Ray Tracing In Anisotropic Media And Weakly Anisotropic Medium Approximation Method Preliminary Study

In recent years, the research of seismic anisotropy is becoming an inevitable trend for seismologist to cognize the earth medium and carry on the seismology research. And it also becoming one of a focus and forward subject in seismology research field under the frequent global earthquake.This thesis is composed by the two following parts:The first part:Using the perturbation theory and considering the change that caused by the medium and slowness vector of christoffel matrix. And then, recalculate the formula about qP wave and qS wave in any weakly anisotropic medium. Calculating phase velocity and polarization vector in orthotropic media by using these formulas and make a contrast for the result made by numerical method of Christoffel equation directly at the same time.Result: In order to obtain phase velocity and polarization vector of the spread in different directions that seismic wave emerged, using these formulas to calculating orthotropic anisotropic media. The feebler anisotropic has(less than 10% normally), the less error between exact solution and the result which was calculated by approximate formula will get. With the increase of Anisotropic medium in intensity, the error will widening. When it is a strong anisotropic medium(anisotropic more than 20%), then the error will be very different which calculated by approximate formula.The second part, let's talk about the inversion about this issue. If we get phase velocity and polarization vector of qP wave from observation, we can compute media's elastic parameter or anisotropy parameter through inversion. The medium which we are studying is a vertical non-uniform weakly anisotropic medium, it has a sense of arbitrary symmetry. For such anisotropic medium, we are looking for one reference isotropic medium, the one which is a little different with anisotropic medium. If slowness vector and polarization vector of qP wave is already given, then, slowness formulas and polarization formulas will from a linear system of equation that can confirm the reference of anisotropic. The method is used in a composite multi-dimensional and many source VSP experiments.The experimental results show that the inversion method suggested in this chapter can identify weakly anisotropic parameters which have a sense of arbitrary symmetry, although we suppose slowness vector's tangential component is zero when in inversion. Using less profile demonstrated that we can get good results if we use slowness formula and polarization formula together. Noise experiments show that slowness formula is a reliable tool to ensure anisotropic parameters.