波动方程有限差分正演技术研究

发布时间：2018-07-11 16:25

本文选题：波动方程 + 正演建模　；参考：《成都理工大学》2015年硕士论文

【摘要】：随着计算机技术的发展,使得波动方程正演由理论研究应用到实际地震勘探中成为了可能,同时在这发展过程中,计算机硬件的发展更加使得波动方程在GPU上正演模型计算变得更加高效。而波动方程有限差分技术作为地震波场模拟技术中的一种关键技术,被广泛应用到正演计算的波形正演中。地震波场的数值模拟技术是在已知地下介质结构和参数的情况下,利用理论计算的方法研究地震波在地下介质中的传播规律,从而合成地震记录的一种技术方法。有限差分法是最常用的一种正演模拟方法,它的基本原理是将波动方程中波场函数关于空间和时间的导数用相应差分来代替,也正是由于这种离散近似,不可避免地降低了数值模拟结果分辨率。为了有效减小数值频散造成的影响,常用的方法即是提高模型的剖分精度。但是当模型精度提高、网格规模增大时,有限差分方法的计算时间也会大幅度提高,若能用并行计算的方法提高求解效率不失为解决该问题的有效方法。英伟达公司开发的基于GPU硬件的统一计算架构平台CUDA,融合了GPU通用计算特性和类C语言编程接口,以计算高效性和开发友好性成为当前高性能计算的研究热点。由于基于时域的有限差分正交网格在计算时,各个节点下一时刻的数值计算与周围节点的计算无关,这就使得差分算法在计算上有着巨大的空间并行性,能非常好地适应GPU多线程分配的并行算法设计思想。本论文正是针对基于GPU的波动方程正演技术及方法展开研究,以CUDA为应用开发平台。主要研究内容如下：(1)从基于GPU的角度出发研究二维波动方程模型建立,并给出其相应的波动方程数学物理公式进行推导,导出波动方程两种不同规格的有限差分公式。(2)同样是从GPU的角度出发,研究三维波动方程模型建立,给出相应的波动方程数学物理公式进行推导,导出波动方程采用不同网格进行差分的有限差分公式。(3)针对波动方程有限差分地震正演建模中遇到的震源、稳定性、边界条件等问题进行研究,并且详细讨论了震源加载方式,二维及三维声波波动方程的稳定性条件,以及两种边界吸收条件的特点等。(4)针对GPU的研究,完成了在CUDA应用平台上的有限差分运算。并在上述情况下,分别给出了二维以及三维的正演模拟效果,最后论证本论文在GPU上实现波动方程正演的有效性。
[Abstract]:With the development of computer technology, it is possible to apply wave equation forward modeling from theoretical research to practical seismic exploration. With the development of computer hardware, the forward model calculation of wave equation on GPU becomes more efficient. As a key technique in seismic wave field simulation, wave equation finite difference technique is widely used in forward calculation waveform forward modeling. The numerical simulation technique of seismic wave field is a technical method to study the propagation law of seismic wave in underground medium by using the method of theoretical calculation when the structure and parameters of underground medium are known. The finite difference method is one of the most commonly used forward modeling methods. Its basic principle is to replace the derivative of wave field function on space and time with the corresponding difference in wave equation, which is precisely due to the discrete approximation. The resolution of the numerical simulation results is inevitably reduced. In order to reduce the influence of numerical dispersion, the commonly used method is to improve the accuracy of the model. However, when the precision of the model is improved and the mesh size increases, the computational time of the finite difference method will also be greatly increased. If the parallel computing method can be used to improve the efficiency of the solution, it is an effective method to solve the problem. The unified computing architecture platform CUDA-based on GPU developed by Nvidia integrates the general computing characteristics of GPU and C-like programming interface, which becomes the research hotspot of high performance computing in order to compute high efficiency and develop friendliness. Because the computation of the finite-difference orthogonal grid based on time domain is independent of the computation of the surrounding nodes at the next moment, the difference algorithm has great spatial parallelism. It can adapt to the parallel algorithm design idea of GPU multi-thread allocation very well. In this paper, the forward modeling technology and method of wave equation based on GPU are studied, and CUDA is used as the development platform. The main contents are as follows: (1) from the perspective of GPU, the establishment of two-dimensional wave equation model is studied, and the corresponding mathematical and physical formulas of wave equation are derived. Two finite difference equations of wave equation with different specifications are derived. (2) from the point of view of GPU, the establishment of three-dimensional wave equation model is studied, and the corresponding mathematical and physical formulas of wave equation are derived. The finite difference formula of wave equation is derived by using different meshes. (3) the source, stability and boundary conditions encountered in forward modeling of wave equation finite difference earthquake are studied, and the source loading mode is discussed in detail. The stability conditions of two-dimensional and three-dimensional acoustic wave equations, as well as the characteristics of two boundary absorbing conditions, etc. (4) the finite difference operation on the CUDA platform is completed for the study of GPU. In the above cases, the forward simulation results of two and three dimensions are given, and the validity of the forward modeling of wave equation on GPU is demonstrated.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4

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