Regularized passive elastic full-waveform inversion with an unknown source

Using full waveform inversion (FWI) to locate passive sources and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of passive events faces incredible nonlin-earity due to the unknown source location (space) and function (time). We develop a regularized elastic FWI of passive seismic events to invert for the source image, source function and the velocity model, without any a prior information about source location or source function in time. We reformulate the elastic problem by representing the source images by P-wave and S-wave perturbation coefficients. The unknown source ignition time is mitigated by convolving reference traces with the observed and modeled data. A total variation regularization is applied to improve the robustness of the velocity inversion considering the limited sources and illumination angles of microseismic experiments. We also include a focusing penalty function applied to the source to overcome the limited aperture coverage of the acquisition. The adjoint-state method is used to derive the gradient for the source image, source function and the velocity. The resulting inversion framework is capable of handling limited aperture data and limited sources. Application to synthetic and real data with limited recording aperture along a well demonstrates the effectiveness of the approach.