Latest developments in seismic texture analysis for subsurface structure, facies, and reservoir characterization: A review

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1 GEOPHYSICS, VOL. 76, NO. 2 (MARCH-APRIL 2011); P. W1 W13, 16 FIGS., 1 TABLE / Latest developments in seismic texture analysis for subsurface structure, facies, and reservoir characterization: A review Dengliang Gao 1 ABSTRACT In exploration geology and geophysics, seismic texture is still a developing concept that has not been sufficiently known, although quite a number of different algorithms have been published in the literature. This paper provides a review of the seismic texture concepts and methodologies, focusing on latest developments in seismic amplitude texture analysis, with particular reference to the gray level co-occurrence matrix (GLCM) and the texture model regression (TMR) methods. The GLCM method evaluates spatial arrangements of amplitude samples within an analysis window using a matrix (a two-dimensional histogram) of amplitude co-occurrence. The matrix is then transformed into a suite of texture attributes, such as homogeneity, contrast, and randomness, which provide the basis for seismic facies classification. The TMR method uses a texture model as reference to discriminate among seismic features based on a linear, least-squares regression analysis between the model and the data within an analysis window. By implementing customized texture model schemes, the TMR algorithm has the flexibility to characterize subsurface geology for different purposes. A texture model with a constant phase is effective at enhancing the visibility of seismic structural fabrics, a texture model with a variable phase is helpful for visualizing seismic facies, and a texture model with variable amplitude, frequency, and size is instrumental in calibrating seismic to reservoir properties. Preliminary test case studies in the very recent past have indicated that the latest developments in seismic texture analysis have added to the existing amplitude interpretation theories and methodologies. These and future developments in seismic texture theory and methodologies will hopefully lead to a better understanding of the geologic implications of the seismic texture concept and to an improved geologic interpretation of reflection seismic amplitude. INTRODUCTION Three-dimensional seismic attribute technology has been instrumental in characterizing subsurface geology (Taner et al., 1979; Chopra and Marfurt, 2005, 2007). In the past few decades, great efforts have been made and significant advances have been achieved in the application of various seismic attribute algorithms to subsurface exploration (Chopra and Marfurt, 2005, 2007). In addition to many classical algorithms (Taner et al., 1979), many emerging algorithms have been developed, which have significantly enhanced the interpreters capability for subsurface seismic characterization. Fundamentally, these algorithms can be categorized into qualitative and quantitative approaches. The qualitative approach directly describes seismic amplitudes and amplitude patterns shown in seismic imagery, which helps enhance the visibility of seismic features in seismic data visualization and interpretation. The quantitative approach directly derives rock properties from seismic amplitude, which helps predict reservoir performance in reservoir description and characterization. Qualitatively, there are many seismic attribute extraction algorithms that have been very popular and well known in exploration geophysics (Taner et al., 1979; Sheriff and Geldart, 1995; Bahorich and Farmer, 1995; Chen and Sidney, 1997; Sheriff, 2002; Brown, 2004; Chopra and Marfurt, 2005, 2007; Carrillat et al., 2008). These attributes are computationally convenient, and their analysis creates practical results. Amplitude is a good example that has been widely used to map the reflection intensity by calculating the average amplitude in a small analysis window (Taner et al., 1979; Sheriff and Geldart, 1995; Manuscript received by the Editor 15 May 2010; revised manuscript received 27 September 2010; published online 17 March West Virginia University, Department of Geology and Geography, Morgantown, West Virginia, U. S. A. Dengliang.Gao@mail.wvu.edu. VC 2011 Society of Exploration Geophysicists. All rights reserved. W1

2 W2 Gao Brown, 2004). Frequency is another example that signifies the spectral component of the waveform in the analysis window (Taner et al., 1979; Sheriff and Geldart, 1995; Brown, 2004). These and many other attributes are particularly useful in the reconnaissance phase of subsurface exploration projects. However, many conventional attributes are simply the first-order statistical measures of amplitude. These seismic attributes are insufficient for detailed structure, facies, and reservoir characterization. For example, two different seismic responses can have the same average amplitude and=or the same dominant frequency, but they have two different amplitude configurations that represent two distinct seismic facies. For more effective seismic feature discrimination and visualization, we need to evaluate second-order statistic measures for amplitude configuration. Quantitatively, there are many popular rock property attributes derived from seismic amplitude inversion (Gray, 1999; Pendrel, 2001; Peeters, 2001; Ma, 2001; Sheriff, 2002; Dufour et al., 2002; Ross, 2002; Pruden, 2002). For example, impedance attributes are derived primarily based on the principle that amplitude is directly related to the impedance contrast at an acoustic interface (Pendrel, 2001; Sheriff, 2002; Russell and Hampson, 2006). The principle provides the physical basis to predict interval properties based on interface reflectivity. That is appealing because the result is derived in a deterministic manner and on a physical basis, and the inverted intervals are precisely defined with physical properties and bounded by clear-cut interfaces, which can be easily used by reservoir engineers in property modeling and flow simulation. However, subsurface geology is much more complex than the simplified 1D cake model used in many of the inversion algorithms. The inverted rock property attributes are highly averaged and do not sufficiently describe the complexities of subsurface geology, which are typical of natural structural, stratigraphic, and reservoir systems. Given that surface seismic imagery and subsurface geology are both more complex than the overly simplified computational model, which is particularly the case in highly heterogeneous and anisotropic reservoirs, many current attributes have major limitations in subsurface characterization. The gap between the simplified model and the complicated geology can explain, at least partially, the many observations that seismic interpretation products failed subsequent well tests. In such cases, it is important to emphasize, rather than to ignore or simplify, the complexity of features of interest in the subsurface, which is a major challenge in subsurface seismic characterization and interpretation. Seismic texture analysis might hold the potential to overcome the challenge because texture is an attribute that describes the complexity of features of interest. Generally, texture features the spatial arrangement of constituents in 3D space that has been typically described by using such terms as smooth versus rough and random versus anisotropic. In the seismic image domain, texture is defined by the spatial arrangement of neighboring amplitudes and is more indicative of spatial variability of amplitude than the average amplitude for discriminating seismic characters. In the physical domain, texture is defined by the spatial configuration of rock units and is more diagnostic of and relevant to deformational fabrics, depositional facies, and reservoir properties than an averaged acoustic property. Although there are quite a number of seismic texture analysis algorithms (e.g., Simaan et al., 1987; Zhang and Simaan, 1989; Pitas and Kotropoulos, 1992; Vinther et al., 1995, 1996; Vinther, 1997; Limia et al., 2000; Randen and Husøy, 1999; Randen et al., 2000; Schlaf et al., 2005; Patel et al., 2008), texture is a developing concept that has been poorly recognized and underutilized in exploration geology and geophysics. The purpose of this paper is to provide a review of latest developments in seismic amplitude texture analysis concepts and methodologies with particular reference to the gray level co-occurrence matrix (GLCM) and the texture model regression (TMR) methods that have potential application in seismic interpretation. Following a description of the amplitude texture concept in general, I will describe the GLCM method and its implications for seismic facies classification as recently applied to 3D seismic exploration projects. Then, I will present the TMR method and discuss its potential applications in seismic structure, facies, and reservoir characterization. Lastly, I will make a proposal for the Fresnel-zone seismic texture analysis as a potential avenue to characterize physical texture from prestack seismic signal. It is my hope that these and future developments in seismic texture theory and methodologies will lead to a better understanding of geologic implications of seismic texture for improved subsurface interpretation and characterization from reflection seismic amplitude. AMPLITUDE TEXTURE CONCEPT An amplitude texture refers to a characteristic pattern defined by the magnitude and variation of neighboring amplitude samples at a given location in an image space. Although studies of image texture have been published since the 1950s, the early concept of image texture analysis was primarily applied to 2D imagery (e.g., Kaizer, 1955; Rosenfeld and Troy, 1970; Haralick et al., 1973; Weszka and Rosenfeld, 1976; Weszka et al., 1976; Laws, 1980; Harwood et al., 1985; Derin and Elliott, 1987; Reed and Hussong, 1989; Vistnes, 1989; Reed and du Buf, 1993; Filho et al., 1996; Mirmehdi and Petrou, 2000). Later, quite a number of texture analysis algorithms have been applied to reflection seismic image visualization and interpretation (e.g., Simaan et al., 1987; Zhang and Simaan, 1989; Pitas and Kotropoulos, 1992; Vinther et al., 1995, 1996; Vinther, 1997; Randen and Husøy, 1999; Limia et al., 2000; Randen et al., 2000; Schlaf et al., 2005; Patel et al., 2008). In 3D reflection seismic image analysis, a seismic amplitude texture refers to the internal configuration of seismic amplitude samples within a small zone centered at a location in 3D image space. In a seismic amplitude volume, the magnitude and variability of neighboring amplitudes at a sample location is an effective attribute to describe seismic patterns. Thus, amplitude texture analysis has important and direct implications for seismic feature discrimination and visualization. Spatial variability in amplitude texture requires that it be evaluated at each sample location based on a small analysis window, which is usually called a texture element (texel) in the literature (Haralick et al., 1973; Reed and Hussong, 1989). Generally, a texture element consists of N x by N y by N z neighboring amplitude samples in the inline, crossline, and vertical directions, respectively. It can be a 3D mini-cube, a 2D mini-window, or a 1D wavelet (Gao, 2003, 2004) (Figure 1). The optimal size of the element depends on the dominant frequency of the trace data of interest and should typically cover approximately

3 Latest developments in seismic texture W3 one average period of the traces. For the data sets presented in this study, the average period is approximately 60 ms, which is equivalent to 15 samples at 4-ms sample increments. A seismic texture element that approximates the average period in its vertical dimension is recommended for seismic texture characterization. There are many amplitude texture analysis algorithms in the literature. In the following sections, I describe two emerging, less well-known but promising methodologies, the GLCM and the TMR methods, to characterize 3D seismic amplitude textures. The methodologies represent new, effective approaches to discriminating and visualizing seismic features that may not be easily recognizable using visual inspection and conventional attribute extraction algorithms. Homogeneity ¼ Xn i;j¼1 Contrast ¼ Xn 1 m 2 Xn m¼0 i¼1 Eði; jþ 2 ; (1) R X n j¼1 ji jj ¼m Eði; jþ R ; (2) GLCM METHOD In general digital image analysis, the GLCM has been a useful tool for image discrimination andsegmentationintwodimensionsbasedona 2D mini-window (Haralick et al., 1973; Reed and Hussong, 1989; Filho et al., 1996). Since the late 1990s, several authors have attempted to apply the GLCM technique to 3D seismic image visualization and facies classification (Gao, 1999; West et al., 2002; Gao, 2003; Chopra and Alexeev, 2005; Chopra and Marfurt, 2005, 2007; Gao, 2007; Angelo et al., 2009). The new application to 3D reflection seismic data requires that amplitude texture be evaluated at each sample location based on a 3D mini-volume (Figure 1). The GLCM algorithm (Figure 2) extracts textural features via a co-occurrence matrix depicting spatial relations or patterns of neighboring amplitudes (Haralick et al., 1973). At a given location in the amplitude volume, the algorithm first retrieves a texel and constructs an amplitude co-occurrence matrix. For a texel that has N g amplitude intensity levels (see Figure 3a and b, in which N g ¼ 16), the corresponding co-occurrence matrix is a square, symmetrical one consisting of N g by N g entries, with the dimensionality of the matrix being related to the amplitude level or bit resolution. The element E(i, j) atith row and jth column of the matrix denotes the number of occurrences (counts) that a sample with amplitude i (<N g ) is neighbored by a sample with amplitude j (<N g ) within the texel in a specific direction defined by a and b (Figure 3c). Based on the amplitude co-occurrence matrix, the algorithm calculates a suite of textural attributes as numeric expressions of the texture. Among the many texture attributes, the homogeneity, contrast, and randomness have proved to be effective in seismic facies analysis (Gao, 2003; Chopra and Alexeev, 2005; Chopra and Marfurt, 2007; Gao, 2007). The textural homogeneity is a measure of the overall uniformity or smoothness of amplitude. The textural contrast emphasizes the magnitude of differences in amplitude of neighboring samples, and it indicates how much amplitude changes from one location to the next. The textural randomness measures the predictability of amplitude from one sample to the next. Mathematically, the three textural attributes are computed using the equations 1, 2, and 3, respectively (after Haralick et al., 1973; Reed and Hussong, 1989): Figure 1. (a) 1D (linear) texture element consisting of one single mini-trace defined by 15 amplitude samples. (b) 2D (planar) texture element consisting of 5 mini-traces, each defined by 15 amplitude samples. (c) 3D (cubic) texture element consisting of 25 mini-traces (5 by 5), each defined by 15 amplitude samples. Figure 2. Flowchart for the GLCM seismic amplitude texture analysis. The input is a regular amplitude volume, and the output is a suite of GLCM texture attribute volumes (e.g., homogeneity, contrast, and randomness), which can be used in multivariate clustering analysis to create a seismic facies classification volume. (After Gao, 2003.)

4 W4 Randomness ¼ Xn i;j¼1 Eði; jþ R log Eði; jþ R where E(i, j) represents the element at the ith row and the jth column of the co-occurrence matrix, and n is the dimension of the matrix. The symbol m is a natural number. The symbol R is a constant for normalization, which denotes the maximum possible number of occurrences (counts) that a sample with amplitude i (<N g ) is neighbored by a sample with amplitude j (<N g ) within the texture element. For example, along the x (inline), y (crossline), and z (time or depth) directions, R is defined by equations 4, 5, and 6, respectively: (3) R x ¼ 2ðN x 1ÞN y N z ; (4) R y ¼ 2N x ðn y 1ÞN z ; (5) R z ¼ 2N x N y ðn z 1Þ (6) Gao where N x, N y, and N z are the number of the constituent samples of the texture element in the inline, crossline, and vertical directions, respectively. As an example, Figure 3 is an amplitude mini-cube, representing a typical textural element at a sample location from within a 3D seismic data set. The element has 405 samples (N x ¼ 9, N y ¼ 5, and N z ¼ 9) and 16 amplitude intensity levels (4-bit resolution). For the simplicity in this demonstration, here, the amplitude co-occurrence is evaluated along three orthogonal (x, y, and z) directions (Figure 3c). Figure 3d, e, and f are the three amplitude co-occurrence matrices M x, M y,andm z of the textural element derived along the x, y, and z directions, respectively. In Figure 3d, for example, 20 in row 1, column 2 indicates there are 20 occurrences (counts) that amplitude 1 is neighbored by amplitude 2 along the x direction (a ¼ 0, b ¼ 0) in the texture element. For each of the three co-occurrence matrices, the textural homogeneity, contrast, and randomness are calculated using equations 1, 2, and 3, respectively. Table 1 shows three different texture expressions in the x (inline), y (crossline), and z (vertical) directions, respectively. These different texture expressions along the three orthogonal directions are also indicated by the distinct distribution of elements in the three amplitude cooccurrence matrices shown in Figure 3d, e, and f (Gao, 2007). Note that all the GLCM are symmetrical because the amplitude relations are mutual between two neighboring samples. For example, if amplitude 1 is neighbored by amplitude 2 five times, then amplitude 2 is neighbored by amplitude 1 five times, too. The GLCM in the y (crossline) direction features a diagonal matrix (focused distribution), indicating that neighboring samples have the same amplitude, which implies a texture with high homogeneity, low contrast, and low randomness, whereas the GLCM in the x (inline) direction features a matrix with a less Figure 3. (a) An example of 3D seismic textural element consisting of 9 by 5 by 9 amplitude samples. (b) A digital representation of the textural element shown in (a) for the calculation of textural attributes using the amplitude GLCM method. The 4-bit amplitude gray levels range from 0 to 15. (c) A notation of vector defining the direction in which the amplitude co-occurrence matrix is evaluated. a and b represent azimuth and dip, respectively. In practice, however, no specific direction is specified to overcome the effect of structural dip and azimuth. (d) GLCM evaluated along the x direction of the texture element. (e) GLCM evaluated along the y direction of the texture element. (f) GLCM evaluated along the z direction of the texture element. (From Gao, 2003.)

