An efficient frequency-domain full waveform inversion method using simultaneous encoded sources

Three-dimensional full waveform inversion (FWI) still suffers from prohibitively high computational costs that arise because of the seismic modeling for multiple sources that is performed at each nonlinear iteration of FWI. Building supershots by assembling several sources allows mitigation of the number of simulations per FWI iteration, although it adds crosstalk artifacts because of interference between the individual sources of the supershots. These artifacts themselves can be reduced by encoding each individual source with a random phase shift during assembling of the sources. The source encoding method is applied to an efficient frequency-domain FWI, in which a limited number of discrete frequencies or coarsely sampled frequency groups are inverted successively following a multiscale approach. Random codes can be regenerated at each FWI iteration or for each frequency of a group during each FWI iteration, to favor the destructive summation of crosstalk artifacts over FWI iterations. Either a limited number of sources (partial assembling) or the total number of sources (full assembling) can be combined into supershots. Wide-aperture acquisition geometries such as land or marine node acquisitions are considered, to allow one to stack a large number of shots in the full computational domain and to test different partial assembling strategies involving sources that are close to or distant from each other. Two-dimensional case studies show that partial-source assembling of distant shots has a limited sensitivity to noise, for a computational saving that is roughly proportional to the number of shots assembled into the supershots. On the other hand, full assembling is more sensitive to noise, and it requires successive inversions of finely sampled frequency groups with a large number of FWI iterations. In contrast, refining the shot interval to improve the fold degrades the models when full assembling is applied to noisy data. Preliminary 3D application of the method leads to the same conclusions that 2D case studies do, with regard to the footprint of crosstalk noise in the imaging.