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 (ε, δ, and γ). In this research, the discrete least-squares approximation will be used to fit the three coefficients (A 2 , A 4 and A*) of the non-hyperbolic P- and SV-wave traveltime curves. The coefficient A 2 determines the short-spread moveout velocity, A 4 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 A 2 , A 4 and the horizontal velocity. For P-wave propagation, the coefficient A 2 depends on vertical velocity (V Po ) and Thomsen parameter d, while the coefficient A 4 is controlled by V Po , d and e. For SV-wave propagation, the coefficients A 2 and A 4 depend on the vertical velocity ratio V Po /V So , δ and ε. And for SH-wave propagation, the coefficient A 2 depends on the Thomsen parameter g and the vertical velocity (V SHo ). 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 A 4 for the SH wave vanishes. The three coefficients depend on the vertical velocities and Thomsen parameters (ε, δ, and γ). Therefore, by combining these coefficients, we will be able to recover the Thomsen parameters and the vertical velocities.
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