[Joint work with Lluis Guasch (S-Cube London) and Felix Herrmann (UBC Vancouver)]
Conventional full-waveform seismic inversion attempts to find a model of the sub-surface that is able to predict observed seismic waveforms exactly; it proceeds by minimising the difference between observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model for which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion provides a new form of full-waveform inversion that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is then formulated such that the sub-surface model is iteratively updated in order to force these Wiener filters towards zero-lag delta functions. As that is achieved, the predicted data evolve towards the observed data, and the assumed model evolves towards the true model. This approach is able to invert both synthetic and 3D field data successfully, beginning from starting models and under conditions, for which conventional full-waveform inversion fails entirely.
Adaptive waveform inversion has a similar computational cost to conventional full-waveform inversion per iteration, and it appears to converge at a similar rate. The principal advantages of this method are that it allows waveform inversion to begin from less-accurate starting models and does not require the presence of low frequencies in the field data. It also appears to provide a better balance between the influence of refracted and reflected arrivals upon the final velocity model, and to have reduced artefacts associated with finite source and receiver apertures. Since there is no minimum in the objective function when the data are cycle skipped, adaptive waveform inversion has complete immunity to the effects of cycle skipping, but it does not have immunity to other causes of local minima that can affect waveform inversion; these often increase in importance as the starting model degrades. In practical applications, the method appears able to begin inversion using models that are about two to three times less accurate than would be required for conventional FWI.
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