2-D PP and PS imaging for VTI with weak equation-converted S-waves

Abstract

For elastic reverse time migration (ERTM) in inhomogeneous isotropy (ISO), the key is to deal with conversions caused by media inhomogeneity. However, for ERTM in vertical transverse isotropy (VTI), researchers also need to handle equation-converted waves (such as S-wave generated with pure explosive source exciting) caused by undecoupling of elastic wave equation generated coincident with incident wave (such as P-wave generated with pure explosive source exciting) in homogeneous VTI, leading to crosstalk artifacts caused by unseparation of waves of the same mode. To analyze equation-converted waves, we define five pseudospatial differential operators and rewrite elastic wave equation of VTI into a form represented by Thomsen parameters. The rewrited equation shows the relationship between equation-converted wave and Thomsen parameters including three anisotropic parameters and two velocity parameters (α and β). Further studies indicate that when explosive source excites in homogeneous weak-anisotropy VTI with α/β = 1.73, the ratio between the energy of equation-converted S-waves and incident P-waves is generally <0.5 and we define equation-converted S-wave whose energy is less than the half of incident P-wave as weak equation-converted S-wave. On this basis, we propose an ERTM method for VTI with weak equation-converted S-waves and its effectiveness is demonstrated by the imaging results for two-layer models and Marmousi2 model.