Directional complex-valued coherence attributes for discontinuous edge detection
Introduction
Detecting subsurface anomalous structures is one of the key objectives in seismic exploration. The sharp discontinuities in seismic data caused by faults, channels, waveform distortion and lithological changes can result in low values of similarity or coherence in the coherence volume. Therefore, the coherence technique (Bahorich and Farmer, 1995) can be utilized to identify such features as faults, channels, mud volcanoes, deltas, beaches, unconformity, reefs, canyons, fan and sand bodies, as well as to detect subtle traps and favorable structural reservoirs. In recent years, this technique has evolved as an important analytic tool for determining migration velocity and migration algorithm, attenuating noise, eliminating acquisition footprint, evaluating the rationality of seismic processing work flow and assessing the efficiency of 3D continuous coverage processing (e.g., Chopra and Marfurt, 2007).
The three classical coherency calculation algorithms are consist of the cross-correlation based C1 algorithm coherence (Bahorich and Farmer, 1995), multi-trace semblance C2 algorithm coherence (Marfurt et al., 1998) and eigen-structure based C3 coherence algorithm (Gersztenkorn and Marfurt, 1999). These widely used coherence algorithms have their own advantages, as well as drawbacks. The three-trace cross-correlation based C1 algorithm calculates efficiently and works well in high-quality seismic data, but is very sensitive to noise. Multi-trace semblance C2 algorithm can accurately estimate coherency, dip and azimuth using a few time samples to detect thin, subtle, stratigraphic features in noisy data environments, but with lower lateral resolution and higher computational expenses if more seismic traces are used. Eigen-structure based C3 algorithm, which successfully solves the spatial averaging effect issue, can suppress noise more effectively and can identify more geological details with higher lateral resolution compared with C1 and C2 algorithms. However, the computation of C3 algorithm, involved constructing covariance matrix with a small sub-volume of traces, is more complex. Furthermore, the original C3 algorithm does not implement dip scanning, so it cannot provide accurate coherence estimation in areas with strong structural dips. Later soon, Marfurt et al. (1999) developed C3.5 and C3.6 algorithms with structural dip scanning to remove low coherence anomalies caused by steep dipping structure, which have advantages of higher lateral resolution and resisting noise effectively. Several modified coherence algorithms (e.g., Cohen and Coifman, 2002, Lu et al., 2005, Browaeys, 2009, Wang et al., 2012, Wang et al., 2015) have also been introduced to improve computational efficiency and achieve high-quality coherence attributes from 3D seismic data. Both the original and improved coherence techniques can be adopted to assist in fast automatic interpretation of faults. Nevertheless, with the increasing degree in oil and gas exploration and development, a detailed characterization of the distribution of faults is necessary, particularly in areas characterized by complex faults. Locating these complex faults and identifying their orientations can help geophysicists in both exploration and reservoir fields to benefit from their presence or avoid their annoyances (Al-Dossary et al., 2004). For instance, detecting the fault direction is crucial to optimize well location, fluid infiltration and injection-production strategy design (e.g., Goodman, 1980, Chopra et al., 2000, Hart et al., 2002, Mittempergher et al., 2009). However, the current coherence algorithms seldom focus on the effect of direction.
In this study, we propose detecting the directional details of geological discontinuous edges by utilizing directional complex-valued coherence attributes. To be specific, for a post-stack migrated data volume, we obtain cross-correlation coefficients between neighboring complex seismic traces normalized by their corresponding envelope within a local time window along an arbitrary spatial direction. This is essentially different from the coherence calculation for pre-stack azimuthal data sub-volumes (Chopra et al., 2000, Al-Dossary et al., 2004). And these aforementioned directional coherence attributes primarily reflect the discontinuities perpendicular to the arbitrary chosen direction. The distinction in different directions is generally evident, and the direction perpendicular to structural strikes shows more discontinuities and geologic abnormalities than that parallel to structural strikes. Therefore, we define the minimum value among complex-valued correlation coefficients of multiple directions as the minimum complex-valued coherence attribute to highlight subtle discontinuities.
We start this paper with the derivation of the directional and minimum complex-valued coherence attributes. Then we use a 3D synthetic data and a 3D field data example to illustrate the performances of the proposed directional and minimum complex-valued coherence attributes for edge detection. Finally, we give some conclusions.
Section snippets
Method
Based on the complex seismic trace analysis (Taner et al., 1979), the complex seismic trace s(t) corresponding to the real seismic trace x(t) can be described aswhere t is time and h(t) is the Hilbert transform seismic trace or orthogonal seismic trace of the real signal x(t). represents the instantaneous amplitude or envelope, which can characterise the subsurface lithological variations, hydrocarbon (bright spot) and gas accumulation. θ(t) represents the
Conclusions
Our proposed directional complex-valued coherence attributes can directly facilitate the determination of the dominant direction of the fault and can assist in magnifying weak or hidden geological discontinuities. The presented minimum complex-valued coherence attribute, which is the result of calculating multi-trace complex-valued cross-correlation perpendicular to the structural trend, can aid in highlighting the lineation as clear as possible and spatial extension direction of geological
Acknowledgments
We thank the Editor Jyoti Behura, reviewer Satinder Chopra and another two anonymous reviewers for their constructive comments and suggestions, which have helped to greatly improve the quality of this paper. We are also grateful to Xusheng Guo and Peidong Shi for providing us help about field data, and Jingbo Wang and Ruyao Huang for providing us good suggestions. This work was supported by the National Key Basic Research Development Program (2013CB228600), National Natural Science Foundation
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