Compressed implicit Jacobian scheme for elastic full-waveform inversion

SUMMARY We present a regularized Gauss–Newton (GN) inversion method for solving the elastic fullwaveform 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 fieldmatricesusingtheadaptivecrossapproximationscheme.Forsomecases,thiscompressed 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.