PS interferometric imaging condition for microseismic source elastic time-reversal imaging

The time-reversal imaging method utilizes the wave equation to back-propagate recorded seismic data and a proper imaging condition to locate a passive seismic source. For an explosive source, the reconstructed wavefield is focused at the seismic source location and origin time. Although the elastic time-reversal wavefield for a moment tensor source may not exhibit a maximum at the true location at the origin time, it does exhibit a quasi-symmetrical spatial distribution around the source location that represents the radiation pattern of the moment tensor source. We propose the use of an interferometric imaging condition to solve the radiation pattern problem, which is combined with elastic PS cross-correlation imaging condition (referred to as the PS interferometric cross-correlation imaging condition) to locate a moment tensor source using elastic time-reversal imaging method. 2-D and 3-D numerical tests demonstrate that our proposed method can identify the moment tensor source location in complex velocity models with a high noise level. In tests of the sensitivity of the method to the accuracy of the velocity model, we find that the method can still get focused images under about 10–25 per cent random perturbations in P- and S-wave velocities, but only under about 5 per cent correlated perturbation of global P- and S-wave velocities with a potential bias in the location.