High-Order Elastic Wave Equation Forward Modeling And Reverse-Time Migration

The paper includes two aspects. One is the high-precision and multi-dimension elastic wave forward numerical modeling, and the other is high-precision pre-stack and post-stack elastic wave reverse time depth migration. The first one is based on elastic wave theory, which can reserve seismic wave's characters of kinematics and dynamics, is an important mean of understanding the rules of seismic wave propagation, and is a tool for us to identify the seismic wave field. It also is the basic of pre-stack and post-stack elastic wave reverse time depth migration. Elastic wave simulation technique is used in almost every aspect of seismic data acquisition, processing, interpretation and oil exploitation engineering. To do further research about seismic wave modeling is the urgent need to meet the high request of exploration precision and more and more complicated exploration task. It may help us to get more knowledge about seismic wave propagation theory in complicated exploration target, and to solve the current difficult problems in oil and gas exploration and exploitation.In order to solve the basic problems of elastic wave forward numerical modeling such as precision, stability, absorbing conditions and so on, this paper, based on previous research work, discusses the issues in detail from theoretical angle, for example, where the precision errors come from, the mechanism of how is the instability generating, the boundary reflection mechanism and so on. And put forward some ideas, such as the numerical precision can be improved by combination of high-order staggered-grid finite difference method and flux correction transport technology (FCT), boundary reflection phenomenon can be weakened or removed by using PML absorbing boundary condition or using optimized paraxial approximation weighted absorbing boundary condition, under the above conditions, the instability phenomenon can be effectively restrained or delayed by means of the spatial or temporal step which satisfies the stable condition and low-pass filter and so on. Based on above research, we propose an improved 3D random modeling method which is used to depict complex volcanic rock model, and at the same time, develop 3D elastic wave field separation numerical modeling method to solve the problem on difficulty to exactly separate P-wave and S-wave from hybrid wave field. The method is tested by simple model and complex model, and the results show that it is exact and valid. Then successfully apply it to two-phase medium numerical modeling, the quick/slow P-wave and S-wave are completely separated. Achieve 2D/3D acoustic wave, single-phase anisotropy/isotropy medium, two-phase anisotropy/isotropy medium elastic wave numerical modeling with high-order elastic wave equation, the results indicate that the paper's high-order method has advantages such as high precision, easy to identify the wave character, stability of the numerical process, no boundary reflection phenomenon, and so on. In addition, the high-precision pre-stack and post-stack reverse time depth migration arithmetic is successfully carried out with reverse time extrapolation method, the test with complex model shows that it is better than the rest actual pre-stack and post-stack depth migration arithmetic, and also shows that all of the depth migration arithmetic especially the reverse time depth migration arithmetic are sensitive with velocity variation. Then apply the method to up-ward wave of VSP to achieve reverse time depth image, the theoretical velocity model's interfaces are clearly and correctly imaged, what's more, we extend the method to anisotropy medium and isotropy medium elastic wave pre-stack and post-stack reverse time depth migration, the complex model tested is accurately imaged. The numerical results show that the paper's method can meet the needs of high-precision multi-wave and multi-component seismic exploration. This thesis's research work is hoping to give some reference to domestic and foreign colleague who is engaged with the work of elastic wave forward numerical modeling and depth image.