CONVERTED-WAVE MOVEOUT AND CONVERSION-POINT EQUATIONS IN LAYERED VTI MEDIA: THEORY AND APPLICATIONS

Abstract

We have developed improved equations for calculating the conversion point of the P-SV converted wave (C-wave) in transversely isotropic media with a vertical symmetry axis (vertical transverse isotropy (VTI)). We have also derived modified C-wave moveout equations for layered VTI media. The derived equations for the conversion-point are valid for offsets about three-times the reflector depth (x/z=3.0) and those for the C-wave moveout about twice the reflector depth (x/z=2.0). The new equations reveal some additional analytical insights into the converted-wave properties. The anisotropy has a more significant effect on the conversion point than on the move-out, and using the effective binning velocity ratio γeff only is often insufficient to account for the anisotropic effect, even when higher-order terms are considered. Also for C-wave propagation, the anisotropy appears to affect the P-wave leg more than the S-wave leg. The ratio of the anisotropic contributions from P- and S-waves is close to the vertical velocity ratio γ0. Consequently S-wave anisotropic parameters may be recovered from converted-waves when P-wave anisotropic parameters are known. The new equations suggest that the C-wave moveout in layered VTI media over intermediate-to-far offsets is determined by the anisotropic parameter χeff in addition to C-wave stacking velocity VC2, and the velocity ratios γ0 and γeff. We refer to these four parameters as the C-wave ''stacking velocity model''. Two practical work flows are presented for determining this model: the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that although the single-scanning flow is less accurate than the double-scanning flow, it is more efficient and, in most cases, can yield sufficiently accurate results.