Velocities from amplitude variations with offset

Abstract

The sensitivity of amplitude variations with offset (AVO) to normal‐moveout (NMO) velocity errors has usually been taken to be a significant limitation of the method. However, this sensitivity can, in most cases, be exploited to obtain more accurate velocities from a fully automated procedure. The error due to velocity in the AVO gradient is in phase quadrature with the AVO zero‐offset intercept. Furthermore, if the majority of reflectors within a suitable data window contain a similar gradient quadrature component, then it may be inferred that this component is due to an NMO velocity error. Both the intercept and gradient traces may be made analytic (complex) by combining them with i times their Hilbert transforms. The imaginary part of their joint correlation coefficient quantifies the gradient quadrature component and is proportional to the average of the fractional NMO velocity error over the data window. Unlike semblance, which is always positive, the sign of the imaginary correlation coefficient indicates whether the NMO velocity is too high or too low. The optimal NMO velocity, according to this criterion, is the one which nulls this imaginary correlation. This criterion minimizes the AVO gradient error, but does not necessarily maximize the full stack energy or yield the optimal stacking velocity. Because a null is picked, not a peak, the NMO velocity resolution is greatly improved. A velocity picking method is presented, which consists of the following steps: AVO analysis, removal of NMO stretch errors, calculation of the joint statistics between the analytic intercepts and gradients, and picking an NMO velocity to null this indicator. The velocity picking may be performed either manually or automatically through iteration. Automatic picking is computationally more efficient than it would be with semblance because only one correlation trace is calculated for each iteration, instead of one for every trial velocity. This efficiency makes velocity picking of every gather in a 3‐D survey feasible.