An adjoint-based Jacobi-type iterative method for elastic full waveform inversion problem

Full waveform inversion (FWI) is a promising technique that is capable of creating high-resolution subsurface images of the earth from seismic data. However, it is computationally expensive, especially when 3D elastic wave equation is considered. In this paper an adjoint-based computational algorithm has been proposed to address the computational challenges. The important strategy in this work is to decouple the two Lamé parameters so that two half-sized subproblems are resulted and solved separately. Mathematically, the inverse problem is formulated as a PDE-constrained optimization problem in which the objective functional is defined as the misfit between observational and synthetic data. The parameters to be recovered are the spatially varying Lamé parameters which are of great interests to geophysicists for the purpose of hydrocarbon exploration and subsurface imaging. The gradient of the misfit functional with respect to the Lamé parameters is calculated by solving the adjoint elastic wave equation, whilst the Quasi-Newton method (L-BFGS) is used to minimize the misfit functional. Numerical experiments demonstrated that the new method is accurate, efficient and robust in recovering Lamé parameters from seismic data.