Velocity model-based adapted meshes using optimal transport
Thiago Dias dos Santos, Alexandre Olender, Daiane Iglesia Dolci, Bruno Carmo · Geophysics · 2024
ABSTRACT In geophysical numerical models using the finite-element method or its variant, the spectral-element method, to solve seismic wave equations, a mesh is used to discretize the domain. Generating or adapting a mesh to complex geologic properties is a challenging task. To tackle this challenge, we develop an r-adaptivity method to generate or adapt a 2D mesh to a seismic velocity field. Our scheme relies on the optimal transport theory to perform vertices relocation, which generates good-shaped meshes and prevents tangled elements. The mesh adaptation can delineate different regions of interest, such as sharp interfaces, salt bodies, and discontinuities. The algorithm has a few user-defined parameters that control the mesh density. With typical seismic velocity examples (e.g., Camembert, SEAM Phase, and Marmousi-2), mesh adaptation capability is illustrated in meshes with triangular and quadrilateral elements, commonly used in seismic codes. In addition to its potential use in mesh generation, the method developed can be embedded in seismic inversion workflows such as multiscale full-waveform inversion to adapt the mesh to the field being inverted without incurring the input-output cost of remeshing and load rebalancing in parallel computations. The method can be extended to 3D meshes.