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Frequency-domain waveform inversion is typically perfomed using frequency-domain finite-difference modelling techniques. In 3D, these methods face significant computational challenges that limit any application to full-scale seismic applications. An alternative approach is to use a 3D time-domain finite-difference method and extract the frequency-domain wavefield by computing the terms of a discrete Fourier transform at each time step. This method combines the computational efficiency of 3D time-domain modelling while permitting casting the inverse problem in the frequency domain.
Sirgue et al. (Tue,) studied this question.