Novel Hybrid Numerical Simulation of the Wave Equation by Combining Physical and Numerical Representation Theorems and a Review of Hybrid Methodologies
Chao Lyu, Liang Zhao, Yann Capdeville
Abstract
Abstract We present a novel hybrid method to simulate wave propagation through remote regional models. By reviewing and refining the two main existing hybrid categories, the multiple point sources method and direct discrete differentiation method, containing five distinct subcategories, the proposed hybrid method has the following three advantages. (a) The meshing of the local target model is completely independent of that of the global reference model. (b) Only three physical quantities, that is, the gradient ∇ q , potential q , and second temporal derivative of the potential ∂ tt q for the acoustic wave equation (traction, displacement, and acceleration for the elastic scenario) are required to construct the hybrid inputs during the first global simulation. They are located exactly on the two‐dimensional (2D) hybrid interface, which is highly accurate and memory efficient for three‐dimensional (3D) hybrid numerical simulations. The required memory of hybrid inputs can be reduced fourfold if the very high polynomial degree spectral element method (SEM) is used for the 3D local hybrid simulation. (c) An efficient artificial perfectly matched layer (PML) can be adopted naturally without any elements overlapping between the local and PML domains in the second hybrid simulation. We build on theoretical analysis and 2D/3D numerical forward simulations based on the SEM to illustrate this new hybrid method and demonstrate its validity. The proposed hybrid method is promising for efficiently probing key 3D structures anywhere within the Earth using the so‐called “box tomography.”