Pre-stack AVA Inversion by Using Propagator Matrix Forward Modeling

Most existing amplitude variation with angle (AVA) inversions are based on the exact Zoeppritz equation or its approximations. These modeling methods, which are ray-tracing-based and describe P-wave primary reflections only, lead to exacting requirements for pre-processing of the input data. Current processing is inadequate to satisfy these demands, especially for removing the effects of transmission losses, P-wave multiples and various converted-wave modes. By using input data with processing errors, inversion results of primary-only methods are predictably not accurate enough. The propagator matrix (PM), like the reflectivity method, uses an analytical solution to the wave equation and considers full-wave propagation effects in horizontal or nearly horizontal multilayered earth models. The numerical examples verify that a PM can effectively estimate transmission losses, multi-reflections and the comprehensive responses of thin interbedded layers, and also has higher reflection sensitivities to P-wave and S-wave velocity and density, as compared with ray-tracing-based AVA modelling. A pre-stack AVA three-parameter inversion by using a PM as the forward engine is proposed. Following a Bayesian approach, the inversion is stabilized by including the correlation of P-wave velocity, S-wave velocity and density. For inversion accuracy, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method is used to solve the augmented function, and the generalized cross-validation (GCV) criterion (Huang et al. in J Geophys Eng 14(1):100–112, 2017) is introduced to adaptively acquire the regularization parameter. Theoretical model inversion analysis shows that the proposed inversion can make use of transmission losses, P-wave multiples and converted wave modes, which not only cost-effectively simplifies the pre-processing, but also generates reasonable inverted results for multilayered conditions. The proposed inversion is then applied to a set of real data, and a comparison with Zoeppritz equation-based inversion demonstrates that PM inversion is clearly superior to Zoeppritz equation-based inversion in terms of stability and accuracy.