Two-dimensional anisotropic acoustic wave modelling using the support operator method

We developed an algorithm to simulate two-dimensional frequency domain acoustic-wave response in a transversely isotropic medium with a tilted symmetry axis. The algorithm employs a support operator finite-difference method for modelling. This method constructs a nine-point stencil finite-difference scheme for second-order elliptic equations for generalized anisotropic physical properties. The medium's properties are described as P-wave velocity on the symmetric axis, density, Thomsen's anisotropic parameters (epsilon and delta) and the tilt angle. The benchmarking analysis of the modelled amplitude is illustrated using an isotropic whole-space model. Several synthetic experiments are conducted to evaluate the accuracy of the scheme for anisotropic models. The results suggest that the developed algorithm simulates the P-wave solution and the fictitious S-wave mode as reported in the literature. Simulation for a heterogeneous model with a spatially varying tilt angle of the medium symmetry axis is performed to ascertain the algorithm's robustness. The outcomes of the numerical experiments demonstrate that the developed algorithm can accurately simulate the frequency domain response of acoustic waves in the tilted anisotropic media.