Gao 2004 Geophysics

GEOPHYSICS, VOL. 69, NO. 4 (JULY-AUGUST 2004); P. 958–967, 8 FIGS.10.1190/1.1778239

Texture model regression for effective feature discrimination: Applicationto seismic facies visualization and interpretation

Dengliang Gao∗

ABSTRACT

The classical approach to feature discrimination requiresextraction and classification of multiple attributes. Such anapproach is expensive in terms of computational time andstorage space, and the results are generally difficult to in-terpret. With increasing data size and dimensionality, alongwith demand for high performance and productivity, the ef-fectiveness of a feature-discrimination methodology has be-come a critically important issue in many areas of science. Toaddress such an issue, I developed a texture model regres-sion (TMR) methodology. Unlike classical attribute extrac-tion and classification algorithms, the TMR methodologyuses an interpreter-defined texture model as a calibratingfilter and regresses the model texture with the data tex-ture at each sample location to create a regression-gradientvolume. The new approach not only dramatically reducescomputational cycle time and space but also creates bet-ters results than those obtained from classical techniques,resulting in improved feature discrimination, visualization,and interpretation.

Application of the TMR concept to reflection seismicdata demonstrates its value in seismic-facies analysis. In

order to characterize reflection seismic images composedof wiggle traces with variable amplitude, frequency, andphase, I introduced two simple seismic-texture models inthis application. The first model is defined by a full cycleof a cosine function whose amplitude and frequency arethe maximum amplitude and dominant frequency of wig-gle traces in the interval of interest. The second model isdefined by a specific reflection pattern known to be asso-ciated with a geologic feature of interest, such as gas sandin a hydrocarbon reservoir. I applied both models to a sub-marine turbidite system offshore West Africa and to a gasfield in the deep-water Gulf of Mexico, respectively. Basedon extensive experimentation and comparative analysis, Ifound that the TMR process with such simple texture mod-els creates superior results, using minimal computationalresources. The result is geologically intriguing, easily in-terpretable, and consistent with general depositional andreservoir-facies concepts. Such a successful application maybe attributable to the sensitivity of image texture to physi-cal texture in the Fresnel zone at an acoustic interface andtherefore to lithology, depositional facies, and hydrocarbonsaturation.

INTRODUCTION

Feature discrimination and visualization are fundamentalto exploratory data analysis in many areas of science. Con-ventionally, feature discrimination and visualization involvemultiple processes, computationally intensive algorithms, andhigh-dimensional data sets to reduce nonuniqueness (e.g., Reutet al., 1985; Richards, 1993; Sheriff and Geldart, 1995; Ahern,1999; Roweis and Saul, 2000; Seung and Lee, 2000; Bertrand,2001; Freedman et al., 2001). Basically, a typical workflow iscomposed of three dependent components. First, a suite of al-gorithms performs attribute extraction by calculating multiplequantities from an original data set that represent observa-tions from different perspectives (e.g., Haralick et al., 1973;

Manuscript received by the Editor December 11, 2002; revised manuscript received March 15, 2004.∗Marathon Oil Company, P.O. Box 3128, Houston, Texas 77056. E-mail: [email protected]© 2004 Society of Exploration Geophysicists. All rights reserved.

Taner and Sheriff, 1977; Taner et al., 1979; Reed and Hussong,1989; Turcotte, 1992; Gao et al., 1998; Gao, 2002, 2003). Second,dimensionality reduction is achieved by transforming the high-dimensional, observational attributes into low-dimensional,condensed attributes (Jolliffe, 1986; Cox and Cox, 1994). Third,condensed attributes are reduced further into a final thematicset that groups features into a limited number of categories ina process called multivariate classification (Ritter and Hepner,1990; Richards, 1993; Gurney, 1997).

The workflow from attribute extraction through dimension-ality reduction to multivariate classification requires significantamounts of computational time, storage space, and manual in-tervention, making the approach impractical for large volumesof data, such as three-dimensional (3D) seismic data sets that

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Texture Model Regression for Facies Analysis 959

are typically on the order of 109 samples. Also, the result fromsuch an approach is usually difficult to interpret and resistantto interactive quality control because the result is shown as adiscrete number of classes on a classification map and relieson any number of input attributes whose physical implicationsare usually unknown. This deficiency is particularly acute infrontier regions where little calibration data are available.

