The second category uses the volumetric dip and azimuth to com-pute coherence. The crosscorrelation shifts traces by an assumed dip(Bahorich and Farmer, 1995). Marfurt et al. (1998) generate the co-herence algorithm by computing semblance in a suite of windowsaligned with candidate reflector dips. Marfurt et al. (1999) generatethe coherence algorithm by using the eigenstructure of seismictraces along the reflectors’ dip. The semblance-based coherence isfurther improved by using a multiple-window Kuwahara filtering(Marfurt, 2006). Luo et al. (2002) and Wang et al. (2008) use seis-mic volumetric dip and azimuth to detect sharp edges by usingedge-preserving smoothing. Donias et al. (2007) detect and isolatefaults from noise by using the steered data-analysis window over aset of dip and azimuth directions. Qi et al. (2017) propose a newway to compute the energy-ratio coherence for azimuthally limited

Manuscript received by the Editor 4 October 2018; revised manuscript received 17 March 2019; published ahead of production 16 April 2019; publishedonline 28 May 2019.

1The University of Alabama, Department of Geological Science, Tuscaloosa, Alabama, USA. E-mail: ylou6@crimson.ua.edu; bzhang33@ua.edu.2Pennsylvania State University, Department of Energy and Mineral Engineering, University Park, Pennsylvania, USA. E-mail: ruw372@psu.edu.3CNPC, Department of Middle East E&P, RIPED, Beijing, China. E-mail: lintf@petrochina.com.cn.4China University of Petroleum (East China), School of Geoscience, Qingdao, China. E-mail: caodp@upc.edu.cn.© 2019 Society of Exploration Geophysicists. All rights reserved.

O73

GEOPHYSICS, VOL. 84, NO. 4 (JULY-AUGUST 2019); P. O73–O80, 10 FIGS.10.1190/GEO2018-0678.1

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

comprehensive data volumes. Some other researchers (Neff et al.,2000; Cohen et al., 2006; Hale, 2009; Wu and Zhu, 2017) suggestsmoothing along fault strikes and dips to enhance fault features byscanning over all possible combinations of fault strikes and dips.Similarly, Hale (2013) and Wu and Hale (2016) scan over all possiblefault orientations to compute fault likelihood or fault-oriented sem-blance. Other methods, such as gradient magnitude (Aqrawi andBoe, 2011) and geosteering phase attributes (Wang et al., 2018; Yuanet al., 2018), have been proposed to detect structural discontinuities.Several researchers have proposed methods to improve the qual-

ity of coherence attributes. Pedersen (2007, 2011) proposes to en-hance fault features along paths of “artificial ants” by assuming thatthe paths follow faults. Qi and Castagna (2013) detect the faults ofthe Barnett Shale by applying principal component analysis to theseismic attributes. Zhang et al. (2014) improve the coherence attrib-utes by using a vein pattern recognition algorithm. Qi et al. (2017,2018) build a workflow to enhance and skeletonize coherence faultimages along fault planes. Wu and Fomel (2018) propose an effi-cient method to extract optimal surfaces following maximum faultattributes and use these optimal surfaces to vote for enhanced faultimages of fault probabilities, strikes, and dips.All coherence algorithms are computed using an oblique window

centered at each analysis voxel consisting of user-defined traces(horizontal) and time samples (vertical). Because the size of theanalysis window is oriented vertically along the traces, the staircaseartifacts are caused by the vertical extent of the analysis window, inwhich larger vertical extent results in larger, smoother staircase ar-tifacts (Marfurt and Lin, 2017). A remedy is to limit the vertical

analysis window to approximately the dominant period of the seis-mic data, thereby avoiding mixing discontinuities from deeper orshallower horizons (Marfurt and Lin, 2017). However, it is difficultto determine the window size that approximately equals to the localdominant period of the seismic data. In this paper, we develop a newmethod to minimize the staircase artifacts and undesired strati-graphic anomalies using a local fault model. Our method belongsto the second category of fault detection algorithms. We assume thatthere exists a fault plane passing through each voxel of our seismicdata. The fault plane subdivides the original oblique analysis win-dow into two subwindows. We determine the fault dip and azimuthby analyzing the computed coherence of the two subwindows.Then, we smooth the fault probability along the local orientationof the fault plane to minimize staircase artifacts and undesired strati-graphic anomalies. We begin with illustrating how to compute thenew fault attributes by using a local fault model. We then demon-strate the effectiveness of our workflow by applying it to a syntheticdata and two real seismic data acquired over offshore Netherlands(F3) and marine New Zealand (Kerry 3D), respectively.

