Slowness-domain kinematical characteristics for horizontally layered orthorhombic media. Part II: Pre-critical slowness match

Part II of this paper is a direct continuation of Part I, where we consider the same types of orthorhombic layered media and the same types of pure-mode and converted waves. Like in Part I, the approximations for the slowness-domain kinematical characteristics are obtained by combining power series coefficients in the vicinity of both the normal-incidence ray and an additional wide-angle ray. In Part I, the wide-angle ray was set to be the critical ray (‘critical slowness match’), whereas in Part II we consider a finite long offset associated with a given pre-critical ray (‘pre-critical slowness match’). Unlike the critical slowness match, the approximations in the pre-critical slowness match are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. Moreover, for the pre-critical slowness match, there is no need to distinguish between the high-velocity layer and the other, low-velocity layers. The form of the approximations in both critical and pre-critical slowness matches is the same, where only the wide-angle power series coefficients are different. Comparing the approximated kinematical characteristics with those obtained by exact numerical ray tracing, we demonstrate high accuracy. Furthermore, we show that for all wave types, the accuracy of the pre-critical slowness match is essentially higher than that of the critical slowness match, even for matching slowness values close to the critical slowness. Both approaches can be valuable for implementation, depending on the target offset range and the nature of the subsurface model. The pre-critical slowness match is more accurate for simulating reflection data with conventional offsets. The critical slowness match can be attractive for models with a dominant high-velocity layer, for simulating, for example, refraction events with very long offsets.