5 Latest developments in seismic texture W5 Table 1. Textural homogeneity, contrast, and randomness calculated along three orthogonal (x, y, and z) directions for the textural element shown in Figure 3a. (After Gao, 2007.) Direction Texture x y z Homogeneity Contrast Randomness focused distribution, which corresponds to a texture with moderate homogeneity, moderate contrast, and moderate randomness. The GLCM in the z (vertical) direction perpendicular to bedding features a scattered distribution, which corresponds to a texture with a low homogeneity, high contrast, and high randomness. These are typical of reflection seismic imagery because of the stratal nature of sediments featuring least lateral but most vertical variability. In the case of dipping beds, the common practice is to evaluate the amplitude co-occurrence parallel or perpendicular to the bedding or in no specific direction, thereby minimizing the effect of dipping reflectors on texture analysis. The process proceeds sequentially from sample to sample in the 3D amplitude volume (Figure 4a), thereby creating textural homogeneity (Figure 4b), contrast (Figure 4c), and randomness (Figure 4d) volumes. These three texture attribute volumes are used as input to the subsequent seismic facies interpretation and classification. Case studies (Gao, 2007) have shown that textural homogeneity, contrast, and randomness are effective in identifying and classifying critical seismic facies, such as channel sand, levee, overbank, mass transport complex, marine shale, and salt in deep-marine depositional systems (Figure 5). Back-projection of facies classes (Figure 5) to regular amplitude and three GLCM texture attributes (Figure 4) indicates that each facies class has a characteristic amplitude pattern that has different texture homogeneity, contrast, and randomness (Gao, 2007). The GLCM texture extraction technique has three major limitations. First, it is computationally expensive in terms of run time and storage space, which is particularly true of large data volumes with high-bit (e.g., 16- or 32-bit) resolution. Second, the objective is limited to the seismic amplitude pattern or seismic facies, but seismic structures become invisible in the attribute volumes. Third, it is difficult to calibrate the results with well data in an interactive manner, which is particularly the case where all the wells need to be cross-validated in the whole area and the entire interval of interest. TMR METHOD Unlike the GLCM texture attribute extraction, the TMR method uses an interpreter-defined texture model as a reference (calibrator) to evaluate the similarity of seismic texture at each data location (x, y, z) relative to the model via a liner leastsquares regression analysis (Gao, 2004) (Figure 6). The similarity is evaluated from the perspective that is defined by a specific model composed of n amplitude samples. Generally, the workflow consists of 5 steps. 1) Construction of a mini-volume model M i (i ¼ 1 n) consisting of n amplitude samples. 2) Retrieval of mini-volume data (texture element) D i (x, y, z) (i ¼ 1 n) consisting of n amplitude samples centered at a location (x, y, z) in 3D amplitude volume. Figure 4. An example from a case study in the deep water offshore Angola (west Africa) showing seismic facies defined by using the GLCM texture algorithm. (a) Regular amplitude cube. (b) Texture homogeneity cube. (c) Texture contrast cube. (d) Texture randomness cube. (After Gao, 2007.) Figure 5. Seismic facies classification volume generated from the regular amplitude volume (Figure 4a) by clustering analysis of textural homogeneity volume (Figure 4b), contrast volume (Figure 4c), and randomness volume (Figure 4d). (After Gao, 2007.)

6 W6 Gao 3) Linear least-squares regression between the mini-volume model M i and the mini-volume data (texture element) D i (x, y, z). 4) Output the regression gradient at each location g(x, y, z), correlation coefficient r(x, y, z), and intercept i(x, y, z). 5) Repeat steps 2 through 4 at all the sample locations. By performing linear least-squares regression between the amplitude samples in the data and those in the model, the algorithm calculates the regression gradient (g), correlation coefficient (r), and intercept (i) using equations 7, 8, and 9, respectively: g ¼ r ¼ 1 n X n P n i¼1 i¼1 ðm i MÞðD i DÞ P n i¼1 ðm i MÞ 2 ; (7) ½D i D þ gðm i MÞ Š 2 ; (8) i ¼ D g M (9) where D and M denote the mean values of the element D i and M i, respectively, and n is the number of amplitude samples of the model. The TMR method can be used to achieve different objectives by implementing user-defined texture model schemes. This paper describes three texture model schemes defined using a simple mathematic trigonometric function to demonstrate the effectiveness of the process. The three different model schemes were designed specifically for seismic structure, seismic facies, and seismic reservoir characterization, respectively. because such information serves as the critical reference for analyzing folds and faults. In regular wiggle-trace imagery, visibility of reflection events and their discontinuities is limited in many cases because of weak reflection energy, low dominant frequency, and poor signal-to-noise ratio. These limitations make it difficult for interpreters to perform structural geometry and kinematic analysis. The seismic coherence (Bahorich and Farmer, 1995) and other similar attributes are effective at highlighting high-angle faults, fractures, and other lateral discontinuities in the map view. However, the coherence and other similar attributes have two fundamental limitations in structural visualization and interpretation. First, they remove all the reflection events for the purpose of highlighting the discontinuities, thereby losing the visibility of critical structural fabrics. For that reason, they are not quite as useful in cases where the primary objective is to define the kinematic relationship of folds and faults, trapping geometry, and extent of closures. Second, the coherence in the cross-sectional view is basically useless for structural geologists and stratigraphers who are interested in defining the nature of folding and faulting and their kinematic relations to depositional facies. Here, the algorithm (Figure 7) uses a trigonometric function as the base model with a constant phase (Taner et al., 1979; TMR for seismic structure characterization Structural interpretation is one of the primary objectives in subsurface exploration. Structural interpretation requires an unbiased observation of both folds and fractures in 3D (Harding and Lowell, 1979; Suppe, 1985; Lisle, 1994). For seismic data, structural interpretation relies on the visibility of reflection events and their discontinuities from both map and cross-sectional views Figure 6. Schematic graphical representation of linear leastsquares regression between the amplitude samples in the data texture element (D i ) and those in the model (M i ), from which the regression gradient (g), correlation coefficient (r), and intercept (i) are derived. (After Gao, 2004.) Figure 7. Flowchart of the TMR algorithm using a model with a constant phase for seismic structure enhancement. The input is a regular amplitude volume. At each sample location, the algorithm calculates the absolute value of the regression gradient (g) to create a seismic structure volume. (After Gao, 2006a.)

