3-D seismic discontinuity for faults and stratigraphic features:

The coherence cubeMIKE BAHORICHAmoco Corporation

Denver, CO

Seismic data are usually acquired and processed for imag-ing reflections. This paper describes a method of processingseismic data for imaging discontinuities (e.g., faults andstratigraphic features). One application of this nontraditionalprocess is a 3-D volume, or cube, of coherence coefficientswithin which faults are revealed as numerically separated sur-faces. Figure 1 compares a traditional 3-D reflectionamplitude time slice with the results of the new method.

To our knowledge, this is the first published method ofrevealing fault surfaces within a 3-D volume for which nofault reflections have been recorded.

Traditional 3-D seismic interpretation. A major advantageof 3-D technology is that, unlike 2-D which is essentially lim-ited to vertical cross-sections, it allows seismic data to be dis-played in horizontal or “map” form. Geoscientists havetraditionally used two kinds of seismic map displays: ampli-tude time and seismic horizon slices. The former is a hori-zontal plane through the 3-D data volume (Figure 1 a) withoutreference to a stratigraphic horizon. It permits an interpreterto view geologic features in map form without having to firstpick seismic events. In spite of this advantage, leading voicesin the industry (such as Alistair Brown) maintain the timeslice is quite underutilized. A probable reason is that ampli-tude time slices are often difficult to interpret.

When using traditional methods, it is often difficult to geta clear and unbiased view of faults and stratigraphic featureshidden in the 3-D data. Faults are (often) readily seen onindividual vertical cross-sections, but many of these must beexamined to determine the lateral extent of faulting. Strati-graphic changes are difficult to detect on vertical seismiclines because of the limited profile they present in this view.Time slices are more suitable for detecting and followingfaults and stratigraphy laterally.

However, interpretation is often complicated by the factthat time slices can cut through different stratigraphic hori-zons. This problem can be avoided through the use of thehorizon slice - the set of seismic amplitudes associated withan interpreted horizon surface, generally at some consistentstratigraphic level. Although horizon slices are more usefulthan amplitude time slices for following faults and strati-graphic features, they too have disadvantages. The geoscien-tist must pick a stratigraphic horizon. This can be difficultand time consuming, and it also imposes an interpretive biason the data set.

3-D coherence. Coherence calculations can help with theproblems mentioned above. 3-D seismic data are generallybinned into a regular grid. By calculating localized waveformsimilarity in both in-line and cross-line directions, estimatesof 3-D dimensional seismic coherence are obtained (Figure

STEVE FARMERAmoco Corporation

Tulsa, OK

2). Small regions of seismic traces cut by a fault surface gen-erally have a different seismic character than the correspond-ing regions of neighboring traces (Figure 3). This results in asharp discontinuity in local trace-to-trace coherence. Calcu-lating coherence for each grid point along a time slice resultsin lineaments of low coherence along faults. When thisprocess is repeated for a series of time slices, these linea-ments become fault surfaces, even though fault plane reflec-tions have not been recorded. Stratigraphic boundariesgenerate similar discontinuities. The technique may be em-ployed to produce coherence horizon slice maps, or to trans-form a reflection amplitude 3-D data volume into an entirelynew volume or “cube” of coherence coefficients.

Map views of coherence data afford the opportunity to seestratigraphic changes more clearly. For example, the channelfeatures that are readily apparent to laymen in the coherencetime slice of Figure 4a are very difficult to see in a traditionalamplitude time slice.. . even for an experienced geoscientist.Coherence information provides a different perspective whenused in conjunction with amplitude data. In areas where highseismic amplitudes are often associated with hydrocarbonaccumulations (such as the Gulf of Mexico), the stratigraphicand structural context may be identified more clearly fromcoherence data. As an example, the bright spot in Figure 4bis located within the channel seen on the coherence display(Figure 4a).

Faults parallel to strike. Conventional amplitude timeslices are often useful for viewing faults that run perpendic-ular to strike. However, when faults run parallel to strike, theybecome more difficult to see because the fault lineamentsbecome superimposed on bedding lineaments. The coherencecalculation suppresses laterally consistent features, in effectremoving the bedding. Because of this, the 3-D coherencealgorithm reveals faults in any orientation equally well. Fig-ures from a 3-D survey in Trinidad illustrate this point. A faulttrace is highlighted with dots on the amplitude slice in Figure5a. The fault is clear until it cuts parallel to the strike of bed-ding, where it becomes quite difficult to see on the time slice.The fault is clear in every orientation on the coherence timeslice of Figure 5b.

