| As a fast and effective approximative calculate method of wave field,raytracing has a very important meaning to the research of the seism wave theory and the seism wave's invertion and excursion imaging process. The theory foundation of the raytracing is that under the conditions of high-frequency approximate the major energy of the seism wave transmits along the radial trace. The traditional raytracing methods comprise the try-shooting method of the initial value problem and the bending method of the border value problem. According to the circs of a bunch of rays set up from the source to the receive point, the try-shooting method gets the traveltime at the receive point by the interpolation between two traveltime of rays close to the receive point. The bending method begins with a imaginary radial road from the source to the receive point, then disturb the ray road base on the minimum traveltime rules and at last get the traveltime and the raytrace. In recent years, the Kirchhoff's intergral fore-stack depth migrations get much useful in the complex formation imaging. As one of its algorithm basises, the raytracing metods develop very fast. Large number of new algorithms different from the traditional raytracing methods have appeared. The main features of these methods are that they aren't limited by the descriptions of the travetime and raytracing of the seism wave. They set out directly from the principle of Huygens and the Fermat theory and then descript the features of the seism wave fields by adopting the equivalent fore-waves. Under my supervisor's guiding, I have studied traditional raytracing methods and their new developments and then get a grid raytracing method according to the ideas in correlate documents. At last I practise the method on difference models.All traditional raytracing methods set out from the ray-equations and after divergence to the medium they get the traveltime and raytace from the ray-equations. But they have many deficiencies and main problem is that:Hard to handle the stronger change of velocity of the medium.Hard to work out the global minimum traveltime of hypervalue traveltimes.Calculation efficiency is lower.The shortage of the rays overlay density in the shadow areas.However, it is very limited to consider the minimum traveltime in the seism wave traveltimes only. Even if considering the ray migration, it is far not enough. As a result, in the recent years, it concentrates primarily the calculations of the multivalue traveltimes. The development of the research is that:The improvement on the foundation between traditional try-shooting method and bending method, eg. Various wave front reconstruction methods. In addition to multivalue traveltimes, they have resolved the calculation efficiency and the shadow areas problems.The improvement of the minimum traveltime algorithms, for example, slowness matching method. It is a extend of the shortest path methods.The combinative method between the traditional methods and the shortest traveltime method, such as HWT method, it calculate ray path by the wave front transmitting.The text expands two raytracing methods in common use, that is the finite difference method and the ordered wave front reconstruction method. They all have resolved the defects of the traditional raytracing methods. The finite difference method brings up eikonal equation finite difference method for the traveltime calculation. It can get exact result even in greater speed model. But for complicated velocity model in flat-out construction, it can't find the minimum traveltime similar to the Vidale algorithm. Therefore it still needs to find a kind of efficient search scheme to let the finite difference method realize the wave front tracing really. The ordered wave front reconstruction method has features as follows:a. Put up the raytracing calculation by the actual wave front expand instead of the expand square matrix. Better to hold the raytrace trend. Increase the calculation precision.b. The calculations of the minim...
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