Here, a fundamental issue is the effectiveness of an at-tribute or a combination of multiple attributes in discriminatingfeatures. Theoretically, each additional uncorrelated attributeadds a new dimension to the attribute space and, thus, con-tributes to better discrimination because features are more sep-arable in a higher-dimensional attribute space than in a lowerone. Practically, however, increasing data dimensionality re-quires more computation time and storage space and makes vi-sualization/interpretation complicated. Therefore, many inter-preters have difficulty managing and interpreting a large num-ber of seismic attributes, and some authors (e.g., Kalkomey,1997) recommended avoiding the use of a large number of at-tributes to classify geologic features of interest to avoid falsecorrelation. As the number of attributes and dimensionality ofattribute space are reduced, the computational time and stor-age space decrease, and the interpretation and classificationprocesses become easier. Ideally, if a single, powerful attributecould well-represent important features, the weight of that at-tribute relative to the others would be overwhelmingly high;thus, one such single attribute would contribute much more toa robust discrimination than a combination of many others.

Therefore, there is a need to develop an algorithm that iscomputationally efficient, conceptually inclusive, functionallyversatile, and physically meaningful. The texture model regres-sion (TMR) methodology discussed in this paper satisfies thesecriteria. In the following sections, I introduce the TMR concepton a general basis to emphasize its broad applicability. Then,I apply the concept to reflection seismology to demonstrateits value for seismic-facies analysis. I suggest that the success-ful application is attributable to a genetic link between imagetexture and physical texture in the Fresnel zone at an acousticinterface. Such a link is critical to better understand the geo-logic implications of the TMR methodology for seismic faciesinterpretation.

CONCEPTS AND METHODOLOGY

To make the TMR methodology simple and easy to com-prehend, consider a familiar word-pattern search, for examplegas sand in a word document. The use of just a single charac-ter g as a filter most likely results in a large number of words,most of which have no bearings on gas sand. Instead, if I usethe eight-character gas sand as a filter, I can discriminate andisolate the word much more effectively because all charactersand their lateral relationships are involved in the process toreduce nonuniqueness.

To make this process more practical, consider a general casein which the word pattern to be searched is unknown or un-certain. In such a case, I can use the word model gas ???? as afilter for word patterns that begin with gas throughout the worddocument. As a result, all gas-related word patterns, includinggas sand, are identified with enhanced efficiency and produc-tivity. However, a major limitation of this process is the dif-ficulty in distinguishing gas sand from other gas-related word

patterns such as gas cap and gas chimney, since the three wordpatterns are grouped into the same category.

To make the process even more effective, assume that theword-search engine has an advanced functionality that calcu-lates a continuum of pattern similarities relative to the modeland color codes all word patterns based on their similarity val-ues. Although gas sand is not identical to the model gas ????,all such word pairs should have the same similarity value (e.g.,0.55), permitting them to be distinguished and isolated fromgas cap, gas chimney, and the rest of the text. Furthermore, Ican still discriminate and isolate gas sand using a different wordmodel as a filter, simply because it is the similarity difference,not the absolute value, that makes gas sand distinguishablefrom other word patterns.

Similar to word-pattern recognition, amplitude-patternrecognition in a digital image domain is based primarily uponimage texture that is defined by the magnitude, variation, andrelationship of data samples at a given sample location in theimage space. At each sample location, texture is characterizedby using a small analysis window, which is usually called a tex-ture element or texel by workers in this area to imply its func-tionality (e.g., Haralick et al., 1973; Reed and Hussong, 1989;Gao et al., 1998; Gao, 1999a, 1999b, 2001, 2002, 2003) (Fig-ure 1). The work flow for the TMR is fundamentally a processthat characterizes a texel at each sample location in the imagespace using a user-defined texel model as a regression filter(Figure 2).

