Focusing of elastic waves for microseismic imaging

Microseismic events generate compressive waves and shear waves, which can be recorded at receivers. We present a theory that shows how elastic P and S waves separately backpropagate to the original source location. These refocused P and S wavefields are free of singularities. We also demonstrate a technique that enhances the ability to image the spatial focus for each wave type using elastic waves. The improved spatial focus obtained is achieved in a velocity model for which the interface boundaries are approximate but where the mean slowness is correct. Deconvolution designs a signal to be rebroadcasted from the receivers, using only the waves recorded at each receiver, such that the wavefield has an optimal temporal focus at the source location. We demonstrate theoretically and numerically that improved temporal focusing of elastic waves leads to improved spatial focusing for each wave type. This proposed technique only involves a simple pre-processing step to the recorded data and its cost is hence negligible compared to the total cost of microseismic imaging.