Mapping the P‐S conversion point in vertical transversely isotropic (VTI) media

Abstract

The important aspect of converted-wave (P-S) seismology is that the exact location of P-S conversion point at the reflector is not well known. For a single horizontal layer, the position of the conversion point can be calculated exactly from an analytic expression. In multi-layered strata, the conversion point is not at a constant offset from the source, but traces a trajectory that moves towards the receiver as the depth decreases. The earth is known to be anisotropic, although basic seismic survey planning and data-processing are based on the isotropic assumption. The most common anisotropic case is Vertical Transversely Isotropic (VTI) media. In VTI media, there can be a large difference between the true coordinate of the conversion point and the one obtained from the isotropic single-layered model. This horizontal displacement of the conversion point in VTI media from that in the isotropic case is dependent on the offset-to-depth ratio, velocity ratio, and anisotropic parameters e and δ defined by Thomsen. The relationship linking the displacement and the anisotropic parameters, and offset-to-depth ratio, can be complicated. An algorithm to calculate this relationship is developed using Thomsen’s anisotropy equations, both the linear approximation and the exact forms. A VTI model is designed using NORSAR2D software and the common-shot raytracing is performed to obtain the conversion-point coordinate. The displacement of the conversion point increases with the increasing offset to depth ratio and the anisotropy parameter e. The value of δ can also have large influence on the displacement of the conversion point. We conclude that when the anisotropic parameter e is smaller than δ, the conversion point is displaced towards the receiver relative to its location in an isotropic medium. When e is larger than δ, the conversion point moves towards the source compared to that in the isotropic medium. There is no large difference between the results from Thomsen’s linear equations and the results from exact equations at small offset-todepth ratios. INTRODUCTION Converted waves have been more and more widely used in seismic exploration, for they can provide high-quality images where conventional images are poor (Stewart et al., 1999). Figure 1 shows the geometry of the converted wave in a thick, uniform isotropic layer. A ray emitted as a P-wave at angle θP from the source reflects from the bottom of the layer as an S-wave at an angle θS and is received at the receiver at a certain offset. These two angles are related by Snell’s law: