A Hierarchical Prestack Seismic Inversion Scheme for VTI Media Based on the Exact Reflection Coefficient

Seismic exploration of unconventional hydrocarbon reservoirs (e.g., shale rocks) must take into account the transverse isotropy with a vertical axis of symmetry (VTI) characteristics. Prestack inversion for VTI media is more complex than the isotropic case, since the forward engine is highly nonlinear and more unknowns (five instead of three) are involved, which aggravate the ill-posedness of the inverse problem. Here, we propose a hierarchical inversion scheme to improve the estimation of the five parameters, where the exact reflection coefficient is used as forward engine (instead of the commonly-used approximations which lack accuracy). To handle the highly nonlinear inverse problem, we perform the prestack anisotropic inversion in two steps, namely, a preliminary linear result is used to reduce the search window and to formulate the constrain term and initial models of the subsequent nonlinear step. Specifically, for a reasonable preliminary estimation, we introduce a data-driven model building algorithm to provide reliable initial models, and employ the limited-memory Broyden–Fletcher–Goldfarb–Shanno combined with the momentum technique (LBFGS-MT) optimization to increase the convergence speed. We derive the Fréchet derivatives of the exact forward operator with respect to the parameters, i.e., the key factors of the linear part. Besides, we introduce a hybrid global optimization, the particle swarm optimization aided by very fast simulated annealing (PSO-VFSA) to enhance the accuracy and computational efficiency of the nonlinear stage. Synthetic tests demonstrate the effectiveness and accuracy of the proposed scheme. The field application shows that the method is capable to obtain reliable elastic information of shale reservoirs.