Full-waveform inversion via source-receiver extension
Full-waveform inversion produces highly resolved images of the subsurface and quantitative estimation of seismic wave velocity, provided that its initial model is kinematically accurate at the longest data wavelengths. If this initialization constraint is not satisfied, iterative model updating tends to stagnate at kinematically incorrect velocity models producing suboptimal images. The source-receiver extension overcomes this “cycle-skip” pathology by modeling each trace with its own proper source wavelet, permitting a good data fit throughout the inversion process. Because source wavelets should be constant (or vary systematically) across a shot gather, a measure of source trace dependence, for example, the mean square of the signature-deconvolved wavelet scaled by time lag, can be minimized to update the velocity model. For kinematically simple data, such measures of wavelet variance are mathematically equivalent to traveltime misfit. Thus, the model obtained by source-receiver extended inversion is close to that produced by traveltime tomography, even though the process uses no picked times. For more complex data, in which energy travels from source to receiver by multiple raypaths, Green’s function spectral notches may lead to slowly decaying trace-dependent wavelets with energy at time lags unrelated to traveltime error. Tikhonov regularization of the data-fitting problem suppresses these large-lag signals. Numerical examples suggest that this regularized formulation of source-receiver extended inversion is capable of recovering reasonably good velocity models from synthetic transmission and reflection data without stagnation at suboptimal models encountered by standard full-waveform inversion, but with essentially the same computational cost.
full-waveform inversion; deconvolution; frequency domain