Unlike other digital images, a reflection seismic image iscomposed of wiggle traces that appear to be similar to a cyclictrigonometric function with variable amplitude, phase, and fre-quency (Taner and Sheriff, 1977; Taner et al., 1979; Sheriff and

Figure 1. Hierarchy of visualization terms from a 2D pixel,through a 3D voxel, to a 3D texel. The texel is geometricallyequivalent to a cubic window, but here it is so called to denote itsfunctionality as a texture element and also for convenience ofdescription in image texture analysis. In this example, the texelis composed of 405 (9 by 9 by 5) voxels (samples). At each of thesample locations in a 3D image space, a texel is characterized byanalyzing and evaluating its internal amplitude configuration.

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Geldart, 1995). Wiggle traces are aligned in x and y directionsto depict geologic features, with limited resolution. Therefore,recognizing seismic texture is actually characterizing the set ofwiggle traces.

To characterize seismic wiggle traces effectively, I experi-mented with two prototype models. First, I tested a standardmodel (model case 1) defined by a full cycle of a trigonometriccosine function (Figure 3a), whose amplitude and frequencyare the maximum amplitude and the dominant frequency, re-spectively, of the wiggle traces in the interval of interest. Thedominant frequency is obtained using a Fourier transform, butin practice, it is estimated simply by measuring the averagetravel time between neighboring peaks or troughs of wiggletraces within the interval of interest. Because of its affinityand sensitivity to seismic wiggle traces, I thought such a cosinemodel might be effective in characterizing reflection seismicfacies in frontier sedimentary basins where little well-bore in-formation is available. Second, I tested a texture model derivedfrom seismic data (model case 2) that represents a specific de-positional or reservoir facies based on well-bore information(Figure 3b). Unlike model case 1, the model case 2 subroutinefirst investigates the volume on a running-window basis to findan object pattern of interest. Typical model patterns include,for example, high amplitude and low frequency, with troughover peak; low amplitude and high homogeneity; high ampli-tude and high contrast; and hummocky or chaotic amplitudeand high randomness, etc. It can also be a synthetic seismo-gram computed from sonic and density logs. Specifically, if aninterpreter is interested in a seismic facies that is related to oiland gas accumulation, the algorithm extracts from the reser-voir interval a texture model that is considered most likely to bethe hydrocarbon-related feature, thus, helping to extrapolateand predict depositional and reservoir facies in well-developedsedimentary basins where extensive well data are available.

With the model texel determined, I retrieve a data texel ateach sample location that is set to be the same size as the modeland plot a scattergram between model and data texels. Then Iperform a linear regression analysis on the scattergram. Typi-

Figure 2. A flowchart showing TMR methodology.

cally, I use a least-squares technique to calculate gradient (α),intercept (β), and scattering (γ ) of the regression line using thefollowing equations:

α =

n∑i=1

{[T D

i (x, y, z)− T D(x, y, z)](T M

i − T M)}

n∑i=1

(T M

i − T M)2

, (1)

β = T D(x, y, z)− αT M , (2)

and

γ = 1/nn∑

i=1

[T D

i (x, y, z)− T D(x, y, z)+α(T Mi − T M

)]2,

(3)where n is the number of samples in the texel, and T D(x, y, z)and T M denote the mean values of the data texel T D(x, y, z)and the model texel T M , respectively. The regression gradient(α), which ranges from 0.0 to 1.0, is a measure of similarity ofthe data texture relative to the model texture.

The linear, least-squares technique has limitations that mayaffect the effectiveness of the TMR concept. First, for equation(1) to be mathematically meaningful, its denominator must notbe zero; that is, the amplitude of the model texture must not beconstant (plain texture). Second, there are certain cases wheredifferent features may not be distinguishable based solely onthe α value. In such cases, the values of β and γ may provideadditional constraints. The β value is a measure of amplitudebulk shift that usually results from amplitude scaling, whereasthe γ value is a measure of the deviation of amplitude fromthe regression line, a measure that generally indicates regres-sion quality. Although a nonlinear regression subroutine couldmake the TMR process more effective, the linear, least-squaressubroutine has the advantage of computational efficiency and,in most cases, achieves the objective.

