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Elastic waveform inversion using the finite-difference contrast source inversion method

The finite difference contrast source inversion (FDCSI) method is a nonlinear inversion method under the framework of inverse scattering theory. In this work, we use the FDCSI method for the elastic wave equation inversion problem to simultaneously reconstruct the P-wave velocity and S-wave velocity. First, we derive the contrast source and the contrast function of P-wave and S-wave velocity based on another form of the elastic wave equation, then we can further inverse the P-wave and S-wave velocity directly by updating the contrast source and the contrast function. In order to improve the computational efficiency and accuracy, we choose the optimised 25-point finite difference operator to construct the finite-difference operator. Since the finite-difference operator is only related to the background medium and the given frequency, the construction of the finite-difference operator and the matrix decomposition only need to be performed once in each iteration, which makes the method more efficient. The numerical simulation results show that our method can reconstruct the P-wave and S-wave velocity directly and accurately, and also show the effectiveness and good imaging capability of our method.