A field data application of regularized elastic passive equivalent source inversion with full waveform inversion

Using full waveform inversion (FWI) to locate passive events allows for an automatic process. Passive seismic data are often acquired on solid surfaces including the bottom of the sea, in which multi-component measurement under the elastic assumption is important. We develop a regularized elastic FWI of passive seismic events to invert for the source image, source function and the velocity model, simultaneously, without any a prior information about the source. 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 applied a focusing function to the source to overcome the possible limited aperture coverage of the acquisition, especially in well recording. The adjoint-state method is used to derive the gradient for the source image, source function and 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.