Application of the Compressed Implicit Jacobian Scheme for Elastic Full-waveform Inversion

We present a regularized Gauss-Newton inversion method for solving the elastic full-waveform inversion problem in the frequency domain. The main bottleneck of this method is the Jacobian matrix storage and the computational cost of calculating the Gauss-Newton step (inner-loop calculation). In this work, we managed to significantly reduce the memory usage by calculating the Jacobian matrix on implicitly in each inner-loop iteration. By doing so the computational cost of calculating the Gauss-Newton step increases; however, this overhead is mitigated by compressing the displacement fields that are needed in the implicit Jacobian calculation using the adaptive cross approximation scheme.