Detection and extraction of fault surfaces in 3D seismic data Israel Cohen 1 , Nicholas Coult 2 , and Anthony A. Vassiliou 2 ABSTRACT We propose an efficient method for detecting and extract- ing fault surfaces in 3D-seismic volumes. The seismic data are transformed into a volume of local-fault-extraction LFE estimates that represents the likelihood that a given point lies on a fault surface. We partition the fault surfaces into relative- ly small linear portions, which are identified by analyzing tilt- ed and rotated subvolumes throughout the region of interest. Directional filtering and thresholding further enhance the seismic discontinuities that are attributable to fault surfaces. Subsequently, the volume of LFE estimates is skeletonized, and individual fault surfaces are extracted and labeled in the order of decreasing size. The ultimate result obtained by the proposed procedure provides a visual and semantic represen- tation of a set of well-defined, cleanly separated, one-pixel- thick, labeled fault surfaces that is readily usable for seismic interpretation. INTRODUCTION Fault surfaces are common subterranean structures that are asso- ciated with displacements or offsets of subsurface layers. Their con- sistent and reliable detection in 3D-seismic data provides an inter- preter with very powerful means to quickly visualize and map com- plex geological structures. A common tool for facilitating structural and stratigraphic inter- pretation is the coherency cube, originated by Bahorich and Farmer 1995, 1996. It is calculated from seismic data using a coherency measure that quantifies the seismic discontinuity at each point. Dis- continuities that are attributable to fault surfaces include dip, azi- muth, and offset changes of seismic reflectors, and waveform and amplitude variations caused by defocusing. Such discontinuities ap- pear on coherence slices as incoherent linear or curved features e.g., Marfurt et al., 1999; Gersztenkorn et al., 1999; Neff et al., 2000; Lees, 1999. The most acceptable coherence measures are based on crosscorre- lation Bahorich and Farmer, 1995, semblance Marfurt et al., 1998, or eigenstructure Gersztenkorn and Marfurt, 1996a, 1996b; Kirlin, 1992 techniques. These methods typically suffer from a lack of robustness, especially when dealing with noisy data Marfurt et al., 1999; Gersztenkorn and Marfurt, 1999. Recently, we introduced a multiscale analysis method for the estimation of seismic coherency that is both robust for noise and computationally efficient Cohen and Coifman, 2002. It involves another measurement, namely, the local structural entropy LSE, which evaluates the dissimilarity of subvolumes that enclose a given analysis point. Dealing with sub- volumes, rather than individual traces, leads to robustness, yet avoids the expensive computations of eigenstructure-based large co- variance matrices and eigenvalues. A major drawback of coherency-based fault analysis is that seis- mic discontinuities also may be the result of geological features that are unrelated to faults. Furthermore, creating a consistent geological interpretation from large 3D-seismic-data volumes often requires manual intervention, which is time-consuming, tedious, and impre- cise. In this paper, we propose a robust and computationally efficient method for the extraction of fault surfaces in 3D-seismic volumes. The seismic data are transformed into a volume of local-fault-extrac- tion LFE estimates, which provides the interpreter with a much clearer visual indication of the fault surfaces. The LFE estimate at a given analysis point is obtained by the following procedure. First, a 3D-analysis cube that is tilted and rotated about the analysis point is selected by the interpreter. The analysis cube moves throughout the seismic volume and outputs a measure of normalized differential en- tropy NDE for each point. The NDE value represents the likeli- hood of a fault surface whose dip and azimuth are similar to those of the analysis cube to intersect with the analysis point. Subsequently, the local average of the NDE is removed, and portions of fault sur- faces, approximately aligned with the analysis cube, are extracted by directional filtering. The filtered NDE coefficients are thresholded and filtered back to produce directional LFE volumes. Next, the LFE attribute is given by the maximal directional LFE, over the presum- ably tested set of dips and azimuths. This approximately gathers the Manuscript received by the Editor November 22, 2004; revised manuscript received July 1, 2005; published online July 12, 2006. 1 Technion — Israel Institute ofTechnology, Department of Electrical Engineering, Haifa, Israel 32000. E-mail: icohen@ee.technion.ac.il. 2 GeoEnergy Incorporated, 3000 Wilcrest Drive, Houston, Texas 77042. E-mail: coult@coult.net; avassili@geoenergycorp.com. © 2006 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 71, NO. 4 JULY-AUGUST 2006; P. P21–P27, 6 FIGS. 10.1190/1.2215357 P21