AVO inversion using P- to S-wave velocity ratio and P-wave velocity

The estimation of P- to S-wave velocity ratio in the subsurface has many applications in gas-bearing reservoir prospecting, lithology discrimination and anomalous pore pressure prediction. Conventionally, it is estimated with the P-wave and S-wave velocities/moduli/impedances that are directly obtained from pre-stack seismic data using the existing reflection coefficient equation (e.g. the Aki-Richards approximation). However, this indirect inversion method creates cumulative errors for the estimated PSR results. To eliminate cumulative errors, we first propose a novel generalized elastic impedance that has more explicit physical meaning compared with conventional elastic impedance. Then, we derive a linear P-wave reflection coefficient equation in terms of the P- to S-wave velocity ratio, P-wave velocity and density under the assumption of weak contrast. Furthermore, a robust AVO inversion method is constructed with the proposed reflection coefficient equation in the Bayesian framework. Cauchy and Gaussian probability distributions are used as the priori probability distribution of the model parameter and likelihood function, respectively, to predict the maximum posteriori probability solution for P- to S-wave velocity ratio, P-velocity and density. Synthetic and field examples illustrate that the proposed direct inversion method performs with higher accuracy compared with the indirect method that inverts for the P-wave and S-wave velocities and also illustrate the feasibility of our method for inverting the three parameters even with strong noise. Our inverted results conform to the drilling results, which validates the robustness of the proposed direct inversion method. © 2022 Society of Exploration Geophysicists.