旋转轴对称介质中的qP波一阶射线追踪

Elastic anisotropy is a very common phenomenon in the Earth’s interior, especial for sedimentary rock as important gas and oil reservoirs. But in the processing and interpretation of seismic data, it is assumption that the media in the Earth’s interior is completely elastic and isotropic, and then the methods based on isotropy are used to deal with anisotropic seismic data, so it makes the seismic resolution lower and the error on images is caused. The research on seismic wave simulation technology can improve our understanding on the rules of seismic wave propagation in anisotropic media, and it can help us to resolve problems caused by anisotropy of media in the processing and interpretation of seismic data. So researching on weakly anisotropic media with rotated axis of symmetry, we study systematically the rules of seismic wave propagation in this kind of media, simulate the process with numerical calculation, and get the better research results. The first-order ray tracing (FORT) formulas of qP wave derived can adapt to every anisotropic media with arbitrary symmetry. The equations are considerably simpler than the exact ray tracing equations. The equations allow qP waves to be treated independently from qS waves, just as in isotropic media. They simplify considerably in media with higher symmetry anisotropy. In isotropic media, they reduce to the exact ray tracing equations. In contrast to other perturbation techniques used to trace rays in weakly anisotropic media, our approach does not require calculation of reference rays in a reference isotropic medium. The FORT-method rays are obtained directly. They are computationally more effective than standard ray tracing equations. Moreover the second-order travel time corrections formula derived can be used to reduce effectively the travel time error, and improve the accuracy of travel time calculation. The tensor transformation equations of weak-anisotropy parameters in media with rotated axis of symmetry derived from the Bond transformation equations resolve effectively the problems of coordinate transformation caused by the difference between global system of coordinate and local system of coordinate. The calculated weak-anisotropy parameters are completely suitable to the first-order ray tracing used in this paper, and their forms are simpler than those from the Bond transformation. In the numerical simulation on ray tracing, we use the travel time table calculation method that the locations of the grids in the ray beam are determined, then the travel times of the grids are obtained by the reversed distance interpolation. We get better calculation efficiency and accuracy by this method. Finally we verify the validity and adaptability of this method used in this paper with numerical simulations for the rotated TI model with anisotropy of about 8% and the rotated ORTHO model with anisotropy of about 20%. The results indicate that this method has better accuracy for both media with different types and different anisotropic strength. Keywords: weak-anisotropy, numerical simulation, ray tracing equation, travel time, inhomogeneity