7 Latest developments in seismic texture W7 Sheriff and Geldart, 1995; Sheriff, 2002; Hardy et al., 2003). Specifically, the algorithm defines a full wavelength of trigonometric sine function with a constant phase as a reference model using equation 10: M i ¼ 0:5 þ 0:5a sinðx2pi=nþ (10) where x is frequency in hertz, n is the number of samples defining the model, i is a natural variable denoting the ith sample ranging from 1 to n, a is an amplitude scaling constant related to the bit resolution or dynamic range of the seismic data, and p is a constant ( ). Typically, the reference model M i defaults to a full wavelength of a sine function with a zerocrossing in the center of the wavelength, a maximum amplitude equal to that of the seismic data, and a constant frequency the same as the dominant frequency of seismic data in the interval of interest. In practice, the frequency of the model can be defined based on the two-way time between neighboring peaks or troughs or zero-crossings of wiggle traces. At a given sample location, the algorithm retrieves a segment of data trace defined by n amplitude samples, which in this case is a 1D wavelet that is equivalent to 4n ms at a 4-ms sampling rate. Then, the algorithm performs least-squares linear regression using the two sets of amplitude samples, reference waveform samples x i and data trace samples y i, on the x-y crossplot. The general equation for a regression line is given by equation 11: y ¼ gx þ i (11) where g is the gradient (slope) of the regression line, and i is the intercept. An estimate of g can be obtained using equation 7 by solving a least-squares linear minimization problem. Finally, by taking the absolute value of the regression gradient, the algorithm maps the absolute regression gradient abs(g) to the corresponding location in the new absolute regression gradient volume. The above steps are repeatedly executed from sample to sample along a wiggle trace before moving to the next one (Figure 8). Consequently, a regular amplitude volume is transformed into an absolute regression gradient volume with enhanced structural visualization. Comparative analysis indicates that the result derived from this version of the TMR algorithm is advantageous over regular wiggle trace data in imaging structural details (Figure 9). First, the process leads to more frequent occurrence of reflection events than regular wiggle trace, thereby significantly improving the visibility of structural and stratigraphic details. Second, least-squares linear regression analysis of image texture is a statistical filtering process that helps enhance the signal-to-noise ratio. Third, because regression gradient represents amplitude texture similarity, the result helps lateral stratigraphic correlation. Unlike the coherence algorithm that was designed to highlight discontinuities (Figure 9), the TMR algorithm in this version was designed to aid structural interpretation. In the map view, it Figure 8. Schematic representation of the TMR algorithm using a model with a constant phase. Regression analysis between the model and the corresponding data is performed at each sample location as the model moves along the wiggle trace (left), creating an absolute regression gradient trace with enhanced visibility and frequency of structural events (right). Three regression lines are shown (middle) at three sample locations, labeled 1, 2, and 3, along the trace, which are indicated by red, green, and blue, respectively. (After Gao, 2006a.) Figure 9. An example from a case study in Angola (west Africa) demonstrating improved structure visualization after processing by the TMR algorithm using a model with a constant phase. (a) Regular amplitude section. (b) Enhanced section using the TMR algorithm. (c) Coherence section. (After Gao, 2006a.)

