Compressed implicit Jacobian scheme for elastic full-waveform inversion

We present a regularized Gauss–Newton (GN) 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 GN step (the inner-loop calculation). In this work, we managed to reduce the memory usage by calculating the Jacobian matrix on the fly in each inner-loop iteration. By doing so the computational cost of calculating the GN step increases; however, this overhead is mitigated by compressing the field matrices using the adaptive cross approximation scheme. For some cases, this compressed implicit Jacobian scheme may even speed-up the GN step calculation and further regularizes the GN method. As examples, we present inversion results of cross-well seismic and surface seismic data.