Scalar imaging condition for elastic reverse time migration

Polarity changes in converted-wave images constructed by elastic reverse time migration cause destructive interference after stacking over the experiments of a seismic survey. This polarity reversal is due to PS and SP reflectivities reversing sign at certain incidence angles, e.g., at normal incidence in isotropic media. Many of the available polarity correction methods are complex and require costly transformations, e.g., to the angle domain. We derive a simple imaging condition for converted waves to correct the image polarity and reveal the conversion strength from one wave mode to another. Our imaging condition exploits pure P-and S-modes obtained by Helmholtz decomposition. Instead of correlating Cartesian components of the vector S-mode with the P-mode, we exploit all three components of the S wavefield at once to produce a unique image. We generate PS and SP images using geometric relationships among the propagation directions for the P-and S-wavefields, the reflector orientation, and the S-mode polarization direction. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our imaging condition is simple and robust and does not significantly increase the cost of reverse time migration. Several numerical examples were used to test the effectiveness of our new imaging condition using simple and complex models.