8 W8 Gao helps delineate lateral extent, trend, and geometry of the structural and stratigraphic features. In the cross-sectional view, it helps laterally correlate critical structural and stratigraphic events (e.g., faults, folds, pinch-outs, and unconformities). Both perspectives are equally important in unraveling structural geometry, style, kinematics, and history. Combination of the TMR algorithm with the coherence, curvature, and other algorithms is particularly powerful in seismic structure characterization and interpretation. Figure 10a is the result created by applying an edge enhancement algorithm to the regular amplitude data, whereas Figure 10b is a new result created by first applying the TMR algorithm and then the edge enhancement algorithm. By comparison, the latter sees significant improvement in delineating faults and fractures that control the primary fluid flow. This was confirmed by the tracer test of the injected CO 2 in the fractured hydrocarbon reservoir (M. Uland and T. Duan, personal communication, 2007). TMR for seismic facies characterization 3D seismic facies analysis is performed by making facies maps or by slicing the facies volume using stratigraphic surfaces (Brown, 2004). The other common practice for facies analysis is to isolate distinct seismic features in 3D space as facies bodies (called geobodies in the visualization community). In any of these practices for seismic facies characterization, it is important to remove or to minimize the effect of the wavelet phase. Figure 11 is the TMR workflow using a model with a variable phase to differentiate waveform characters in seismic facies analysis. By instantaneously adapting the phase of the model to that of the data in the regression analysis, the algorithm helps downplay the structural interference with seismic facies visualization and interpretation. The result helps identify, isolate, and visualize seismic facies elements such as channel fill, mass transport complex, levee, overbank, marine shale, carbonate, and salt. Unlike the TMR algorithm using a model with a constant phase, this version of the TMR algorithm uses a model with a variable phase. Specifically, the algorithm defines the variablephase model using equation 12: M i ¼ 0:5 þ 0:5a sinðx2pi=n þ wþ (12) where x is frequency in hertz, w is a phase variable, n is the number of samples defining the model, i is a natural variable denoting the ith sample ranging from 1 to n, and a is an amplitude scaling constant related to the bit resolution or dynamic range of the seismic data. Typically, the reference model M i defaults to a full wavelength of a sine function with an adaptive phase, a maximum amplitude equal to that of the seismic data, and a constant frequency the same as the dominant frequency of seismic data in the interval of interest. In practice, the frequency of the model can be defined based on the two-way time between neighboring peaks or troughs or zero-crossings of wiggle traces. At a given sample location, the algorithm retrieves a segment of data trace defined by n amplitude samples, which in this case Figure 10. (a) Fault network in a fractured reservoir derived from regular amplitude data. (b) Enhanced fault network in the same fractured reservoir derived after applying the TMR algorithm. Note the significant enhancement in fracture resolution and visibility after the TMR processing. The light blue surface represents top of the reservoir. Dark blue linear features are detected faults. Red solid lines are well bores. Red dots are CO 2 injection and trace test wells, and red arrow indicates fluid flow direction based on tracer tests. (After Gao, 2006a.) Figure 11. Flowchart of the TMR algorithm using a model with a variable phase for seismic facies enhancement. The input is a regular amplitude volume. To minimize the impact of phase of the trace on facies visualization, the algorithm keeps updating the phase of the model instantaneously while moving along the data trace on a sample-by-sample basis. At each sample location, the algorithm calculates the regression gradient (g) to create a seismic facies volume. (After Gao, 2006b.)

9 Latest developments in seismic texture W9 is a 1D wavelet that is equivalent to 4n ms at a 4-ms sampling rate. Then, the algorithm performs least-squares linear regression using the two sets of amplitude samples, reference waveform samples x i and data trace samples y i, on the x-y crossplot. The general equation for a regression line is given by equation 11. Estimate of g can be obtained using equation 7 by solving a least-squares linear minimization problem. Unlike the TMR using a model with a constant phase for structural enhancement, this algorithm implements a model with a variable phase to minimize the impact of wavelet phase, thereby downplaying structural interference (Figure 12). Computationally, that is achieved by instantaneously changing the phase of the model until a maximum regression gradient is found between the model and the data, at which the maximum regression gradient max(g) is written at the location in the facies volume. The above steps are repeatedly executed from sample to sample along a wiggle trace (Figure 12) before moving to the next one. As a result, the regular amplitude volume is transformed into a regression gradient volume that enhances seismic facies visualization with minimum structure interference. Figure 13a through 13d indicates that the TMR algorithm is superior to those created using amplitude extraction and other routine attribute extraction algorithms. Figure 13a demonstrates that the current method helps define detailed facies variations along and across channels in deep water (>2000 m below the sea level) offshore Angola (west Africa). Systematic distribution patterns and variations are interpreted to be possibly related to different facies elements ranging from channel fill, lobes, levee, and overbank to marine shale in a typical turbidite system (Kolla et al., 2001; Posamentier and Kolla, 2003). By comparison, the conventional seismic attribute methods (Figure 13b through 13d) are less effective defining facies variations in as much detail as the TMR method (Figure 13a). The coherence attribute map (Figure 13b) effectively delineates outlines of channels; however, it was designed to map the edge of facies but not to map facies, because the coherence algorithm calculates lateral correlation between neighboring traces without a calibrating model, which is not indicative of amplitude textural (waveform) characters. The resulting facies volume enables interpreters to map seismic facies variability at a specific geologic time using a single stratigraphic surface. It also allows interpreters to unravel the evolution of facies by sequentially slicing a series of stratigraphic surfaces through the facies volume continuously and interactively. For example, in the Miocene and Pliocene stratigraphic intervals in the deep water offshore Angola (Figure 14), several major facies elements, such as channel fill, leveeoverbank, lobes, and marine shale, are evident based on the spatial relationship and amplitude characters of different facies elements, along with regional geology and exploratory well bores in the nearby survey areas (J. Milliken, personal communication, 2005). These maps demonstrate both spatial variation and temporary evolution of turbiditic channels and associated facies. Figure 12. Schematic representation of the TMR algorithm using a model with a variable phase. Regression analysis between the model and the corresponding data is performed at each sample location as the model (right) moves along the trace (left). To minimize the impact of phase of the trace on facies visualization, the algorithm keeps updating the phase of the model while moving along the data trace. Three models with three different phases are shown at three sample locations labeled 1, 2, and 3 along the trace, which are indicated by red, green, and blue, respectively. (After Gao, 2006b.) Figure 13. An example from a test case study in offshore Angola (west Africa) deep-marine depositional setting demonstrating the advantages of the variable-phase TMR method in seismic facies analysis over other popular attribute maps. (a) TMR gradient map. Color represents values of the regression gradient, indicating a continuum of texture classes possibly ranging from shale-dominated (black) to sand-dominated (red) lithofacies based on regional geology, outcrop analogs, and exploratory well bores in the nearby survey areas. Not only does it delineate the outlines of the channels and other facies, but it also differentiates among channel fill, levee, overbank, and lobes. (b) Coherence map. (c) Root mean square amplitude map. (d) Instantaneous frequency map. (After Gao, 2006b.)

