A METHOD OF DETERMINING THE RATIO OF THE VELOCITIES OF COMPRESSIONAL AND SHEAR WAVES IN SUBTERRANEAN FORMATIONS

Maximum likelihood estimation theory is applied to the determination of the ratio of P-wave velocity to S-wave velocity (Vp/Vs) from P-wave and S-wave seismic sections obtained along the same line of exploration. For a certain statistical model, the optimal estimate for Vp/Vs is determined, and shown to be equivalent to maximizing the simple mathematical correlation between P-wave and stretched S-wave seismogram segments. The maximum likelihood method provides a data-dependent formula for the mean square error associated with the Vp/Vs estimate. Alternatively, the latter formula provides a measure of the Vp/Vs information contained in the data. The information measure also provides optimal weighting for computing multitrace Vp/Vs averages, and provides for the determination of the statistical error in such averages.