Microseismic Event Estimation Based on an Efficient Wavefield Inversion

Full-waveform inversion (FWI) has shown its potentials in active seismic scenario in extracting a high-resolution velocity model of the subsurface. In the microseismic scenario, the source function is unknown, and FWI can be applied to optimize the source image and the velocity model, simultaneously. However, FWI is a highly nonlinear optimization problem, and it causes a bigger challenge when the source location and origin time are unknown. To mitigate these issues, we propose a two-stage scheme to invert for the source function and the velocity using an efficient wavefield inversion (EWI). We use outer-loop iterations to repeat the process until we achieve convergence. We specifically formulate an optimization problem to linearly reconstruct the wavefield that tries to fit both the data, as well as the wave equation corresponding to the background model. In the first stage, the reconstructed wavefield is used to calculate a source function using the background wave equation modeling operator without any inversion or update process. In the second stage, we use the computed source function to represent the true source to update the velocity model in the same way we use EWI in the active seismic case. Applications on data generated from a modified Marmousi model with a single microseismic event and multiple simultaneous events demonstrate the ability of the proposed method. An application to field dataset also demonstrates that the proposed method is effective in locating the microseismic event and inverting for a reasonably good velocity model, sequentially.