Full waveform inversion in absence of low-frequency data based on n-th power operation: Application to encoded multisource waveform inversion

摘要

The conventional full waveform inversion (FWI) often minimizes the objective function using some local optimization algorithms. As a result, when the initial model is far from the true solution, the inversion process will drop into a local minimum. It is known that the low-frequency components in seismic data are very important for reducing the initial model dependence and mitigating the cycle-skipping phenomenon of FWI. In this paper, we propose to compress the time-domain seismic data and extending their frequency band using the high-order power operation, which is a non-linear process. Based on this, we construct a new objective function using the n-th power wavefield, and derive the corresponding gradient formula. The new objective function shows better property to overcome local minimum than the conventional one. When conduct inversion, we can invert from high-order to low-order successively, and using the result of the last scale as the initial model of the current scale, which is a new multiscale strategy. Then we extend the proposed method to encoded multisource waveform inversion. The numerical example on the Marmousi model demonstrates that the proposed method can effectively mitigate the cycle-skipping of FWI.