Last, I map the values of α, β, and γ in the highest resolu-tion (32 bit). Although the values of β and γ may be used asadditional constraints to reduce nonuniqueness of the α value,I usually elect to calculate the α value alone and visualize it onhorizon slices to facilitate interactive facies interpretation.

GEOLOGIC IMPLICATIONS

A reflection seismic response is a composite function of manyphysical properties at an acoustic interface in the subsurface.Typically, a reflection seismic response has been attributed toacoustic/elastic impedance and Poisson’s ratio changes at aninterface. However, a seismic signal is reflected from a Fres-nel zone rather than a single “point” at an interface. Physicaltexture in the Fresnel zone at an interface, defined by morpho-logical features such as roughness or rugosity, may contributesignificantly to seismic amplitude and waveform as a result ofconstructive and destructive interference by signals reflectedfrom contributing “micromirrors” in the Fresnel zone. Sincephysical texture at an acoustic interface is critical to partition-ing of backscattered, reflected, and transmitted acoustic en-ergy, its acoustic impact and geologic implications cannot beignored.

Physical texture in the Fresnel zone at an acoustic interfaceis a function of morphological characteristics and is suggestiveof lithology, depositional environment, and fluid saturation.


For example, a carbonate-shale interface has a rougher texturethan a sand-shale interface; marine shale in a highstand systemstract has a smoother texture than channel sand and mass trans-port complex in a lowstand systems tract; similarly, a maximumflooding surface may have a texture distinct from a sequenceboundary; a fluid contact may have a smoother texture thana regular lithofacies contact; and an interface with an abruptlithologic change has a sharper texture than one with a grada-tional lithologic change. Therefore, seismic texture characteri-zation provides an important basis for predicting and inferringdepositional environment and facies, although not in as muchdetail as from direct observation of outcrops. This situationis analogous to side-scan sonar imagery, where backscatteredamplitude intensity and texture have been well-recognized asreliable indicators of sea-floor sediments and roughness (e.g.,Reut et. al., 1985; Reed and Hussong, 1989; Gao et. al., 1998).

Figures 4 and 5 illustrate the application of the TMR method-ology to seismic-facies analysis in a submarine turbidite systemoffshore Angola, West Africa. Since little well data are avail-able in the study area, I elected to use model case 1 as the

Figure 3. Two examples of texture-model construction scenarios in the TMR process.(a) A standard model consisting of a full cycle of trigonometric cosine waves. (b) Awiggle-trace model consisting of data traces of gas sand in a reservoir interval drilledby exploration and production well bores.

regression filter in the TMR process. The dominant frequencywas obtained by measuring the average time between neigh-boring troughs in the interval of the middle Miocene channel-fan deposits. The average time is 60 ms, which is equivalent to afrequency of 16.7 Hz for the model to be used in the regressionprocess. After initial processing, the result obtained using thissimple model significantly helped delineate the geometry, arealextent, and lateral relationships of critical depositional facies,such as the bypassed channel fill, levee/overbank, and lobes inthe turbidite system. Experiments and comparisons with classi-cal attribute-extraction algorithms showed this simple model-regression process to be not only computationally efficient butto produce superior results that are more inter pretable thanthose obtained using classical attribute-extraction algorithms.

Figure 4 shows a channel-fan system imaged at a depthof 4000 ft (1220 m) below the sea floor. The well-organizeddistribution pattern and details shown in the TMR result(Figure 4b) are most intriguing and very consistent with a typi-cal turbidite depositional pattern. The meandering, migrating,and cross-cutting channels are easily recognizable and inter-

