Introduction

Data processing of converted waves generally yields estimated values for both P velocity and S velocity in the area of study. These values are usually seen in the form of two parameters: 1) the multiplication of both velocity fields, and 2) the ratio of both velocity fields. Traditionally the ratio of the P and S velocities, which is known as the $\gamma$ value, is the result of an extensive combined analysis on the PS data and the single P-mode data. Knowledge of $\gamma$ is important not only for seismic processing but also for rock property estimation. Traditionally, $\gamma$ is estimated through a combined processing of the PS data and the PP data, as described by Thomsen (1998) and Audebert et al. (1999).

In this note, I present an analytical procedure to estimate an initial value of $\gamma$ that depends only on the most basic processing scheme, the NMO stacking process. Several authors have discussed the stacking process for converted waves Castle (1988); Huub Den Rooijen (1991); Iverson et al. (1989); Tessmer and Behle (1988). Tessmer and Behle (1988) apply conventional NMO to converted waves where the RMS stacking velocity is designated as the converted-wave velocity. This NMO procedure uses a hyperbolic approximation of the moveout equation; so, there is not a satisfactory correction of the moveout.

I introduce a non-hyperbolic moveout equation that characterizes converted waves. This moveout equation consists of three main terms. The third term depends on the $\gamma$ function giving us an equation to estimate an approximately constant value of $\gamma$, directly from the PS data alone.