The relationship between semblance and eigenstructure velocity estimators

Abstract

This short presentation gives for the first time a formulation of the semblance coefficient in terms of data covariance matrix eigenstructure. Because the high‐resolution wavefront or spectral eigenstructure methods have received so much interest over the past decade, it is necessary to analytically tie the conventionally used semblance produce to eigenstructure, thereby allowing the seismic signal analyst an opportunity to relate the various displays of velocity spectra using more than visual appearance. The eigenstructure form of semblance is compared to a number of the now well‐known eigenstructure‐based spectral estimators that separate signal and noise (vector) subspaces. Because of the inclusion of noise‐space energy in the coherence measure, conventional semblance does not have the resolving power of the newer methods. We suggest an enhanced semblance, based on the signal and noise subspace separation concept. A brief simulation verifies the visual improvement in the velocity spectrum obtained from the enhanced version.