pretable. On both sides of the channelsare laterally more extensive facies, pos-sibly levee/overbank deposits. Distributedlobes in the frontal portion of the later-ally extensive fan deposits were apparentlyfed by a braid of linear channels upslopefrom the northeast. Although this resultis not derived from a clustering or neuralnetwork-based classification algorithm, thewell-organized pattern is physically mean-ingful and can be easily categorized intogeologically distinctive and spatially asso-ciated facies classes. For example, I recog-nize at least five different depositional fa-cies (denoted as 1, 2, 3, 4, and 5). Basedon their distribution, geometry, and spatialrelationships, coupled with the subregionaldepositional setting and limited explorationwell-bore information, I interpret the pro-gression from facies 1 to 5 to be associatedwith decreasing sand content from a proxi-mal levee to a distal overbank or marine-shale environment. The channel-fill faciesis distinct from the levee facies and possi-bly represents a bypassed channel that isfilled with shale. In addition to the five ma-jor facies, I am also able to recognize andmap more detailed facies changes simplyby fine-tuning the color-mapping functionin an interactive manner. All of these in-terpretations are consistent, in this partic-ular area, with a regional facies architec-ture and, in general, with depositional faciespatterns that are typically observed fromcontemporary and ancient deep-water de-positional systems. In contrast, it is difficultto visualize, map, and interpret detailed fa-cies changes and lateral relationships fromthe regular amplitude data (Figure 4a), eventhough the existence of a major channel-fandepositional system is recognizable.

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Figure 5 shows the same channel-fan system from four dif-ferent perspectives. It is difficult to recognize and visualizethe same level of detail as that shown in Figure 5a from av-erage absolute amplitude (Figure 5b), coherence (Figure 5c),or instantaneous frequency (Figure 5d). Average absolute am-plitude (Figure 5b) indicates extensively distributed high am-plitude but fails to distinguish the channel-fill facies fromlevee/overbank and lobes, and the whole image has a muchlower resolution. Coherence (Figure 5c) iseffective in enhancing lateral discontinu-ities and is particularly useful for delin-eating outlines of channels or fault traceson time slices; however, facies variationsacross boundaries are totally invisible tothe algorithm. Instantaneous frequency(Figure 5d) is not effective at discrimi-nating different facies or even at demon-strating the overall channel-fan geometricpattern.

Figure 6 illustrates a complex channelsystem imaged from four different perspec-tives in the same region as in Figure 5but at a different stratigraphic level. TheTMR result shown in Figure 6a delineatesa channel system that has different geome-try and facies than that shown in Figure 5.The increased sinuosity and α value alongthe channel at this stratigraphic intervalsuggest sand-prone deposits in the downs-lope portion of a turbidite system. Thisvertical change in facies and geometry ofchannel systems may have important im-plications for understanding the deposi-tional history and sequence stratigraphy ofthe system. In contrast, average absoluteamplitude (Figure 6b) has limited resolu-tion, particularly in the eastern portion ofthe channel system. Although coherence(Figure 6c) effectively delineates channelboundaries, it contributes very little toresolving lateral facies variations withinand outside the channel. Instantaneousfrequency (Figure 6d) poorly defines notonly facies variations associated with chan-nels but even the meandering pattern ofchannels.

Figures 7 and 8 show an example froma gas field in the deep-water Gulf ofMexico, illustrating implications of theTMR methodology for reservoir-facies dis-crimination and visualization. The reser-voir, consisting of lower Pliocene high-quality sand, was formed in a steeplydipping monocline that laterally pinchesout against a salt body to the north. To theeast and west, the monoclinal reservoir isbounded by two major subvertical faults.These stratigraphic and structural relation-ships are favorable for migration and en-trapment of hydrocarbons updip along themonocline (Figures 7 and 8). Since move

than 20 wells are available in this field, I constructed a tex-ture model using wiggle traces that are known to be associatedwith gas sand in the reservoir interval (model case 2). The re-sults obtained (Figures 7b and 8a) using such a model helpdifferentiate upslope gas sand from downslope wet sand in allthe major reservoirs, and the interpretation is consistent withdrilling results from exploration and production operations(e.g., Figure 7b and 8a). However, it is difficult to recognize

Figure 4. (a) Original amplitude of a channel-fan system in deep-water offshoreAngola, West Africa. (b) The TMR result derived from the original amplitude datausing a standard cosine model as the regression filter (see Figure 3a). The color coderepresents values of the regression gradient (α) given by equation (1), indicating acontinuum of textural similarity to the model that ranges from 0.0 to 1.0, with 0.0indicating minimal similarity and 1.0 maximum similarity to the model. It is not theabsoluteα value but its variations and well-organized patterns that are geologicallymeaningful and interpretable. Although it is not a discrete classification map, itcan be easily interpreted into distinctive facies categories (e.g., 1, 2, 3, 4, and 5)based on their distribution pattern and lateral relationships. In this specific area,the high α value (red) suggests sand-rich facies such as in the levee/overbankdeposits or lobes in the distal portion of the turbidite system, whereas the low αvalue (black) suggests shale-rich facies, such as the bypassed channel-fill depositsand the sheetlike deposits distant from the channels. For unbiased comparison,both the original amplitude and the TMR result are displayed using the samecolor-mapping function.


