The Calculation Of Ray Path And Travel Time Based On Paraxial Approximation Theory In TI Media

In recent years, with the improvement of the observation technology and the improvement of the theory, anisotropic theory system has been widely used in seismic exploration of quantitative data processing and qualitative interpretation, has become one of the hot spots in geophysical research. However, due to the complexity of the theory and the diversity of the anisotropic species, the study of seismic anisotropy is one of the difficult points in the study of the geophysics.So far, researchers have proposed a variety of anisotropic media, such as TI media, EDA media and PTL media, etc. TI medium(i.e., the transverse isotropic media) is the most widely distributed anisotropic media. Moreover, seventy percent of natural sedimentary layers exhibit characteristics of TI media. It is very important to study the wave field propagation characteristics of TI media, which can simulate the periodic thin layers combination and directional fracture, which is of great significance to the development and utilization of the fractured reservoirs and the complex lithologic reservoirs. For the seismic wave field of TI medium, scholars have studied the propagation matrix and application of TI medium, and made a study on the anisotropic wave theory and finite difference forward modeling. At present, the anisotropic forward algorithm based on wave equation theory has been more mature. But at the same time, there is a very low computational efficiency, high computer memory requirements of the problem; In anisotropic forward calculations, most of the effects of velocity group phase separation are neglected; For TI media, there is very little research on the forward modeling of P and SV waves. The influence of the symmetric axis inclination angle and different velocity model on the wave field of TI medium has not been solved yet.This paper is aimed at the above problems,based on the previous work, the ray tracing method and the ray tracing method were used to calculate the TI medium ray path and travel time. Then, the propagation characteristics of seismic wave field in TI medium are analyzed. Its main contents include:(1) In order to solve the influence of anisotropic strength on the phase velocity separation of the group, a variety of TI media smoothing models are constructed by using the layered modeling method. For the same velocity model, selecting the different strength of anisotropic parameters, the same model parameters are different ray paths and travel time information based on paraxial approximation theory in TI media of ray tracing. The comparative analysis of the group phase velocity separation under different conditions is carried out. What’s more, the ray path and travel time information of P wave and SV are compared systematically, and the phase velocity curves of P wave and SV wave group are compared and studied.(2) In order to study the influence of the symmetry axis inclination angle on the anisotropy of the TI medium, this paper studies the ray tracing and travel time calculation by selecting a variety of symmetrical axes according to the TTI medium model. By comparing the ray path and travel time curve, the influence of the angle on the anisotropy is obtained.(3) In order to study the characteristics of wave propagation in TI medium under different terrain,the uniform model, the layered model, the low velocity layer model, the depression model, the fault model, the tilt model and the international Hess model are selected to carry out the ray tracing of VTI and TTI media. And the wave field analysis is carried out for each terrain.Based on the above research content, through the combination of theoretical analysis and numerical simulation, this paper obtains the following research results:(1) The ray tracing of TI medium based on the paraxial approximation theory is realized. Comparative analysis showed that, VTI, TTI medium and other complex models, the method can accurately calculate the seismic wave propagation path(ray path), The change trend of the travel time curve can well reflect the structural characteristics of the formation.(2) The following facts are proved by calculation: For the P wave in VTI media, When the anisotropy is strong, the change of phase velocity is larger, and the maximum increment is also very large; When the anisotropy parameter is weak, the change of phase velocity is small.(3) By comparing the calculation results of P wave and SV, the effect of SV wave on the increment of velocity and the separation of group phase is obtained, which is weaker than that of P wave, and the overall speed is lower than that of P wave. The strength of anisotropy is mainly reflected in the velocity variation of P wave.(4) For the TTI medium, the wave front can be seen from the travel time curve, the greater the symmetry axis angle, the greater the change of the wave field. The variation of the curvature of the waveform is reflected in the size of the dip angle.To sum up, this paper based on the near axis approximation theory, combined with anisotropic seismic wave theory, the TI medium ray path and travel time calculation and analysis are carried out. The propagation regularity and propagation characteristics of the wave field in a variety of TI media are further studied. This paper has a certain reference significance and practical value for the following treatment of anisotropic seismic data migration and tomography. Provide important theoretical support for the application of anisotropy research in improving the efficiency of oil and gas resource exploration.