Eigenstructure-based coherence computations as an aid to 3-D structural and stratigraphic mapping

Coherence measures applied to 3-D seismic data volumes have proven to be an effective method for imaging geological discontinuities such as faults and stratigraphic features. By removing the seismic wavelet from the data, sei smic coherence offers interpreters a different perspective, often exposing subtle features not readily apparent in the seismic data. Several formulati ons exist for obtaining coherence estimates. The first three generations of coherence algorithms at Amoco are based, respectively, on cross correlatio n, semblance, and an eigendecomposition of the data covariance matrix. Appl ication of these three generations to data from the Gulf of Mexico indicate s that the implementation of the eigenstructure approach described in this paper produces the most robust results. This paper first introduces the bas ic eigenstructure approach for computing coherence followed by a comparison on data from the Gulf of Mexico. Next, Appendix A develops a theoretical c onnection between the well-known semblance and the less well-known eigenstr ucture measures of coherence in terms of the eigenvalues of the data covari ance matrix. Appendix B further extends the analysis by comparing the sembl ance- and eigenstructure-based coherence measures in the presence of additi ve uncorrelated noise.