Regional geologic interpretation. Until recent years, most3-D surveys covered relatively small areas. But the success ofthe technique and falling costs have caused surveys to be-come larger. Now some vast spec 3-D surveys cover hundredsof square kilometers and run to tens of millions of traces.Sorting through that amount of information is a dauntingtask. However, since calculating coherence is an noninter-pretive process, it can quickly provide the geoscientist with aview of regional faulting. Compare Figure 6a (time slice) and

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Figure 1. (a) Traditional 3-D seismic time slice. Faults parallel to strike are difficult to see. (b) Coherency time slice.Faults are clearly visible.

Figure 6b (coherence time slice). A “flip frame” animation of high coherence trapped against fault lineaments. Also notecoherence time slices can provide a quick view of how faults the bright spot within the channel system in the south centralare changing with depth. portion of the survey.

Structure, stratigraphy, and hydrocarbons. Several in-teresting relationships between structure and stratigraphy areapparent in Figure 6b. Two major channels run from north-to-south toward a salt dome. As they approach the intrusive salt,which has caused upward distortion of the bedding adjacentto the intrusion, the channels deflect away from the structuralhigh. On the southeast portion of the display, a channel sys-tem crosses a fault and makes an abrupt turn to the east, par-alleling the fault on the downthrown side. Note the point barthat is clearly seen within the channel. In the northeast por-tion of the survey, bright spots are represented by areas of

Horizon dip/azimuth/edge pitfalls. Several map analysistechniques exist for highlighting faults on an interpreted sur-face. The dip magnitude or dip azimuth of the surface may beestimated and edge detection (or enhancement) techniquesmay be applied. These methods have proven very useful forthe detection of subtle faults. However, these techniques mayonly be employed after the horizon has been interpreted by ageoscientist. In addition, successive horizons must be inter-preted in order to get a 3-D perspective of faulting. Onepotential pitfall in using these methods is that they aredependent upon the skill of the interpreter and upon the

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Figure 2.3-D coherence may be measured by calculatingseismic trace similarity in the inline and crossline direc-tions. A three-trace operator is depicted. This is the min-imum size required for a 3-D calculation although moretraces can be used. Coherence may be measured fromtrace A to trace C and from trace A to trace B. A combi-nation of these 2-D measurements provides a measure of3-D coherence. For a nine-trace operator, coherencemight be measured from the center trace to each of itsneighbors. Even larger operators can be applied in a sec-ond-stage process that is particularly useful when dealingwith noisy data.

Figure 3. Faults are highlighted by the 3-D coherencetechnique because traces are not identical on oppositesides of a fault. In this example, missing stratigraphic sec-tion from one side of a fault to another generates slightlydifferent reflectivity on one side of the fault. The coher-ence is lower when the traces are less similar.

Figure 4. (a) Coherence slice across a channel system. Co-herence images the stratigraphic context better while am-plitude data in the next panel image hydrocarbons moreclearly. (b) Average amplitude over a series of time slices.Note that the bright spot is located within the channelseen on the coherence display.

Figure 5. (a)Time slicefrom Trinidadover typicalcomplex fault-ing. Note thatthe fault isdifficult to seewhen parallelto strike (lookbetween themiddle twodots).(b) Coherenceslice of sameregion.Note thatparallel orperpendicularfaulting ishighlightedequally well.

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Figure 6. (a) Time slice at 1250 ms exhibits two major channels, a minor channel including evidence of a cut bank andpoint bar, en-echelon growth faults, radial faults, a salt dome and bright spots. (Data courtesy of Geco-Prakla).(b) Coherence slice at 1250 ms shows clear relationship between faults and stratigraphic features. The two channels avoidthe high generated by the salt dome. The channel in the lower center of the figure crosses a major fault and abruptly turnsto the east, paralleling the fault and leading to a cut bank and point bar. Note the radial and en-echelon faulting.

