Elastic micro-seismic full waveform inversion with an unknown source

"Using full waveform inversion (FWI) to locate microseismic sources and image microseismic events allows for a data-driven process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop an elastic FWI algorithm geared to handle microseismic events as it inverts for the source image, source function and the velocity model, without any prior information about source location or source function in time. The objective function is based on convolving reference traces with the observed and modeled data to mitigate the cycle skipping problem caused by an unknown source ignition time. A reformulation of the source term in elastic wave equation is used to allow for a source image in elastic media, short of the often underdetermined source moment tensor. The adjoint-state method is used to derive the gradients for the source images, source function and the velocities update. By inverting for all the three unknowns, the proposed method produces good estimates of the source location, ignition time and the background velocity of a modified Marmousi model."