Abstract: Maximum likelihood estimation theory is applied to the determination of the ratio of P-wave velocity to S-wave velocity (V.sub.p /V.sub.s) from P-wave and S-wave seismic sections obtained along the same line of exploration. For a certain statistical model, the optimal estimator for V.sub.p /V.sub.s 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 V.sub.p /V.sub.s estimate. Alternatively, the latter formula provides a measure of the V.sub.p /V.sub.s information contained in the data. The information measure also provides optimal weighting for computing multitrace V.sub.p /V.sub.s averages, and provides for the determination of the statistical error in such averages.