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Figure 7. (a) Dip map generated over a carefully pickedand autotracked horizon in an area of fair-to-poor dataquality. Poor data have caused the generation of spuriouslinear and circular features. Note the fault marked withan arrow has a bend. (b) Coherence slice generated abouta constant time window approximately equivalent to thehorizon of interest in Figure 7a. This coherence sliceappears somewhat out of focus due to the fair-to-poordata quality. Note that the fault marked with an arrowdoes not have a bend. (c) Dip map generated over thesame horizon as Figure 7a after reinterpretation of thehorizon using information from the coherence slice. Notethat the fault marked with an arrow no longer has a bend.

Figure 8. (a) Edge detection performed on the interpretedwater-bottom horizon. The channel is partially visible hutthe fan is not. (b) Coherence calculated on the seismicdata about the water-bottom horizon. The channel is morecontinuous on the coherence data and the fan is visible.

accuracy of the horizon autotracking software. In certain sit-uations, the horizon autotracker may mispick the desiredhorizon. Subsequent analysis with horizon-based fault detec-tion techniques sets up a scenario where the autotrackercreates a discontinuity that the dip, azimuth, or edge mapconfirms.

A dip map was generated from a carefully picked andautotracked horizon interpreted over a land data set with poorsignal-to-noise ratio (Figure 7a). Note that the fault markedwith an arrow has a bend in it. A coherence time slice (Figure7b) was run about a time slice as close as possible to the timeof the horizon of interest. Note that it appears somewhat outof focus due to the poor seismic data quality and that it reveals

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Figure 9. (a) Coherence time slice at 1700 ms in light blue; coherence time slice at 1750 ms dark blue. Top view. (b)Shallow times (1500 ms) are red, medium times (1750 ms) are green, and deeper times (2000 ms) are dark blue. (c) 3-Dvisualization in which high coherence values are transparent and low values remain, revealing fault surfaces. Note thatthe fault orientation is seen in three dimensions though no fault reflections have been recorded. No interpretation has beenperformed to reveal the faults; this is a display of raw seismic after application of the 3-D coherence algorithm.

a continuous fault without a bend. Because of the discrepan-cies between the faults seen on the coherence time slice andthe dip map, the horizon and fault were reinterpreted and thedip map regenerated (Figure 7c). Note that the bend in thefault is now removed and the fault’s overall appearance ismore similar to the one seen on the coherence time slice.

In areas of fair to poor data quality, coherence maps mayappear more out of focus than those obtained with traditionalmap-analysis techniques (dip, azimuth, edge detection, andresidual) although the latter exhibit spurious linear and cir-cular features. If the data are of good quality and the inter-preter and horizon autotracker have performed well,coherence along a horizon may highlight faults in a fashionsimilar to the results obtained with conventional map analy-sis techniques. Stratigraphic features are often better imagedwith the coherence method. An example involves a water-bottom horizon interpreted on a 3-D seismic survey in theGulf of Mexico. 3-D coherence, calculated over a fixed-length window tracking below the water bottom, revealed asubmarine channel system leading to a recent deep-water fan.Figure 8 compares edge detection and coherence displays ofthis feature. Note that portions of the channel are more con-tinuous on the coherence data and the image of the submarinefan is better.

F ault surfaces. In the process of calculating coherence for a3-D data volume, faults become numerically separated fromthe data which surrounds them. In other words, faults gener-ate surfaces of low coherence. By employing visualizationsoftware, these fault surfaces may be observed in threedimensions from any perspective even though no fault planeshave been recorded (Figure 9).

Not only are these surfaces distinctly separated fromneighboring data, they are also numerically separated,enabling them to be picked using horizon autotracing soft-ware. This fault autopicking technique enables the interpreterto have a fault pick on every trace, adding significant detail tothe fault interpretation.

Conclusions. This new method of detecting, imaging, andautotracking faults and stratigraphic features has had imme-diate and significant financial impact evidenced by reserveshighlighted in Amoco’s 1994 annual report to shareholders.

3-D seismic discontinuity/coherence has important applica-tions for the analysis of 3-D structure and stratigraphy, and isa valuable adjunct to conventional amplitude data. Thismethod reveals fault surfaces within a 3-D seismic volumewhere no fault plane reflections have been recorded.

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