Converted-wave seismology in anisotropic media revisited, Part I: Basic theory

We have developed new basic theories for calculating the conversion point and the travel time of the P-SV converted wave (C-wave) in anisotropic, inhomogeneous media. This enables the use of conventional procedures such as semblance analysis, Dix-type model building and Kirchhoff summation, to implement anisotropic processing, and makes anisotropic processing affordable. Here we present these new developments in two parts: basic theory and application to velocity analysis and parameter estimation. This part deals with the basic theory, including both conversion-point calculation and moveout analysis. Existing equations for calculating the PS-wave (C-wave) conversion point in layered media with vertical transverse isotropy (VTI) are strictly limited to offsets about half the reflector depth (an offset-depth ratio, xlz, of 0.5), and those for calculating the C-wave traveltimes are limited to offsets equal to the reflector depth (x/z=l.0). In contrast, the new equations for calculating the conversion-point extend into offsets about three-times the reflector depth (x/z=3.0), those for calculating the C-wave traveltimes extend into offsets twice the reflector depth (x/z=2.0). With the improved accuracy, the equations can help in C-wave data processing and parameter estimation in anisotropic, inhomogeneous media.