Elastic-wave reverse-time migration based on decoupled elastic-wave equations and inner-product imaging condition

Polarity reversal in converted wave images of elastic reverse time migration destructs the reflection events after stacking multi-shot migration profile. We derive a new imaging method for elastic reverse-time migration to automatically circumvent polarity reversal. Instead of obtaining scalar P-wave and vector S-wave potentials from the wavefield by using Helmholtz decomposition as in conventional methods, we obtain vector P- and S-wave displacement wavefields based on a decoupled elastic wave equation, which denotes the displacement component along the propagation direction and perpendicular to the propagation direction, respectively. Based on this decomposition method, the vector P- and S-wavefields preserve the amplitude and phase attributes of the original wavefield. As for the vector wavefields (vector P- and S-wave displacement wavefields), the inner-product imaging condition is proposed to extract reflectivity of specified wave modes at interfaces. The analysis of the imaging kernel demonstrates this imaging condition is valid not only for pure-mode imaging (PP and SS), but also for converted wave imaging (PS and SP) of ground-based seismic exploration. With this new method, we do not have to correct the polarity reversal in converted wave images, which is an essential step in the conventional method with expensive computation costs. Numerical examples with synthetic data have shown that the inner product imaging method works and the quality of the imaging events is effectively improved.