W041 Faults and Fracture Detection based on Seismic Surface Orthogonal Decomposition

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1 W041 Faults and Fracture Detection based on Seismic Surface Orthogonal Decomposition I.I. Priezzhev (Schlumberger Information Solution) & A. Scollard* (Schlumberger Information Solution) SUMMARY A new technology using the latent structure analysis of seismic surface data under conditions of strong noise is proposed. Since the noise has no correlation with faults or other latent features it stands out as separate orthogonal components. For the same reasons, the individual principal components will be for footprints. Another advantage of the proposed method is the possibility to separate results of different geological processes (factors) that are creating orthogonal (uncorrelated) features on the surface. The technology can be applied to unconventional resources exploration and to detection of fracture corridors in carbonates under strong noise conditions included dip water and sub salt exploration. The proposed technology can also be used to analyze the amplitudes of the seismic slices or stratigraphic slices including sets of several slices.

2 Introduction A new method of detecting subtle faults, fractures, and similar features involves the analysis of the latent structure of the seismic surface. The basic methods of such analysis are calculation of the first or second derivative of the function of the two-dimensional surface. Such calculations are done in various ways, such as the parameters of the form of the first derivative, is a local angle and azimuth angle (Dalley et al., 1989; Marfurt, 2006) or calculating the gradient or local anomalies with various ways of averaging. Parameters forming the second derivative are different measures of curvature of the surface or seismic volume under study: the minimum, maximum, Gaussian curvature, and others (Flynn and Jain, 1989, Roberts, 2001; Chopra and Marfurt, 2007). Faults, fracture corridors, or fracture zones are usually reflected in seismic data as incoherent high-frequency features on cross sections and as lineaments on slices or on seismic surfaces. A common problem for conventional technologies is the noise and acquisition footprint sensibility because these also exist in the high-frequency seismic data. To eliminate the noise and footprint influence in results usually requires different methods of filtration or smoothing. As a result of the noise, footprints can be removed from the seismic data but at the same time the fault and fracture reflections also will be removed. The theory of the proposed technology for analyzing the latent structure of seismic reflecting horizons through surface orthogonal decomposition is based on proper orthogonal decomposition (POD), also known as Karhunen Loeve decomposition or principal component analysis (PCA) (Pearson, 1901; Liang et al., 2002; Rathinam and Petzold, 2003; Luo et al., 2007). The method is a powerful tool of data analysis aimed at obtaining a low-dimensional approximate description of some high-dimensional processes. The main idea of this method is the decomposition of the set of snapshots on the orthogonal components. According to POD terminology, a snapshot represents a collection of N measurements times a certain state variable. In our case, for surface analyses a snapshot must be defined for every node and include all values for nodes inside some radius around this node. The radius should be bigger than the correlation radius of the autocorrelation function corresponding to the surface. Orthogonal decomposition based on PCA is widely used in the analysis of geologic and geophysical data. Commonly PCA is used to analyze multidimensional measurements to reduce the dimension and for latent factor analysis (Nikitin, 1986 and Nikitin and Petrov, 2010; Koval, Priezzhev and Ovcharenko, 1984 and 1987). PCA is also used for the analysis of images, including images of the seismic wave field (Scheevel and Payrazyan, 1999). (Nikitin, 1986 ; Nikitin and Petrov, 2010) also used first principal component in moving windows for optimal adaptive filtration. Method We propose to use PCA to analyze the hidden structure of seismic reflecting horizons by expanding these horizons into orthogonal components, based on the computation of eigenvalues and eigenvectors of twodimensional autocorrelation function of the original surface. The main idea of this method is the decomposition of the surface on the orthogonal components (principal components) from its twodimensional autocorrelation function. Each orthogonal component is also a surface, and their sum is equal to the original surface. Orthogonality means that the correlation coefficient between any two components will be about zero. The calculation of principal components reduces to the calculation of eigenvectors and eigenvalues of two-dimensional autocorrelation function of the original surface. It is assumed sorting the principal component by their contribution to the total variance (amplitude) of the studied surface. At the core of PCA is this equation: C T, where C is the covariance matrix for the multidimensional vector X. In our case C is a two-dimensional autocorrelation function and the vector X is the depth (time) of the surface at a given moving window. is the matrix of eigenvectors that are orthogonal to each other, and is the diagonal matrix of eigenvalues. The main property of the PCA is that the eigenvectors, which correspond to principal components, are uncorrelated, which is equivalent to orthogonality. The eigenvector corresponding to the maximum eigenvalue of the covariance matrix determines the first principal component, which is

considered a background factor. As practice shows, the first principal component accounts for up to 99% of the variance of the studied surface.

fault structures. Since the noise has no correlation with faults or other latent features it stands out as separate principal components.

