Summary
Adaptive Waveform Inversion (AWI) was introduced by Warner & Guasch (2014) as a means to avoid cycle skipping during full-waveform inversion. Here we demonstrate the robustness of this new method by applying it to three challenging problems: a 3D field dataset without an accurate velocity model to start the inversion; a highly realistic blind synthetic dataset that contains elastic effects, attenuation, an unknown density model and ambient noise; and a simple synthetic dataset where the inversion proceeds using the wrong source wavelet. AWI outperforms conventional FWI in each of these applications, and remains stable and accurate throughout.
Introduction
Conventional full-waveform inversion minimizes the leastsquares difference between an observed and a predicted dataset. Because seismic data are oscillatory, this formulation leads to an objective function that is also oscillatory, generating local minima that represent cycleskipped solutions where the predicted and observed datasets differ by an integer number of cycles. This behavior is the principal reason why FWI requires low frequencies and a highly accurate starting model.
In contrast, adaptive waveform inversion uses convolutional filters to match predicted and observed data, and the inversion is formulated so that it forces the resultant filter coefficients to become zero-lag delta functions. The resulting AWI scheme appears to be entirely immune to the effects of cycle skipping.
AWI has several additional supplementary benefits that also make it superior to conventional FWI. AWI is more able to extract long-wavelength velocity updates from reflection data than is FWI. Surprisingly, AWI also revealed for the field dataset used here that a previous starting model, obtained using high-quality anisotropic travel-time tomography, was cycle skipped for parts of the dataset even at the lowest frequencies available for inversion. This hitherto unsuspected cycle skipping caused detrimental artifacts within the original conventional FWI model, and AWI successfully removed these artifacts.
AWI is one of a family of methods that work by extending the size of the model space in non-physical ways, and that then seek to drive such non-physicality out of the final recovered model. Conventional wave-equation migration velocity analysis proceeds by following an analogous route.