such differences based on average absolute amplitude (Fig-ures 7c and 8b), coherence (Figures 7d and 8c), or the combi-nation of instantaneous amplitude and frequency (Figures 7eand 8d). For example, in the updip portion of the reservoir,which is expected to have high amplitude in response to gasaccumulation, average absolute amplitude (Figures 7c and 8b)shows no hint of increased amplitude. Coherence (Figures 7dand 8c) provides little discrimination between gas sand andwet sand, because the trace-to-trace similarity is not sensitiveto waveform characteristics, such as trace shape, amplitude,frequency, and phase. The combination attribute of amplitudeand frequency (Figures 7e and 8d), which has been very pop-ular in hydrocarbon exploration, is still not as effective as theTMR result.

DISCUSSION

The TMR process enables scientists to discriminate featuresmore efficiently and interactively from a different perspectivethan the classical multivariate extraction and classification ap-proach. Mathematically, a feature vector at each sample loca-tion is represented by one scatterpoint in a feature vector space.In such a space, a classification algorithm groups clouds of scat-terpoints into a given number of clusters or classes by evaluat-ing iteratively their closeness and distribution in the abstract,high-dimensional feature space. Since the cluster structure isinitially invisible to the classification algorithm, interpretershave to guess at the number of classes on a trial-and-error

Figure 5. A turbidite channel-fan system inthe same area as in Figure 4 imaged fromfour different perspectives, for comparison.(a) TMR. The color code and implicationsare the same as in Figure 4. (b) Average ab-solute amplitude. (c) Coherence. (d) Combi-nation of amplitude and frequency. Arrowsindicate features that are more easily rec-ognizable from the TMR result than fromthe amplitude, coherence, and combinationof amplitude and frequency. For unbiasedcomparison, attributes are computed usingthe same parameters and displayed using thesame color-mapping function.

basis. As a result, the data set may be either underclassifiedor overclassified. In other words, different objects may havebeen grouped into the same class, or similar objects may havebeen split into two or more different classes. Once the classesare defined, it is impossible to split a class into different ones,and it is often difficult to merge multiple classes into a singleone based on the class indexes. Interpreters need to classifythe same data set repeatedly with different numbers of classesuntil a meaningful result is achieved, a process that is time con-suming and can be impractically expensive in the case of large3D regional seismic surveys. Furthermore, in reality, featuressuch as geologic facies generally have transitional propertiesand vague boundaries that may not be easily separable in aphysical space. It may not be worthwhile to seek mathemati-cal boundaries among these patterns in an attribute space in adeterministic manner using a computationally expensive tech-nique. The TMR process, however, uses model texture as areference to evaluate texture similarity at each sample loca-tion. Therefore, features at all sample locations are calibratedrelative to the texture model and are identified independently,based on their respective similarities to the texture model. Theresult is, effectively, a classification that can be interpreted andquality-checked in a more interactive manner than that derivedfrom a classification algorithm, thereby minimizing cycle timeand space and streamlining the interpretation process.

