An improved method of elastic impedance based on the relationships between P- and S-wave velocities

In the elastic impedance (EI) equation proposed by Connolly (1999), the relationship between the P-wave velocity a and S-wave velocity beta, K= beta(2)/alpha(2), is assumed to be constant, which is not consistent with the statistical pattern between P-and S-wave velocities in real rocks, thus affecting the accuracy of elastic impedance analysis. Considering that P- and S-wave velocities satisfy a linear relationship, a new approach for calculating elastic impedance was derived based on a simplified form of Zoeppritz equation proposed by Aki and Richards (1980). This novel approach is formed by multiplication of two terms. The first term represents the similar form for Connolly's EI equation. As for the second term, it is interpreted as the correction of the linear relationship between the P-wave velocity and S-wave. Numerical simulation experiments are used to verify performance of the new EI equation in reproducing the amplitude-versus-offset (AVO) response of artificial sandstone strata generated by two different general empirical linear equations for P- and S-wave velocities. As shown by the results, compared with Connolly's elastic impedance, the reflection coefficient obtained using the new elastic impedance calculation method was more accurate and less affected by the error of S-wave velocity. In addition, the variation tendency of the new elastic impedance with the incidence angle is closely associated with the coefficient of the linear relationship, and proper velocity relationships need to be applied according to the actual conditions for elastic impedance analysis. The general empirical equations between P-and S-wave velocities are suitable for describing the relationships in water saturated sandstone. Through Gassmann's saturated fluid substitution analysis, it was found that the reflection coefficients calculated using the new elastic impedance equation under saturated oil and saturated oil and gas conditions were still more accurate than that calculated using Connolly's equation. At the same time, the difference in empirical equations also has considerable influence on the variation of new elastic impedance at different incidence angles.