Nonlinear multi-parameter hybrid inversion of pre-stack and post-stack seismic data based on Zoeppritz equation
ZHANG Lingyuan1, ZHANG Hongbing1, SHANG Zuoping2, YAN Lizhi1, REN Quan1
1. College of Earth Science and Engineering, Hohai University, Nanjing, Jiangsu 211100, China; 2. College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211100, China
Abstract：At present, Shuey or Gray approximate formula and basis pursuit theory are widely applied in inversion of Poisson ratio. The same is true for the velocity ratio which is calculated from P- and S- waves velocity obtained from pre-stack inversion. But it is not avoidable to reduce the accuracy of inversion parameters. We try to apply Zoeppritz equation in inversion for velocity ratio and Poisson ratio. First we developed a hybrid pre-stack and post-stack seismic inversion workflow by the convolution model based on the reflection coefficient of vertical incidence and Zoeppritz equation. Then we constructed a new objective function which includes edge-preserving regularization to reduce the adverse effect of inversion unsuitability. We applied a fast simulated annealing algorithm to achieve global non-linear optimization. To reduce the influence from the magnitude difference of multiple parameters and the poor stability of multi-parameter simultaneous random search, we used an improved Fatti equation in inversion, which introduces two fitting formulas, a density and P-wave velocity formula, and a S-velocity and P-wave velocity formula, to improve the accuracy and stability of inversion. The inverted results of field data indicate that the velocity ratio obtained by direct Zoeppritz equation inversion is better than that obtained by approximate formulas. The inversion results from the new workflow have good consistency with the logging data. In a word, post-stack inversion obtained more accurate P-wave velocity and density, while the accuracy of velocity ration obtained by pre-stack inversion is higher than that obtained by post-stack inversion, and the inversion of 18°~24° angular trace gathers is better than that of 3°~9° and 33°~39° gathers.
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