In general, the TMR technique characterizes texture witha user-defined, object-oriented texture model. In seismic ex-ploration, the model can be single (1D) or multiple (2D or

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3D) wiggle traces and can be static or dynamic in nature.First, if the model is a 1D cosine with variable frequency, theTMR algorithm discriminates waveform features at differentfrequencies and, thus, degenerates into a volumetric spectral-decomposition algorithm, except that results are α values in-stead of amplitude as in the regular spectral-decompositiontechnique (Partyka et al., 1999). Second, if the model is 1D andconstant in nature, the TMR algorithm characterizes waveformshape and degenerates into a volumetric version of the wave-form classification algorithm, except that TMR produces a con-tinuum of α values as opposed to the discrete number of classesas in the regular classification algorithm (Poupon et al., 1999).Third, if the model is data driven at each sample location, theTMR algorithm degenerates into a lateral, trace-correlation al-gorithm commonly used in seismic-horizon interpretation (e.g.,Johnson et al., 2001) and coherence calculation (Bahorich andFarmer, 1995), in which case, the functionality changes from fa-cies discrimination to structure characterization. Furthermore,since the TMR is sensitive to amplitude, frequency, and phaseof wiggle traces, it also includes classical seismic attributes,such as amplitude and frequency, that have been commonlyextracted using multiple, independent algorithms (Taner andSheriff, 1977). In some sense, all these popular techniques maybe considered to be end members, or specific cases, of the moregeneral and flexible TMR methodology.

Even in these specific cases, the TMR technique has im-portant advantages over the classical, popular algorithms. Forexample, the TMR approach avoids computationally iterativeand intensive waveform classification. Instead of making clas-sification maps with discrete waveform classes based on in-terpreted horizons, the TMR methodology creates a volumewith a continuum of waveform classes (α values) that is in-

Figure 6. A turbidite channel-levee systemimaged from four different perspectives, forcomparison. It is in the same area as in Fig-ure 4 but in a different stratigraphic inter-val. (a) TMR. The color code and implica-tions are the same as in Figure 4. (b) Averageabsolute amplitude. (c) Coherence. (d) In-stantaneous frequency. Arrows indicate thefeatures that are more easily recognizablefrom the TMR result than from the ampli-tude, coherence, and frequency. For unbiasedcomparison, attributes are calculated usingthe same parameters and displayed using thesame color-mapping function.

dependent of interpreted horizons and has the highest reso-lution. By simply applying horizon slicing or depth slicing atany stratigraphic interval throughout the volume, geologistsare now able to make tens of facies maps at a continuum ofstratigraphic levels in less than half an hour, thereby recogniz-ing both lateral and vertical facies changes much more quicklyand interactively than spending more than half an hour tomake a single facies map using a conventional, horizon-basedwaveform classification algorithm. These advantages make theTMR a more plausible approach to seismic-facies analysis thantraditional algorithms. The spectral-decomposition algorithmemphasizes amplitude variation with frequency by decompos-ing a wiggle trace into discrete frequency components, usinga Fourier transform. It effectively identifies amplitude anoma-lies at different frequencies, but it may not be as effective asthe TMR algorithm using a variable-frequency model in char-acterizing wiggle-trace shapes that are critical to seismic faciesdiscrimination.

The ultimate goal of seismic-facies analysis is to tie seis-mic patterns to depositional facies. It is more an interpre-tive process driven primarily by a geologist than a compu-tational process driven by a mathematician or a computerscientist. The latter plays an important role by creating use-ful quantitative information that is otherwise not easily ob-tainable, whereas the former plays a critical role by translat-ing such intermediate quantitative information into geology.Thus, depositional-facies interpretation by a geologist, basedon seismic texture and stratigraphic principles along with theregional depositional setting, may be geologically more reliablethan a computer-generated facies-classification map based ona mathematically robust clustering and neural-network algo-rithm. This distinction is analogous to a structural contour map


made by a geologist based on principles of structural geologyand regional structural style, vis-a-vis a computer-generatedcontour map based on a mathematically robust interpolationand extrapolation algorithm. In order to make geologically ro-bust facies interpretation and prediction from seismic data withlittle well information, it is important to transform regular am-plitude into textural similarity to allow interactive-facies vi-sualization and interpretation. The facies cube obtained fromthe TMR methodology represents one such superior data setthat enhances the visibility and resolution of critical geologicfeatures, thereby facilitating interactive observation, robust in-terpretation, and successful hydrocarbon exploration.

