Quadrangular adaptive mesh for elastic wave simulation in smooth anisotropic media

Abstract

Smooth anisotropic media are often met when implementing effective medium theory, full waveform inversion or seismic imaging. However, computational overburden is often a recurring problem when working with high frequencies or when quantifying uncertainties. In this context, adaptive meshes constitute, in principle, an attractive representation to maximize simulation accuracy while minimizing the computational cost. However, such meshes are difficult to create in the context of smooth anisotropic media as the optimal local size of the elements is not clearly defined. In this work, we present a two-step algorithm to efficiently mesh these media for spectral element method (SEM) simulation in the 2D elastic case. Our algorithm yields quadrangular only meshes which adapt the size of the element to the local and directional S-wave velocity. It relies on a quadtree division introduced by Maréchal (2009) to divide the mesh until the size of each element edge is adapted to the local minimum wavelength that will be propagated. Then, a Laplacian smoothing is applied to further optimize the size of the elements, increasing the global time step and makes the SEM simulation faster while keeping a good accuracy and even improving it in some cases. An application of our method on a 2D section of the homogenized Groningen area shows that simulation time can be reduced by a factor up to 7.