Finite Difference Wave Equation Forward Modeling Technology Research

With the development of computer technology, the wave equation forward modeling by theoretical research is applied to the actual seismic exploration becomes possible and at the same time in the process of this development, the development of computer hardware more make the model of wave equation forward modeling on the GPU computing becomes more efficient. The wave equation finite difference technology as a key technology in seismic wave field simulation technology, widely used in the forward modeling calculation of wave forward.Seismic wave field numerical simulation technology is under the condition of known structure and parameters of underground medium, by using the method of theoretical calculation of seismic waves in the propagation rules of underground medium, thereby a technique method of synthetic seismogram. Finite difference method is the most commonly used a forward modeling method, it is the basic principle of the wave equation wave field in function of space and time derivative with corresponding difference instead of, is also due to the discrete approximation, inevitably reduce the resolution of the numerical simulation results. In order to effectively reduce the impact of the numerical frequency dispersion, the commonly used method is to improve the subdivision precision of the model. But when the model accuracy, the grid size increases, the finite difference method of calculation time will be greatly improved, if can use the parallel computing method of improving the efficiency of solving can yet be regarded as an effective way to solve the problem.Nvidia development unified computing architecture based on GPU hardware platform CUDA, combines the general features and the GPU class C language programming interface, computational efficiency and develop friendly has become one of the hot research topic of high-performance computing. Because the orthogonal grid based on the time-domain finite difference in calculation, the numerical calculation of each node next time has nothing to do with computing nodes around, this makes the difference algorithm in computing parallelism has a huge space, can very well adapt to the distribution of GPU multi-thread parallel algorithm design ideas.This paper is based on the wave equation forward modeling technology and method of GPU research, based on CUDA application development platform. The main research content is as follows:(1) from the perspective of research based on GPU two-dimensional wave equation model, and gives its corresponding derivation formula of wave equation of mathematical physics, export wave equation finite difference formula of two kinds of different specifications.(2) the same from the perspective of the GPU, the three-dimensional wave equation model is established in this paper, gives corresponding derivation formula of wave equation of mathematical physics, wave equation is derived using different grid difference of finite difference equation.(3) according to the finite difference wave equation seismic forward modeling of seismic source, stability, boundary conditions and other issues, and loading ways of the source are discussed in detail, and the stability of two-dimensional and three-dimensional acoustic wave equation, conditions, and the characteristics of the two kinds of boundary absorption conditions.(4) the study of GPU, completed in CUDA application platform of the finite difference computation. And in these cases, are the 2 d and 3 d forward modeling result, finally demonstrated in this paper on the GPU implementation effectiveness of wave equation forward modeling.