←Figure 7. A seismic line showing the major reservoir in a gasfield in the deep-water Gulf of Mexico from 5 different per-spectives, for comparison. (a) Original seismic line from whichall the others are derived. (b) The TMR result that is createdusing a wiggle-trace model (model case 2) (see Figure 3b) as aregression filter that is considered to be gas sand, based on seis-mic data at a well bore penetrating the reservoir interval. Themodel has 27 samples (108 ms) in vertical dimension. The colorcode represents values of the regression gradient (α) given byequation (1), indicating a continuum of textural similarity tothe model (gas sand) that ranges from 0.0 to 1.0, with 0.0 in-dicating minimal similarity and 1.0 maximum similarity to gassand. (c) Average absolute amplitude. (d) Coherence. (e) Com-bination of amplitude and frequency. The vertical dashed linemarks approximately the gas/water contact. Magenta color de-notes wells that penetrate gas sand, whereas light blue colorrepresents wells that penetrate water sand. Notice that the re-sult from the TMR method better defines the boundary be-tween gas sand and wet sand than do the amplitude, coherence,and amplitude/frequency combination. For unbiased compar-ison, attributes are calculated using the same parameters anddisplayed using the same color-mapping function.

CONCLUSIONS

The TMR methodology provides a long-sought-after solu-tion to integrating classical techniques into a unified processthat improves data visualization and interpretation. Differentfrom classical attribute extraction/classification approaches,the TMR technique uses an interpreter-defined texture modelas a calibration filter to discriminate features. In seismic ap-plication, two simple texture models demonstrate the value ofthe TMR concept in seismic-facies analysis. The first model,which is a full cycle of a cosine function defined by the max-imum amplitude and the dominant frequency in the intervalof interest, helps identify detailed facies variations in a tur-bidite system offshore Angola in West Africa. The secondmodel, which is based on seismic data coupled with well in-formation, helps differentiate gas sand from wet sand in a gasfield in the deep-water Gulf of Mexico. Comparative analy-sis indicates that the TMR methodology provides a unifiedand general approach to seismic-facies discrimination, whichincludes functionalities of popular but computationally expen-sive techniques. Not only does the TMR save computationaltime and storage space, but it creates a superior result that en-ables exploration geologists to identify, visualize, and map crit-ical depositional and reservoir facies accurately, quickly, andinteractively.

The effectiveness of seismic texture analysis and its success-ful application to facies discrimination may be attributable toa direct link between image texture and physical texture in theFresnel zone at an acoustic interface because physical textureis generally suggestive of depositional environment and hy-drocarbon saturation. Such a link provides an important basisfor inferring geologic facies from seismic data, although, be-cause of the limited seismic resolution, not in as much detailas from direct observation of outcrops. Therefore, seismic tex-ture analysis has direct and important implications for faciesanalysis and hydrocarbon exploration.

ACKNOWLEDGMENTS

This paper is part of the 3D exploratory data visualizationand interpretation technologies (patent pending) developed

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Figure 8. A reservoir system imaged on a hori-zon slice from four different perspectives, forcomparison, in the same area as in Figure 7(see the location of the horizon at top of thereservoir in Figure 7). (a) TMR. The color codeand implications are the same as in Figure 7.(b) Average absolute amplitude. (c) Coher-ence. (d) Combination of amplitude and fre-quency. Notice that the result obtained fromthe TMR processing better defines the distri-bution of gas sand and the boundary betweengas sand and wet sand than do the average ab-solute amplitude, coherence, and amplitude/frequency combination. For unbiased com-parison, attributes are calculated using thesame parameters and displayed using the samecolor-mapping function.

by the author at Marathon Oil Corporation. Acknowledgmentis made to Marathon management for permission to publishthis work. Thanks go to Sharon Crawford and Tom Evans fortheir support of this study. I also thank Marathon geologistsand geophysicists for their cooperation in applying the tech-nology to worldwide exploration and production projects. Iused the API (Application Program Interface) functions fromParadigm Geophysical, Inc. and Magic Earth, Inc. in program-ming the TMR technology. I thank ChevronTexaco, PetroleumGeo-Services, and WesternGeco for using their 3D digital seis-mic data. I thank Michael Schoenberger for his constructivesuggestions. Journal reviews by Associate Editor Kurt Marfurtand two anonymous reviewers helped improve the quality ofthe paper.

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Gao 2004 Geophysics