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Dispersion‐relationship‐preserving seismic modelling using the cross‐rhombus stencil with the finite‐difference coefficients solved by an over‐determined linear system

Finite‐difference modeling with a cross‐rhombus stencil with high‐order accuracy in both spatial and temporal derivatives is a potential method for efficient seismic simulation. The finite‐difference coefficients determined by Taylor‐series expansion usually preserve the dispersion property in a limited wavenumber range and fixed angles of propagation. To construct the dispersion‐relationship‐preserving scheme for satisfying high‐wavenumber components and multiple angles, we expand the dispersion relation of the cross‐rhombus stencil to an over‐determined system and apply a regularization method to obtain the stable least‐squares solution of the finite‐difference coefficients. The new dispersion‐relationship‐preserving based scheme not only satisfies several designated wavenumbers but also has high‐order accuracy in temporal discretization. The numerical analysis demonstrates that the new scheme possesses a better dispersion characteristic and more relaxed stability conditions compared with the Taylor‐series expansion based methods. Seismic wave simulations for the homogeneous model and the Sigsbee model demonstrate that the new scheme yields small dispersion error and improves the accuracy of the forward modelling.