METHOD

To minimize the effect of staircase artifacts and undesired strati-graphic discontinuities on fault analysis in the seismic image, wepropose a method (Figure 1) to generate the fault attribute usinga local fault model. Our method assumes that we have a local faultplane passing through each analysis point. We obtain the dip andazimuth of the fault plane by rotating the fault plane along a setof discrete dip and azimuth. We obtain the fault probability at theanalysis window by statistically evaluating the computed coherencefor each candidate fault.

Coherence computation using a local fault model

Our method begins by defining a set of assumed fault planescentered at the analysis point. We generate the assumed fault planesby defining the minimum, maximum, and increment of the faultscanning dip and azimuth. The yellow stars and yellow lines in Fig-ure 2a–2c denote the analysis points and three candidate faults,respectively. The dip angles in Figure 2a–2c are 90°, 45°, and thedip angle coincident with the fault plane, respectively. The assumedfaults (the yellow lines in Figure 2a–2c) divide the 2D analysis win-dow into two subwindows. The left and right subwindows are com-posed of the red and blue seismic data, respectively. The yellowsurface in Figure 3 shows a representative assumed fault plane inthree dimensions. The red and blue traces in Figure 3 form two sep-arate subanalysis windows.We then compute the semblance-based coherence S for each sub-

window by considering the local reflector’s dip (Marfurt et al., 1998).

S¼PþMt

mt¼−Mt

��PNn¼1fðτ0þmt−pxn−qyn;xn;ynÞ

�2

þ�P

Nn¼1f

Hðτ0þmt−pxn−qyn;xn;ynÞ�2�

NPþMt

mt¼−Mt

PNn¼1f½fðτ0þmt−pxn−qyn;xn;ynÞ�2þ½fHðτ0þmt−pxn−qyn;xn;ynÞ�2g

;

(1)

where fH is the Hilbert transform of the real seismic trace f, t is thetwo-way traveltime, x and y are the inline and crossline coordinates,respectively, Mt is the half-window size in number of samples, N isthe number of seismic traces in the analysis window, τ0 is the time ofthe center analysis point, and p and q are the reflector dips in theinline and crossline directions, respectively.

Figure 1. Workflow for the new fault attribute based on a local faultmodel.

O74 Lou et al.

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

The coherence values of the seismic data within the left and rightsubwindows are called Cleft and Cright, respectively. We also useequation 1 to compute the coherence Cfull for the full analysis win-dow, in which the full analysis window includes the seismic data inthe left (red) and right (blue) subwindows. Note that we obtain themost coherent seismic traces for the left and right subwindows if theassumed fault plane is coincident with the true fault plane. Weshould obtain the lowest value of Cfull if the assumed fault planeis parallel to the true fault plane. If there is no discontinuity at theanalysis point, we always obtain a high value ofCfull (the green starsin Figure 2). For this reason,Cleft þ Cright andCfull together allow usto evaluate the likelihood of each analysis point.

Figure 4a and 4b shows the Cleft þ Cright and Cfull for the analysispoint indicated by the yellow star in Figure 2 as a function of 2Dscanning of fault dips. The red star indicated by the yellow arrow inFigure 4a is the maximum value of Cleft þ Cright. The x-axis of thered star is the actual fault dip for this analysis point, and it is the

Figure 2. A representative inline seismic section with two analysispoints indicated by the yellow and green stars. Candidate fault planesand 2D analysis windows for the yellow star with dip of (a) 90°,(b) 45°, and (c) the dip angle coincident with the fault plane.

Figure 3. The 3D search-based estimation of coherence using ourlocal fault model.

Figure 4. The 2D coherence results of the yellow star in Figure 2 asa function of discrete scanning windows. (a) Cleft þ Cright and(b) Cfull. The yellow arrows indicate the maximum Cleft þ Crightand its corresponding Cfull.

