Amplitude-preserving P/S wavefield separation with the discontinuous Galerkin method on unstructured meshes

Abstract

The decoupling of P- and S-waves is an essential prerequisite for elastic reverse time migration (RTM), which effectively reduces crosstalk artifacts, but most wavefield separation algorithms are implemented on uniform rectangular grids. We have developed an amplitude- and phase-preserving P- and S-wavefield separation approach on unstructured meshes, which can effectively decompose the original elastic wavefield into P- and S-wavefields. The isotropic case is considered. With the aid of viscoelastic theory, we choose to attenuate P- or S-waves and preserve the other wave mode, so as to achieve wavefield decomposition. Viscoelastic wave equations are first reformulated as decoupling wave equations with a selective strong attenuation. We then use the discontinuous Galerkin (DG) method to simulate decoupling P or S wavefield propagation on triangular and tetrahedral meshes. We adopt a quadrature-free DG approach and the arbitrary mesh is mapped into the reference mesh for numerical calculation, where no additional volume and surface integrations are involved. The amplitude and phase information of this vector decomposition agrees with that of the original elastic data. Four numerical examples are used to demonstrate the superior performance of this vector decomposition algorithm. The isotropic example shows the applicability and correctness of our proposed scheme and the second example displays the superiority in handling strong velocity contrasts. The third example exhibits the mesh flexibility in dealing with complex structures, such as caves, faults, undulating surfaces, etc. The last example shows the effectiveness of our developed algorithm extended to a 3D case.