Study On Nonhyperbolic Traveltime-offset Of Pure Modes For A Horizontal Interface In The TI Media With An Arbitrary Spatial Orientation

In isotropic media, the reflection traveltime-offset of pure (non-converted) modes from a horizontal interface in CMP (Common Middle Point) gathers can be strictly described by a hyperbolic curve for both near and far-offset. While in TI (Transverse Isotropy) media, such reflection traveltime-offset is a hyperbolic curve for near-offset, but a nonhyperbolic curve for far-offset. For VTI, HTI, TTI and weak anisotropy approximation, there are many researches. Yao (2005) presents the exact analytic solution of the NMO velocity for the ATI (TI with an Arbitrary spatial orientation) media. In this thesis, we attempt to extend the study of the nonhyperbolic reflection traveltime-offset for the far-offset to the ATI media with arbitrary anisotropy strength. Our research is divided into two parts: theoretic forward modeling and TI parameter inversion.In the part of forward modeling, we adjust the nonhyperbolic moveout equation and present an exact analytic expression for the quartic moveout coefficient (A₄) of the Taylor series expansion of the squared traveltime [ t² (x²) ] for the ATI media through the coordinates transformation.For the adjusted nonhyperbolic moveout equation, based on our exact analytic solution of A₄, and NMO velocity, a formula of the denominator coefficient (A*) in the nonhyperbolic moveout equation for the far-offset in the ATI media is presented, which makes the nonhyperbolic moveout equation fit the reflection traveltime exactly. Therefore, our work extends the application of the nonhyperbolic moveout equation to the ATI media and makes the nonhyperbolic moveout correction and stack of the far-offset in the ATI media.Our analytic solution of A₄ facilitates anisotropy interpretation, the analyses of the influence factors, the inversion of the anisotropy parameters and improving the imaging quality. The solution of A₄ has no limitation to the anisotropy strength and the TI orientation. It unifies all the special cases in existing researches, such as VTI, HTI, TTI, and weak anisotropy approximation.A comparison between our exact solution and the approximate solution of A₄ for weak anisotropy shows that the approximate solution for weak anisotropy loses its exactness and has notable errors with the increasing anisotropic parametersεandδ. The exact and approximate solutions are different in the magnitude and signs (positive and negative) of A₄ as well as the variations with azimuths. Compared with the exact traveltime-offset of the ray-tracing algorithm, our exact analytic solution of A₄ can be used for calculating the nonhyperbolic traveltime-offset with different azimuth in the ATI media. The adjusted nonhyperbolic moveout equation can precisely describe the traveltime curves with the different azimuth in the ATI media with arbitrary anisotropy strength, and can also replace the timeconsuming, multioffset, multiazimuth ray tracing method to do the forward modelling of the reflection traveltime for the far-offset in the ATI media.In the second part of our study, we discuss the performance of the parameter inversion of anisotropy and TI orientation by means of the genetic algorithm. For the P-wave reflection, the NMO velocity and A₄ in the ATI media can be described by five parameters (V_p0,ε,δ,θ_c, andφ_c) .In comparison with the VTI media, there are new two parameters (θ_c,φ_c) for the orientation of the symmetric axis in the ATI media. The new two parameters can be obtained through the nonhyperbolic traveltime-offset with different azimuth. Like the case of the VTI, only the nonhyperbolic traveltime data of the P-wave are not sufficient to retrieve the three parameters V_p0,εandδ, suggesting that the inversion can be performed by using multiazimuth nonhyperbolic (long-spread) P-wave reflection traveltime data, and vertical velocity from check shot and drill or log well data. We discuss the feasibility of the inversion condition and the uniqueness of the inversion result. In our inversion with three profiles, we use three different near-offset NMO velocities and one far-offset A₄ in conjunction with vertical velocity or interface depth from the other data. Then, the inversion is performed for anisotropy parameters and the TI orientation with the genetic algorithm. The numerical tests demonstrate that the precision and stability of our inversion is satisfactory.