P- and S-wave energy current density vectors dot product imaging condition of source time-reversal imaging

Abstract

SUMMARY Source time-reversal imaging (TRI) based on decoupled elastic wave equation can utilize vector P- and S-wave time differences and achieve high-precision source location in complex geological models. The imaging condition is critical for TRI. However, because of the orthogonally polarized properties of P and S waves, traditional vector dot product imaging condition directly applied to TRI will decrease the effective imaging values. In contrast, the energy current density vectors of P and S waves represent the propagation directions of the wavefields and are almost parallel. Their dot product can result in the maximum imaging energy. Based on this principle, we propose a P- and S-wave energy current density vectors dot product imaging condition (PSEDPIC), which uses the propagation direction information of P and S waves at the source point to suppress imaging artefacts generated by waves with inconsistent propagation directions. Numerical tests reveal that PSEDPIC can (1) reduce the image artefacts, (2) improve the imaging spatial resolution and (3) allow a shallower imaging region. In addition, if the numerical simulation algorithm used in TRI can reconstruct the seismic wavefield accurately in the presence of surface topography, the impact of an observation system with elevation differences on imaging can be eliminated automatically. For this reason, we use the curvilinear grid finite-difference method to directly reconstruct the wavefield in TRI to solve the problem of data elevation correction. The test results of 3-D synthetic and field data for microseismic monitoring demonstrate the effectiveness of the proposed method.