New fault attribute O75

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

same as the dip of the proposed fault that is coincident with theactual fault in Figure 2c. The red star indicated by the yellow arrowin Figure 4b is the Cfull corresponding to the maximum Cleft þ Cright

in Figure 4a. We treat the Cfull indicated by the yellow arrow as thecoherence of this analysis point in the 2D case. Figure 5a and 5bshows the Cleft þ Cright and Cfull for the analysis point (the purpledot) in Figure 3 as a function of scanning fault dips ðθÞ and azi-muths ðφÞ. The yellow arrows in Figure 5a and 5b indicate themaximum value of the Cleft þ Cright, and the corresponding Cfull,which are calculated when the proposed fault plane is at the samelocation of the actual fault plane. Thus, we treat the Cfull corre-sponding to the maximum Cleft þ Cright as the coherence of theanalysis point. The location ðθ;φÞ of the maximum Cleft þ Cright

defines fault dip and azimuth at the analysis point, respectively. Thegreen star in Figure 2 is the analysis point that is not located at afault. Figure 6a and 6b shows its Cleft þ Cright and Cfull as a functionof scanning fault dips ðθÞ and azimuths ðφÞ, respectively. The

yellow arrows in Figure 6a and 6b indicate the maximum valueof the Cleft þ Cright and its corresponding Cfull. Note that we alwaysobtain a high value of the Cleft þ Cright and Cfull with the changingof the fault dip and azimuth of the assumed fault plane.

Fault probability

We further analyze the statistical features for the computedCleft þ Cright at the analysis point to enhance the fault attribute.For all candidate fault planes, we should have high Cfull and Cleft þCright values at those analysis points that are not located at the faultplanes. In contrast, Cleft þ Cright that are locally high indicates a lo-cal fault plane. As a result, high Cleft þ Cright values should occurfor only a few candidate fault planes. Figure 7a and 7b shows thepercentage ofCleft þ Cright for the yellow and green stars in Figure 2,respectively. Figure 7c and 7d shows the cumulated frequency ofCleft þ Cright for the yellow and green stars in Figure 2, respectively.

Figure 5. The 3D coherence results of the yellow star in Figure 2.(a) The Cleft þ Cright as a function of a set of dip and azimuth.(b) The Cfull as a function of a set of dip and azimuth. The yellowarrows indicate the maximum Cleft þ Cright and its correspondingCfull.

Figure 6. The 3D coherence results of the green star in Figure 2.(a) The Cleft þ Cright as a function of a set of dip and azimuth.(b) The Cfull as a function of a set of dip and azimuth. The yellowarrows indicate the maximum Cleft þ Cright and its correspondingCfull.

O76 Lou et al.

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Note that we have approximately the same maximum Cleft þ Cright

(0.95) for both analysis points. However, the histogram in Figure 7bis shifted toward high value than that in Figure 7a. Furthermore,Figure 7c and 7d demonstrates that the green star has higher accu-mulated percentage for the high Cleft þ Cright than that of the yellowstar. For example, the accumulated percentage of Cleft þ Cright thatis higher than 0.7 accounts approximately 75% for the green star.However, the accumulated percentage of Cleft þ Cright that is higherthan 0.7 accounts approximately 30% for the yellow star. Based onthose observations, we propose to use the accumulated percentageto enhance our new fault attribute. The new fault probability fp isdefined as

fp ¼ C � fc; (2)

fc ¼ 1 −kK; (3)

where C is the outputted Cfull of analysis points, fc is the fault prob-ability confidence of the analysis points, k is the number of candi-date faults where value Cleft þ Cright exceeds a user-definedcoherence value, and K is the total number of candidate faults.

Fault probability smoothing along the fault plane

We smooth the fault probability along the estimated fault planefor every sample, similar to the one described by Wu and Zhu(2017), to further improve the continuity and minimize the noiseof the fault attributes. The smoothing process aims to connect pointsthat belong to the same fault plane. We define a smoothing windowcentered at the analysis point using the calculated fault dip and azi-muth of this sample. We then accumulate the fault probability fp ofsamples on the smoothing window using the cosine window Wn.The new fault attribute fsmoothedðt; x; yÞ is defined as

fsmoothedðt; x; yÞ ¼XNn¼−N

fpn �Wn; with

Wn ¼ cos

�πn

2ðN þ 1Þ�; (4)

where 2N þ 1 is the number of the samples in the smoothing win-dow. The new fault attribute fsmoothedðt; x; yÞ of the analysis pointhas a stronger response when the samples on the smoothing windowhave a similar fault dip and azimuth. Thus, the samples on the truefault planes are highlighted in our new fault attribute volume.

Figure 7. The statistical analysis of coherence values (Cleft þ Cright) for the yellow and green stars in Figure 2. (a) The percentage of Cleft þCright for the yellow star. (b) The percentage of Cleft þ Cright for the green star. (c) The cumulated frequency of Cleft þ Cright for the yellow star.(d) The cumulated frequency of Cleft þ Cright for the green star.

