The relationship between semblance and eigenstructure velocity estimators

A formulation of the semblance coefficient in terms of data covariance matrix eigenstructure is given. The conventionally used semblance procedure is tied to eigenstructure, thereby allowing the seismic signal analyst an opportunity to relate the various displays of velocity spectra using more than visual appearance. After writing semblance in the eigenstructure form, comparisons are made to a number of well-known eigenstructure formulations, which separate signal and noise (vector) subspaces. It is shown qualitatively that semblance should have neither the resolving power nor the computational efficiency of the newer methods