Computations are organized so that the following decomposition of the original surface into orthogonal components whose sum is equal to the original surface.

Synthetic example Figure 1-1 shows a synthetic model surface with faults without noise.

Figure 1-2 shows a model surface with noise that was used as input to fault detection algorithms.

Therefore the amplitude of noise is the same as the amplitude of faults on the surface.

1) 2) 3) 4) 5) 6) 7) 8) Figure 1-1) Model surface and faults, -2) Model surface with faults and noise, -3) Local angles, -4) Minimum curvature, -5)

Figure 1-5 shows the 2D autocorrelation function calculated by model surface with faults and noise (see 1-2).

3 considered a background factor. As practice shows, the first principal component accounts for up to 99% of the variance of the studied surface. The following major components are connected with local peculiarities of the surface, and extended linear elements can be explained as a manifestation of the fault structures. Since the noise has no correlation with faults or other latent features it stands out as separate principal components. By the same reasoning, the individual principal components will be footprints. Computations are organized so that the following decomposition of the original surface into orthogonal components whose sum is equal to the original surface. A unit of these components is equal to the unit of the original surface (milliseconds or meters). Synthetic example Figure 1-1 shows a synthetic model surface with faults without noise. The faults were added to the surface with amplitude 1/1000 to surface amplitude. Figure 1-2 shows a model surface with noise that was used as input to fault detection algorithms. The noise was added according to Gaussian law with standard deviation equal to 1/1000 of the surface amplitude. Therefore the amplitude of noise is the same as the amplitude of faults on the surface. Figures 1-3 and 1-4 show that the result of use of conventional algorithms on 1-3 is local angles and on 1-4 is minimal curvatures. 1) 2) 3) 4) 5) 6) 7) 8) Figure 1-1) Model surface and faults, -2) Model surface with faults and noise, -3) Local angles, -4) Minimum curvature, -5) Autocorrelation function, -6) First, -7) Second, and -8) Third orthogonal components. Figure 1-5 shows the 2D autocorrelation function calculated by model surface with faults and noise (see 1-2). It is clear that the first orthogonal component (1-6) is the restored model surface without noise, and on the second and third orthogonal components (1-7, 1-8) can be seen the faults that were on the source model surface. On the map with minimum curvatures and local angles (1-3, 1-4) we cannot see the same result. Unconventional resources exploration In gas shales and oil shales it is very difficult to detect faults and fractures using seismic data. The main problem is the noisy land seismic data, which must be smoothed. To get an unsmoothed surface we apply a whitening procedure to the source cube (Priezzhev, 2010a, 2010b) and use autotracking to get an unsmoothed surface for analyses (Figures 2-1, 2-2, 2-3, 2-4, 2-5, 2-6). Results show very good correspondence to microseismic data (Figures 2-7, 2-8).

1) 2) 3) 4) 5) 6) 7) 8) 9) Figure 2-1) Montney

-2) Amplitude spectrum of source seismic, -3)

shale according seismic data after whitening,

Surface pictures (2-6,2-7,2-8,2-9) also show

Carbonates example Figure 3 shows results of

calculated at the top of carbonates, which

$lineaments, which can be explained as fracture$ corridors.

4 1) 2) 3) 4) 5) 6) 7) 8) 9) Figure 2-1) Montney (courtesy WesternGeco) seismic cross section, -2) Amplitude spectrum of source seismic, -3) Top of shale surface according source seismic, -4) Seismic data after whitening, -5) Amplitude spectrum after whitening, -6) Top of shale according seismic data after whitening, -7) Second orthogonal component -8) Third orthogonal components and -9) Fourth orthogonal component (noise and footprint). Surface pictures (2-6,2-7,2-8,2-9) also show microseismic data results in the shale layer. Carbonates example Figure 3 shows results of analyses of the seismic data surface calculated at the top of carbonates, which were performed using different technologies. On the third orthogonal component are lineaments, which can be explained as fracture corridors. 1) 2) 3) Figure 3-1) Local angles, -2) Minimum curvatures, and -3) Third orthogonal component calculated by top of carbonates.

