Useful approximations for converted-wave AVO

Converted-wave amplitude versus offset (AVO) behavior may be fit with a cubic relationship between reflection coefficient and ray parameter. Attributes extracted using this form can be directly related to elastic parameters with low-contrast or high-contrast approximations to the Zoeppritz equations. The high-contrast approximation has the advantage of greater accuracy the low-contrast approximation is analytically simpler. The two coefficients of the low-contrast approximation are a function of the average ratio of compressional-to-shear-wave velocity (alpha/beta) and the fractional changes in S-wave velocity and density (Delta beta/beta and Delta rho/rho). Because of its simplicity, the low-contrast approximation is subject to errors, particularly for large positive contrasts in P-wave velocity associated with negative contrasts in S-wave velocity. However, for incidence angles up to 40 and models confined to /Delta beta/beta/ <0.25, the errors in both coefficients are relatively small. Converted-wave AVO crossplotting of the coefficients Of the low-contrast approximation is a useful interpretation technique. The background trend in this case has a negative slope and an intercept proportional to the alpha/beta ratio and the fractional change in S-wave velocity. For constant cell ratio, an attribute trace formed by the weighted sum of the coefficients of the low-contrast approximation provides useful estimates of the fractional change in S-wave velocity and density. Using synthetic examples, we investigate the sensitivity of these parameters to random noise. Integrated P-wave and converted-wave analysis may improve estimation of rock properties by combining extracted attributes to yield fractional contrasts in P-wave and S-wave velocities and density. Together, these parameters may provide improved direct hydrocarbon indication and can potentially be used to identify anomalies caused by low gas saturations.