New fault attribute O77

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

RESULTS

To demonstrate the superiority of our proposed method, we applyit to a 2D synthetic and two 3D real seismic data. We use the analy-sis window with the same size to compute the fault probability inthe synthetic and real seismic data. The size of each subwindow is3 × 9 and 3 × 3 × 9 in the 2D synthetic data and two 3D real seismicdata, respectively. The size of the time window is nine samples cen-tered at the analysis points. The synthetic data consist of a reversefault and X-shaped faults with continuous and parallel seismic re-flection events. The real seismic data are from the F3 block, off-shore Netherlands, and the Kerry 3D survey within the Kupe fieldof the Taranaki Basin, New Zealand.

Comparative analysis for noisy synthetic seismic data

We first apply our proposed method to the synthetic seismic datashown in Figure 8a. Figure 8b shows the result of semblance-basedcoherence. Note that noticeable staircase artifacts (the blue arrow)and stratigraphic anomalies (the green arrows) are shown in Fig-ure 8b. The semblance-based coherence also fails to highlight thefault in noisy zones indicated by the red arrows in Figure 8b. How-ever, the new fault attribute computed using our proposed methodsuccessfully highlights the faults indicated by the red arrows inFigure 8c. The blue and green arrows in Figure 8c indicate thatthe staircase artifacts and stratigraphic anomalies are minimizedusing our proposed method.

Comparative analysis for the F3 block seismic survey

We then apply our proposed method to the 3D seismic data set inthe offshore Netherlands (F3). The F3 seismic survey consists of550 inlines and 800 crosslines with a sample increment of 4 ms,and a 25 × 25 m bin size. Figure 9a shows a chair display throughthe seismic amplitude volume. Figure 9b and 9c shows the result ofsemblance-based coherence and our new fault attribute overlaid onseismic data, respectively. The semblance-based coherence fails tohighlight the fault in noisy zones indicated by the red arrows inFigure 9b. Note that we have a more continuous fault attributein noisy zones indicated by the red arrows in Figure 9c. The purplearrows in Figure 9b and 9c indicate that our proposed method en-hances fault attributes in vertical sections and on time slices. Thestaircase indicated by the blue arrows is minimized using our pro-posed method.

Comparative analysis for the Kerry seismic survey

Our second test real data is the Kerry from the New ZealandPetroleum and Minerals (NZPM). This data set consists of 700crosslines and 250 inlines with a time increment of 4 ms, and a25 × 25 m bin size. Figure 10a shows the chair display of the seis-mic data. Figure 10b and 10c shows the semblance-based coherenceand our fault attribute overlaid on the seismic data, respectively. Ourproposed method minimizes the staircase artifacts and stratigraphicanomalies, which are obvious in semblance-based coherence, indi-cated by the blue and green arrows in Figure 10b and 10c, respec-tively. The semblance-based coherence fails to detect faults in thearea with a low signal-to-noise ratio indicated by the red arrows inFigure 10b. In contrast, our proposed method generates a more con-tinuous fault attribute indicated by the red arrows in Figure 10c. Thefault attributes generated using our method are more continuous andhave stronger response in the area with a low signal-to-noise ratio.Thus, our proposed method is superior to conventional coherencemethod in enhancing faults and depressing staircase artifacts andstratigraphic anomalies.

DISCUSSION

We assume that each analysis sample within the seismic surveymay belong to a fault surface with a single fault dip and azimuth. Weobtain the best local fault plane by analyzing the coherence of win-dowed seismic data divided by the local fault plane. The time analy-sis window size of the coherence computation is one of the mostcritical parameters in our method, and we suggest the time analysisof coherence computation window size should approximately equal

Figure 8. (a) The synthetic noisy image. (b) The result of the sem-blance-based coherence. (c) The result of the fault attribute gener-ated using our proposed method. The red arrows indicate the faultmasked by noise. The blue and green arrows indicate the staircaseartifacts and stratigraphic anomalies, respectively.

O78 Lou et al.

