Subspace methods for time-lapse elastic full-waveform inversion

The application of elastic full waveform inversion on time-lapse seismic data is arising from the boom in conventional full waveform inversion. In the past few years, many different inversion strategies are introduced for the time-lapse case, taking advantage of the power of FWI in capturing small changes. However, all methods tend to suffer from the imperfect repeatability of the data acquisition and the weakness in FWI in focussing on the affected areas (i.e. the reservoir). Thus, we modify the subspace method and apply it to time-lapse elastic full waveform inversion. A soft mask calculated using the gradients of the baseline and monitoring data, which acts as a pre-conditioner, is introduced to localize the update area to the affected regions. Specifically, we suppress the similarities of the two gradients and at the same time highlight their differences when calculating the soft mask. The calculated soft mask can reduce the dimensionality of the inverse problem with a delicately selected threshold, which provides a feasible way to calculate the reduced Hessian matrix. Besides, it is a data-driven approach free of human intervention or apriori knowledge. For comparison, we also use a hard mask surrounding the injection area. The numerical example shows that the proposed soft mask performs better than the hard mask.