10 W10 Gao Investigating this spatial and temporal variability is instrumental in evaluating the bathymetric gradient, play fairway, and hydrocarbon potential in the deep water offshore Angola and other deep-marine depositional settings. TMR for reservoir property calibration In seismic reservoir characterization, one of the critical components is to calibrate seismic data (soft data) with reservoir properties observed from wells (hard data) in a specific reservoir interval of interest. However, reliable calibration is challenging due to the nonuniqueness of seismic response along with the inaccurate spatial coregistration of seismic data with well data in both lateral (x, y) and vertical (z) positions. The gap between the requirement of accurate coregistration and the typical inaccuracy in time-depth conversion makes calibration particularly challenging and misleading. There are many different ways to calibrate seismic to reservoir properties, including multiattribute supervised classification using neural network (Carrillat et al., 2005, 2008; Leite and de Souza Filho, 2009). Unfortunately, multiattribute classification requires preextraction of potential attributes. Not only is the process resource consuming in terms of computational time and storage space but also the result is biased by the input attributes that might have little relevance or correlation to reservoir properties, leading to incorrect calibration for reservoir properties. Another method is to directly extract the waveform at the well-bore location as the model and then to calculate the correlation between each of the seismic waveform and the model waveform extracted at the well-bore location. Because the calibrating model is from a single or a limited number of wells, it might be practically difficult to reach a consensus among all the wells across the reservoir. This problem is particularly acute in large fields with extensive wells. The more the wells there are in the field, the more difficult it is for interpreters to make consistent calibration among all the wells. Furthermore, relying solely on one specific well, the result might be biased and misleading if that well happens to have poor coregistration to seismic, if it has low seismic signal-to-noise ratio, or, even more fundamentally, if there is no unique correlation between seismic response and the reservoir property at that specific well location. In any of these cases, the reservoir property might be calibrated incorrectly. The TMR method is designed to help resolve these problems by implementing a fully dynamic texture model with variable amplitude, frequency, and dimension as a calibration filter (Figure 15). Unlike the algorithms for structure and facies Figure 14. Sequential horizon slices in (a and b) Miocene and (c and d) Pliocene through facies volume (offshore Angola, West Africa). Color represents a continuum of texture facies classes possibly ranging from sand-dominated (red) to shale-dominated (black) deposits (channel fill, levee/overbank, lobes, and marine shale) based on regional geology and exploratory well bores in the nearby survey areas (J. Milliken, personal communication, 2005). Notice the signification changes through time in lithology, width, sinuosity, and flow direction of the channel-fan systems. (After Gao, 2006b.) Figure 15. Flowchart of the TMR algorithm using a dynamic model with a variable amplitude, frequency, and dimension for reservoir property calibration based on well-bore data. The input is a regular amplitude volume. The algorithm keeps updating the model until an optimal correlation is achieved to all the well-bore observations.