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

the time duration of one reflection event. The time analysis windowsize of fault attribute enhancement is another important parameter inour method, and we suggest the time analysis window size of faultattribute enhancement should approximately equal the length of thesmallest faults planes within the seismic survey. Our fault modelassumes that the fault plane is locally planar. Thus, our method

cannot properly address the intersecting points of the X-shapedfaults (Figure 8). However, we believe that the smoothing processwould properly “replace” high coherence values with low coher-ence values for voxels nearby intersecting points of X-shaped faults

Figure 10. Chair diagram showing data from the New ZealandKerry survey: (a) amplitude, clockwise-oriented, (b) semblance-based coherence, and (c) new fault attribute. The red arrows indicatethe fault masked by noise. The blue and green arrows indicate thestaircase artifacts and stratigraphic anomalies, respectively.

Figure 9. Chair diagram showing data from the Netherlands F3 sur-vey: (a) amplitude, clockwise-oriented, (b) semblance-based coher-ence, and (c) new fault attribute. The red arrows indicate the faultmasked by noise. The blue arrows indicate the staircase artifacts.The purple arrows indicate the fault location with discontinuousfault attributes.

New fault attribute O79

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

if we use the anisotropy smoothing filter. The anisotropic filterwould also fail to replace high coherence values with low coherencevalues if we have more than two fault sticks passing through thesame voxel. Fortunately, we have rare real cases in which more thantwo fault sticks intersect at the same voxel. The seismic data qualitydefinitely affects the effectiveness of our method. Our method can-not detect the orientation of fault planes if the semblance of seismicdata fails to highlight the faults locations.

CONCLUSION

We propose to calculate the fault attribute using a 3D scanningstrategy constrained by a local fault model. Our proposed methodsuccessfully minimizes staircase artifacts and stratigraphic anoma-lies and generates a more continuous fault attribute. The proposedmethod also precisely highlights faults in the seismic image and hasbetter antinoise performance. The fault attribute generated using ourproposed method is more continuous along the fault plane in theinline and crossline sections when compared with that of sem-blance-based coherence. However, the computation cost of our pro-posed method is higher than that of semblance-based coherence.The computation cost is proportionally increasing with the numberof hypothesized local fault plane. The number of the hypothesizedlocal fault plane equals the product between the number of discretedip and the number of azimuth of local fault plane. The discrete dipand azimuth of fault plane in this paper range from −40° to 40° and0° to 180°, respectively. The increments of the dip and azimuth offault plane are 10° and 20°, respectively. Thus, our computation costis approximately 80 times higher than the conventional semblance-based coherence.

ACKNOWLEDGMENTS

The authors thank the Netherlands Organization for AppliedScientific Research (TNO) and NZPM for providing the seismicdata used in this study to the general public.

DATA AND MATERIALS AVAILABILITY

Data associated with this research are available and can be ac-cessed via the following URL: https://wiki.seg.org/wiki/Open_data.

REFERENCES

Aqrawi, A. A., and T. H. Boe, 2011, Improved fault segmentation using a dipguided and modified 3D Sobel filter: 81st Annual International Meeting,SEG, Expanded Abstracts, 999–1003, doi: 10.1190/1.3628241.

Bahorich, M., and S. Farmer, 1995, 3D seismic discontinuity for faults andstratigraphic features: The coherence cube: The Leading Edge, 14, 1053–1058, doi: 10.1190/1.1437077.

Bakker, P., L. J. van Vliet, and P. W. Verbeek, 1999, Edge-preserving ori-entation adaptive filtering: Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition 1, 535–540.

Barnes, A. E., 1996, Theory of 2-D complex seismic trace analysis:Geophysics, 61, 264–272, doi: 10.1190/1.1443947.

Cohen, I., N. Coult, and A. A. Vassiliou, 2006, Detection and extraction offault surfaces in 3D seismic data: Geophysics, 71, no. 4, P21–P27, doi: 10.1190/1.2215357.

Donias, M., C. David, Y. Berthoumieu, O. Lavialle, S. Guillon, and N.Keskes, 2007, New fault attribute based on robust directional scheme:Geophysics, 72, no. 4, P39–P46, doi: 10.1190/1.2718605.

Fehmers, G. C., and C. F. Höcker, 2003, Fast structural interpretation withstructure-oriented filtering: Geophysics, 68, 1286–1293, doi: 10.1190/1.1598121.

Hale, D., 2009, Structure-oriented smoothing and semblance: CWP Report,635, 261–270.

Hale, D., 2013, Methods to compute fault images, extract fault surfaces, andestimate fault throws from 3D seismic images: Geophysics, 78, no. 2,O33–O43, doi: 10.1190/geo2012-0331.1.

