Robust full-waveform inversion with Radon-domain matching filter

Cycle skipping is a severe issue in full-waveform inversion. One option to overcome it is to extend the search space to allow for data comparisons beyond the “point-to-point” subtraction. A matching filter can be computed by deconvolving the measured data from the predicted ones. If the model is correct, the resulting matching filter would be a Dirac delta function in which the energy is focused at zero lag. An optimization problem can be formulated by penalizing this matching filter departure from a Dirac delta function. Because the matching filter replaces the local sample-by-sample comparison with a global one using deconvolution, it can reduce the cycle-skipping problem. Because the matching filter is computed using the whole trace of the measured and predicted data, it is prone to unwanted crosstalk of different events. We perform the deconvolution in the Radon domain to reduce crosstalk and improve the inversion. We first transform the measured and the predicted data into the $τ-p$ domain using the local Radon transform. We then perform deconvolution for the trace indexed by the same slope value. The main objective of the proposal is to use the slope information embedded in the Radon-transform representation to separate the events and reduce the crosstalk in the deconvolution step. As a result, the objective function tends to be more convex and stabilizes the inversion process. The result obtained for the modified Marmousi model demonstrates the proposed Radon-domain matching-filter approach can converge to a meaningful model given data without the low frequencies of less than 3 Hz and a $v(z)$ initial model. Compared to the conventional time-space matching-filter approach, the Radon-domain approach indicates fewer artifacts in the model and better fitting of the measured data. The result corresponding to the Chevron 2014 benchmark data set also indicates the good performance of the proposed approach.