5 Conclusions A new technology using the latent structure analysis of seismic surface data under conditions of strong noise is proposed. Since the noise has no correlation with faults or other latent features it stands out as separate principal (orthogonal) components. For the same reasons, the individual principal components will be for footprints. Another advantage of the proposed method is the possibility to separate results of different geological processes (factors) that are creating orthogonal (uncorrelated) features on the surface. The technology can be applied to unconventional resources exploration and to detection of fracture corridors in carbonates under strong noise conditions included dip water and sub salt exploration. The proposed technology can also be used to analyze the amplitudes of the seismic slices or stratigraphic slices including sets of several slices. Acknowledgments The authors thank Schlumberger for the opportunity to spend the time necessary to develop this technique and also for permission to publish the results of the work. References 1. Chopra, S. and Marfurt, K.J. [2007] Volumetric curvature attributes for fault/fracture characterization. First Break, 25(7), Dalley, R.M., Gevers, E.C.A., Stampfli, G.M., Davies, D.J., Gastaldi, C.N., Ruijtenberg, P.A., and Vermeer, G.J.O. [1989] Dip and azimuth displays for 3D seismic interpretation. First Break 7(3), Flynn, P.J. and Jain, K.J. [1989] On reliable curvature estimation. IEEE Conference on Computer Vision and Pattern Recognition, San Diego, Koval, L.A., Ovcharenko, A.V., and Priezzhev, I.I. [1987] Interpretation technology of complex airborne materials in the system ASOM-AGS/ES and the results of their use in Eastern Tuva. Geology and Geophysics 6, Koval, L.A., Priezzhev, I.I., and Ovcharenko, A.V. [1984] Interpretation of complex data based on recognition and classification in an automated system for processing airborne system. Geology and Geophysics 9(277), Liang, Y.C., Lee, H.P., Lim, S.P., Lin, W.Z., Lee, K.H., and Wu, C.G. [2002]. Proper orthogonal decomposition and its applications part I: Theory, Journal of Sound and Vibration, Vol. 252, No. 3, Luo, Zhendong, Zhu, Jiang, Wang, Ruiwen, and Navon, I.M. [2007] Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model. Comput. Methods Appl. Mech. Engrg. 196, Marfurt, K.J. [2006] Robust estimates of 3D reflector dip and azimuth. Geophysics 71(4), July- August 2006; P29 P Nikitin, A.A. and Petrov, A.V. [2010] Theoretical bases for statistical methods separation of geophysical anomalies. Russian State Geological University, Nikitin, A.A. [1986] The theoretical basis of geophysical data processing. - M.: Nedra, Pearson, K. [1901] On lines and planes of closest fit to a system of points in space, Philosophical Magazine 2, Priezzhev, I. [2010a]. Prestack and poststack seismic inversion workflow in frequency domain. EAGE/EAGO/0SEG, 4th Saint Petersburg international conference, B24, 4 p. 13. Priezzhev, I. I. [2010b], Seismic inversion based on the angle stack (AVO inversion) in the frequency domain. Geoinformatica 1, Rathinam, M. and Petzold, L. [2003]. A new look at proper orthogonal decomposition, SIAM J. Numer. Anal. 41(5), Roberts, A. [2001] Curvature attributes and their application to 3D interpreted horizons. First Break 19(2), Scheevel, J.R. and Payrazyan, K. [1999] Principal component analysis applied to 3D seismic data for reservoir property estimation, SPE 56734, SPE Annual Technical Conference and Exhibition, Houston, Texas, 3 6 October.

Using Curvature to Map Faults, Fractures

Using Curvature to Map Faults, Fractures by SATINDER CHOPRA and KURT J. MARFURT Editor s note: Chopra is with Arcis Corp., Calgary, Canada; Marfurt is with the University of Oklahoma. Both are AAPG members.