Luo, Y., W. G. Higgs, and W. S. Kowalik, 1996, Edge detection and strati-graphic analysis using 3D seismic data: 66th Annual International Meet-ing, SEG, Expanded Abstracts, 324–327, doi: 10.1190/1.1826632.

Luo, Y., M. Marhoon, S. Al-Dossary, and M. Alfaraj, 2002, Edge-preservingsmoothing and applications: The Leading Edge, 21, 136–158, doi: 10.1190/1.1452603.

Marfurt, K. J., 2006, Robust estimates of 3D reflector dip and azimuth: Geo-physics, 71, no. 4, P29–P40, doi: 10.1190/1.2213049.

Marfurt, K. J., R. L. Kirlin, S. H. Farmer, and M. S. Bahorich, 1998, 3Dseismic attributes using a running window semblance-based algorithm:Geophysics, 63, 1150–1165, doi: 10.1190/1.1444415.

Marfurt, K. J., and T. Lin, 2017, What causes those annoying stair stepartifacts on coherence volumes?: AAPG Search and Discovery, Article37830.

Marfurt, K. J., V. Sudhakar, A. Gersztenkorn, K. D. Crawford, and S. E.Nissen, 1999, Coherency calculations in the presence of structural dip:Geophysics, 64, 104–111, doi: 10.1190/1.1444508.

Neff, D. B., J. R. Grismore, and W. A. Lucas, 2000, Automated seismic faultdetection and picking: U.S. Patent 6,018,498.

Pedersen, S., 2007, Image feature extraction: U.S. Patent 7,203,342.Pedersen, S., 2011, Image feature extraction: U.S. Patent 8,055,026.Qi, J., and J. Castagna, 2013, Application of a PCA fault-attribute and

spectral decomposition in Barnett Shale fault detection: 83rd AnnualInternational Meeting, SEG, Expanded Abstracts, 1421–1425, doi: 10.1190/segam2013-0674.1.

Qi, J., F. Li, and K. J. Marfurt, 2017, Multiazimuth coherence: Geophysics,82, no. 6, O83–O89, doi: 10.1190/geo2017-0196.1.

Qi, J., B. Lyu, A. AlAli, G. Machado, Y. Hu, and K. J. Marfurt, 2018, Imageprocessing of seismic attributes for automatic fault extraction: Geophys-ics, 84, no. 1, O25–O37, doi: 10.1190/geo2018-0369.1.

Qi, J., G. Machado, and K. J. Marfurt, 2017, A workflow to skeletonizefaults and stratigraphic features: Geophysics, 82, no. 4, O57–O70, doi:10.1190/geo2016-0641.1.

Wang, S., S. Yuan, T. Wang, J. Gao, and S. Li, 2018, Three-dimensionalgeosteering coherence attributes for deep-formation discontinuity detec-tion: Geophysics, 83, no. 6, O105–O113, doi: 10.1190/geo2017-0642.1.

Wang, W., J. Gao, and K. Li, 2008, Structure-adaptive anisotropic filter withlocal structure tensors: Second International Symposium on IntelligentInformation Technology Application 2, 1005–1010.

Wu, X., 2017, Directional structure-tensor based coherence to detect seismicchannels and faults: Geophysics, 82, no. 2, A13–A17, doi: 10.1190/geo2016-0473.1.

Wu, X., and S. Fomel, 2018, Automatic fault interpretation with optimal surfacevoting: Geophysics, 83, no. 5, O67–O82, doi: 10.1190/geo2018-0115.1.

Wu, X., and D. Hale, 2016, 3D seismic image processing for faults:Geophysics, 81, no. 2, IM1–IM11, doi: 10.1190/geo2015-0380.1.

Wu, X., and Z. Zhu, 2017, Methods to enhance seismic faults and constructfault surfaces: Computers and Geosciences, 107, 37–48, doi: 10.1016/j.cageo.2017.06.015.

Yuan, S., Y. Su, T. Wang, J. Wang, and S. Wang, 2018, Geosteering phaseattributes: A new detector for the discontinuities of seismic images: IEEEGeoscience and Remote Sensing Letters, 99, 1–5, doi: 10.1109/LGRS.2018.2881674.

Zhang, B., Y. Liu, M. Pelissier, and N. Hemstra, 2014, Semiautomatedfault interpretation based on seismic attributes: Interpretation, 2, no. 1,SA11–SA19, doi: 10.1190/INT-2013-0060.1.

O80 Lou et al.

Dow

nloa

ded

07/3

1/19

to 6

8.97

.115

.26.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/