Extended wave-equation imaging conditions for passive seismic data

The information obtained from seismic monitoring at injection sites is often limited to seismic event properties (e.g., location, origin time, moment tensor), the accuracy of which greatly depends on the assumed or estimated elastic velocity models. Current traveltime-based methods to calibrate velocity models rely on having distinct arrivals. In surface seismic monitoring, however, the signal-to-noise ratio of arrivals is often too poor for pick-based methods, and migration techniques are needed. Wave-equation migration can image microseismic sources without the need for picking or knowledge of the onset time by reconstructing the wavefield through the model space and applying an imaging condition. We have devised extended imaging conditions for passive seismic wave-equation imaging algorithms, and we have found that they represent a key step toward verifying and updating elastic velocity models. By extending imaging conditions away from zero lag in time and space, we can better evaluate the focusing of a given event based on a self-consistency principle that direct arrival waves focus at zero lag only when the velocity models were correct. We have determined that given an elastic medium and multicomponent recordings, we can propagate and correlate microseismic P- and S-wavefield modes to compute extended imaging conditions that are sensitive to P-and S-wave velocity perturbations. The extended image volume is robust to sparsely sampled data and high levels of noise and is sensitive to velocity model errors. The extended image volume can be used to determine relative P-and S-wave velocity updates to improve focusing.