Elastic full waveform inversion on unstructured meshes by the finite element method

Abstract

Abstract In this paper, we develop a new numerical method for elastic full waveform inversion (FWI) on unstructured triangular meshes. With the triangular meshes, the elastic wave system is solved by the finite element method in the frequency domain and so irregular topography and nonuniform data sampling in space are allowed. The inversion is an optimization iterative process to minimize the residual between the synthetic data and observed data. It is implemented iteratively based on the nonlinear conjugate gradient method from low frequency to high frequency successively. Furthermore, the inverse result at current frequency is used as the initial model for the next frequency inversion, which avoids local minima of objective function effectively. The inverted parameters in the method are approximated by a piecewise linear polynomial rather than point values like the finite difference method, which improves the inversion accuracy. To improve accuracy further in the noise case, the iterative Tikhonov regularization is incorporated into FWI effectively. Unlike the commonly used regularization methods in FWI on rectangular meshes, the developed iterative Tikhonov regularization can be computed efficiently on the unstructured triangular meshes. Numerical computations for models with irregular topography and complex structures are completed. The results show that our method can adapt complex topography effectively while it yields very high accurate inversion results even in the case of certain noise.