P -wave signatures and notation for transversely isotropic media: An overview

Abstract Progress in seismic inversion and processing in anisotropic media depends on our ability to relate different seismic signatures to the anisotropic parameters. While the conventional notation (stiffness coefficients) is suitable for forward modeling, it is inconvenient in developing analytic insight into the influence of anisotropy on wave propagation. Here, a consistent description of P-wave signatures in transversely isotropic (TI) media with arbitrary strength of the anisotropy is given in terms of Thomsen notation. The influence of transverse isotropy on P-wave propagation is shown to be practically independent of the vertical S-wave velocity VS0, even in models with strong velocity variations. Therefore, the contribution of transverse isotropy to P-wave kinematic and dynamic signatures is controlled by just two anisotropic parameters, ε and δ, with the vertical velocity VP0 being a scaling coefficient in homogeneous models. The distortions of reflection moveouts and amplitudes are not necessarily correlated with the magnitude of velocity anisotropy. The influence of transverse isotropy on P-wave normal-moveout (NMO) velocity in a horizontally layered medium, on small-angle reflection coefficient, and on point-force radiation in the symmetry direction is entirely determined by the parameter δ. Another group of signatures of interest in reflection seisimology–the dip-dependence of NMO velocity, magnitude of nonhyperbolic moveout, time-migration impulse response, and the radiation pattern near vertical–is dependent on both anisotropic parameters (ε and δ) and is primarily governed by the difference between ε and δ. Since P-wave signatures are so sensitive to the value of ε − δ, application of the elliptical-anisotropy approximation (ε = δ) in P-wave processing may lead to significant errors. Many analytic expressions given in the paper remain valid in transversely isotropic media with a tilted symmetry axis. Moreover, the equation for NMO velocity from dipping reflectors, as well as the nonhyperbolic moveout equation, can be used in symmetry planes of any anisotropic media (e.g., orthorhombic).