Approximate parameters of anisotropy from reflection traveltime curves

Siriporn Chaisri, R. James Brown

For elastic-wave propagation in a transversely anisotropic medium, there are five elastic parameters, which may be expressed as the two vertical velocities and the Thomsen parameters (, , and ). In this research, the discrete least-squares approximation will be used to fit the three coefficients (A2, A4 and A*) of the non-hyperbolic P- and SV-wave traveltime curves. The coefficient A2 determines the short-spread moveout velocity, A4 gives the correction for nonhyperbolic moveout (in the case of strong anisotropy) and A* is a parameter for correcting the behavior of moveout at large offset, which depends on A2, A4 and the horizontal velocity. For P-wave propagation, the coefficient A2 depends on vertical velocity (VPo) and Thomsen parameter d, while the coefficient A4 is controlled by VPo, d and e. For SV-wave propagation, the coefficients A2 and A4 depend on the vertical velocity ratio VPo/VSo, and . And for SH-wave propagation, the coefficient A2 depends on the Thomsen parameter g and the vertical velocity (VSHo). In a homogeneous transversely isotropic medium, the wavefront of the SH wave is always elliptical, and the SH-moveout is hyperbolic, so that the coefficient A4 for the SH wave vanishes. The three coefficients depend on the vertical velocities and Thomsen parameters (, , and ). Therefore, by combining these coefficients, we will be able to recover the Thomsen parameters and the vertical velocities.