Abstract
In this paper, based on the acoustic Born kernel, we propose a flexible method to calculate the gradient and the approximate Hessian in frequency-domain full waveform inversion (FWI) by matrix decomposition. In this method, neither the kernel nor the approximate Hessian is necessarily stored in memory. We name FWI using this method as matrix decomposition FWI (MDFWI). Most of the calculation in MDFWI depends on the forward modeling from sources and unrepeated receivers in frequency domain. For the first order direction, this method is a good replacement of adjoint-state FWI (ADFWI) when the source number ns is more than half of number of the receiver stations nr, such as in controlled source exploration, OBS exploration, and natural seismology. For the second order direction, MDFWI is senior to commonly used ADFWI when source-station number is more than only a few percent of the receiver-station number. The effectiveness of MDFWI is proved through 2D numerical experiments.
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