11 Latest developments in seismic texture W11 analysis, the algorithm using a fully dynamic texture model is virtually a trial-and-error process testing for an optimal model based on all the well data (not just one single well) in the reservoir interval. Essentially, such a process facilitates seismic calibration to all the wells in a more interactive and objective manner. By experimenting with various models, the algorithm serves to optimize the correlation of seismic to reservoir properties from a specific perspective as defined by the thematic model found from the trial-and-error process. Unlike the constant-phase and variable-phase waveform models, the dynamic waveform model is defined by variable amplitude, frequency, and dimension. Specifically, the algorithm defines the dynamic-waveform model using equation 13: M i ¼ 0:5 þ 0:5a sinðx2pi=n þ wþ (13) where x is a frequency variable in hertz, w is a phase variable, n is a variable number of samples defining the size of the model, i is a natural variable denoting the ith sample ranging from 1 to n, and a is a variable amplitude related to the bit resolution or dynamic range of the seismic data. Typically, the reference model M i begins with a full wavelength of a sine function with a specific phase, an amplitude equal to that of the seismic data, and a frequency the same as the dominant frequency of seismic data in the interval of interest. In practice, the start-up frequency of the model can be defined based on the two-way time between neighboring peaks or troughs or zero-crossings of wiggle traces. At a given sample location, the algorithm retrieves a segment of data trace defined by n amplitude samples, which in this case is a 1D wavelet that is equivalent to 4n ms at a 4-ms sampling rate. Then, the algorithm performs least-squares linear regression using the two sets of amplitude samples, reference waveform samples x i and data trace samples y i, on the x-y crossplot. The general equation for a regression line is given by equation 11. An estimate of g can be obtained using equation 7 by solving a leastsquares linear minimization problem. A critical first step is to define the reservoir level (top or base) and interval of interest that has been tested by a sufficient number of wells. The interval is populated with properties at all the well bores with reliable time-depth conversion. Then, at all the well bores in the defined reservoir interval of interest, the algorithm interactively and iteratively updates the model by changing the parameters defined in the equation 13 as necessary until an optimal match is realized for all the wells in the reservoir interval (Figure 16). At that point, the final model is used to create a thematic volume that is optimally calibrated to a specific reservoir property observed from all the well bores. The TMR algorithm using a testing model with variable amplitude, frequency, and dimension is particularly useful for calibrating reservoir properties in cases where extensive well bores are available as in mature sedimentary basins or in the development phase of a hydrocarbon reservoir. Such a process is instrumental in honoring all the well data in a consistent manner and thereby achieving a statistically robust calibration. To the extent that the resulting attribute has an optimal correlation to a reservoir property at all the wells, such a calibrated result can be used as a secondary continuous seismic property in modeling reservoir properties in 3D space, thereby leading to more reliable reservoir characterization and flow simulation. FUTURE WORK: DISCUSSION Until now, the concept of seismic texture has been used exclusively as an amplitude pattern recognition tool for seismic feature discrimination and visualization in the poststack seismic image domain. Similar to other poststack seismic attribute analysis algorithms, poststack amplitude texture analysis is a qualitative approach to subsurface characterization that is more visual than physical. Our future research focus needs to shift to a quantitative approach that is based more on physical processes. Quantifying seismic texture analysis is challenging. As opposed to the amplitude texture in poststack image domain, physical texture is not typically recognizable from regular poststack seismic amplitude imagery but requires using prestack seismic signal. Three outstanding questions remain to be addressed: (1) What is the physical link between prestack seismic amplitude and geologic texture? (2) At what scale can geologic texture be seismically visible and detectable in prestack seismic amplitude? (3) How can geologic texture be characterized quantitatively from prestack seismic amplitude? As opposed to a nondimensional point of incidence that can be described by the average impedance (contrast) at the point, texture analysis in a physical space requires the reliance on a three-dimensional zone because texture is a context property characterized by the internal configuration of neighboring components in the zone. Given that a bulk seismic response is an Figure 16. An example from a case study in an oil field in Wyoming showing different seismic signatures at the reservoir top from different perspectives as defined by using a dynamic texture model, which can be instrumental in achieving optimal match between seismic and reservoir properties from wells. The blue vertical lines are well bores.

12 W12 Gao integral of reflected wavelets from those microreflectors with favorable dips and azimuths at a specific incidence angle in a local zone of incidence, which is well known as the Fresnel zone, it is not simply the impedance (contrast) at a point of incidence but the impedance texture in a zone of incidence that contributes to the seismic response. The Fresnel zone might provide a window for characterizing geologic texture on a physical basis from limited offset and limited azimuth amplitude data. CONCLUSIONS Although a number of seismic texture algorithms have been published in the literature, seismic texture is a developing concept, and its geologic applications and geophysical implications are not well known in the field of exploration geology and geophysics. This paper provides a review of the most recent developments in seismic texture analysis concepts and methods, with particular reference to the GLCM and TMR methods, both of which have potential usefulness in seismic interpretation. The GLCM algorithm describes the spatial distribution of neighboring amplitude samples by creating a co-occurrence matrix for the neighboring amplitude samples in a small analysis window. It then calculates textural attributes from the amplitude cooccurrence matrix to translate seismic amplitude into textural homogeneity, contrast, and randomness for seismic facies analysis. The TMR algorithm uses a texture model as a reference to evaluate seismic textural similarity relative to the model via a least-squares regression analysis. By implementing three customized texure models, the TMR method can be used for seismic structure, facies, and reservoir property characterization. A texture model with a constant phase is effective at enhancing the visibility and resolution of seismic structural fabrics, a texture model with a variable phase is helpful for visualizing seismic facies, and a texture model with variable amplitude, frequency, and size is instrumental in calibrating seismic to reservoir properties by interactively updating the model to achieve an optimal correlation to the available well data. Gazing into the future, this paper proposes to characterize geologic texture on a physical basis. Because texture is a context property that can only be defined in a three-dimensional zone rather than at a nondimensional point, texture analysis requires reliance on a mini-volume in 3D physical space, whereas the Fresnel zone might serve the purpose and open a window to achieve the objective by investigating prestack seismic amplitude data. ACKNOWLEDGMENTS Thanks go to Marathon Oil Corporation for permission for the publication of previous seismic texture analysis methodologies. The 3D seismic data used in this publication are provided courtesy of WesternGeco, Houston, TX. Thanks go to Tom Wilson for his comments. I am grateful to Enders Robinson, Gary Margrave, and an anonymous reviewer for their constructive peer reviews and recommendations. This paper is partially supported by the U.S. Department of Energy/NETL FY11 research project Developing new seismic waveform model regression technologies for improved geologic evaluation for reservoir storage capacity and retention permanency in the subsurface, awarded to Dengliang Gao and Tom Wilson. This study is a contribution to the West Virginia University Advanced Energy Initiative program. REFERENCES Angelo, S. M., M. Matos, and K. J. 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