3D PS-wave imaging with elastic reverse-time migration

Abstract

One of the important features of elastic reverse-time migration is that it is a depth domain prestack migration method based on a vectorial wavefield. PP- and PS-wave images can be easily generated by implementing an imaging condition to pure wave modes separated with divergence and curl operators in isotropic media. In the 3D case, however, the curl calculation will generate a 3C vector S-wave, which makes it impossible to generate a scalar PS image with the crosscorrelation imaging condition. Therefore, we first analyzed the polarity distribution of a 3D S-wave and concluded that the separated S-wave keeps perpendicular to a plane determined by the particle motion direction and the propagation direction of the S-wave. This specific plane is the raypath plane when the S-wave is excited by an incident P-wave. The normal direction of the raypath plane can be calculated by computing the vector product of the propagation directions of source and receiver wavefields. Then, we used this normal direction as the reference direction of the S-wave to scalarize the S-wave. Scalarization can be achieved by assigning a positive sign if the vector S-wave is equidirectional with the reference direction or a negative sign if the vector S-wave is contradirectional with the reference direction. Additionally, the scalar S-wave has the same absolute value as the vector S-wave. Next, the P-wave and the scalar S-wave can be applied to an imaging condition to generate a scalar PS image. Numerical examples with true velocity models and those in the presence of velocity error and data noise are presented to demonstrate the potential of the proposed method.