Effective reflection coefficients for curved interfaces in transversely isotropic media

摘要

Plane-wave reflection coefficients (PWRCs) are routinelyused in amplitude-variation-with-offset analysis and for generat-ing boundary data in Kirchhoff modeling. However, the geomet-rical-seismics approximation based on PWRCs becomes inade-quate in describing reflected wavefields at near- and postcriticalincidence angles. Also, PWRCs are derived for plane interfacesand break down in the presence of significant reflector curvature.Here, we discuss effective reflection coefficients (ERCs) de-signed to Overcome the limitations of PWRCs for multicompo-nent data from heterogeneous anisotropic media. We representthe reflected wavefield in the immediate vicinity of a curved in-terface by a generalized plane-wave decomposition, which ap-proximately reduces to the conventional Weyl-type integral com-puted for an apparent source location. The ERC then is obtained as the ratio of the reflected and incident wavefields at each pointof the interface. To conduct diffraction modeling, we combineERCs with the tip-wave superposition method (TWSM), extend-ed to elastic media. This methodology is implemented for curvedinterfaces that separate an isotropic incidence half-space and atransversely isotropic (TI) medium with the symmetry axis or-thogonal to the reflector. If the interface is plane, ERCs generallyare close to the exact solution, sensitive to the anisotropy param-eters and source-receiver geometry. Numerical tests demonstratethat the difference between ERCs and PWRCs for typical TImodels can be significant, especially at low frequencies and inthe postcritical domain. For curved interfaces, ERCs provide apractical approximate tool to compute the reflected wavefield.We analyze the dependence of ERCs on reflector shape and dem-onstrate their advantages over PWRCs in 3D diffraction model-ing of PP and PS reflection data.