三维复杂介质弹性波场有限差分数值模拟方法研究

发布时间：2018-11-08 16:34

【摘要】：地震勘探在能源矿产及工程勘查中都有着广泛的应用,但多为二维地震勘探及相应的二维地震波场数值模拟。近年来三维甚至四维地震勘探有较大的发展趋势,本文主要针对三维地震进行数值模拟。地下实际具有各向异性和粘滞性等特点,对三维异性介质及粘弹介质中地震波场的传播特性的模拟是地震勘探学研究的重要课题之一,可以利用三维波场模拟验证理论算法、识别波场特征以及对野外观测系统设计具有指导作用。本文使用旋转交错网格模拟三维一阶速度应力波动方程,将传统交错网格中的速度、应力分量和介质参数重新分布。应力分量、弹性模量和速度分量、密度被分别放置在单元网格沿对角线的两个顶点上,通过对角线方向上的四个导数值近似计算水平方向和垂直方向上的导数。采用旋转交错网格正演模拟时,不需要对弹性模量求平均,使得在模拟地震波在粘弹介质、各向异性介质中传播时克服了传统交错网格计算结果不稳定的缺点,提高了波场模拟的精度。文中讨论了弹性各向异性介质中的地震波场数值模拟,使用Kelvin介质模拟粘弹性介质,并对其进行波场模拟,分析了粘弹性介质相对弹性介质的波场差异。针对数值模拟中的人工边界条件,使用CE吸收边界和非分裂的NPML吸收边界对波场在模型边界附近进行吸收衰减,对比了两种边界条件在相同情况下的吸收效果。有限差分数值模拟时,网格间距、采样间隔选取不合适时,会出现数值频散,引入FCT通量校正技术对数值模拟中的数值频散进行有效压制,对同等规模模型进行波场模拟时,可以加大网格间距或采样间隔或降低空间差分阶数,在一定程度上可以加快计算效率。使用组合边界条件模拟面波,利用三维数值模拟的优势,对面波传播过程中的质点运动状态进行了描述。使用三维地震波场数值模拟对认识实际介质中的地震波场传播有很大的指导意义。程序设计方面,采用分布式共享存储方式使用MPI+OpenMP函数库对程序进行并行设计,提高了程序计算效率和硬件的利用率。
[Abstract]:Seismic exploration is widely used in energy mineral exploration and engineering exploration, but most of them are two-dimensional seismic exploration and corresponding two-dimensional seismic wave field numerical simulation. In recent years, three dimensional and even four dimensional seismic exploration has a great trend of development. This paper mainly focuses on the numerical simulation of three dimensional seismic. The simulation of the propagation characteristics of seismic wave field in three-dimensional anisotropic medium and viscoelastic medium is one of the most important topics in seismic exploration, and the theoretical algorithm can be verified by three-dimensional wave field simulation. The recognition of wave field features and the design of field observation system are instructive. In this paper, the rotation staggered grid is used to simulate the three-dimensional first-order velocity stress wave equation, and the velocity, stress component and medium parameters in the traditional staggered grid are redistributed. The stress component, elastic modulus and velocity component, density are placed on two vertices of the grid along the diagonal line, and the derivatives in the horizontal and vertical directions are approximately calculated by the four conductance values in the diagonal direction. In the forward modeling of rotating staggered grids, there is no need to average the elastic modulus, which makes the traditional staggered grid calculation results unstable when simulating seismic waves propagating in viscoelastic medium and anisotropic medium. The accuracy of wave field simulation is improved. In this paper, the numerical simulation of seismic wave field in elastic anisotropic medium is discussed. The wave field of viscoelastic medium is simulated by using Kelvin medium, and the difference of wave field between viscoelastic medium and elastic medium is analyzed. According to the artificial boundary conditions in numerical simulation, the absorption attenuation of the wave field near the model boundary is carried out by using the CE absorbing boundary and the non-splitting NPML absorbing boundary. The absorption effects of the two boundary conditions are compared under the same conditions. In finite difference numerical simulation, numerical dispersion will occur when the mesh spacing and sampling interval are not properly selected. The numerical dispersion can be suppressed effectively by introducing FCT flux correction technique, and the wave field simulation of the same scale model will be carried out. The grid spacing or sampling interval can be increased or the order of spatial difference can be reduced, and the computational efficiency can be accelerated to a certain extent. The combined boundary condition is used to simulate the surface wave and the advantage of 3D numerical simulation is used to describe the motion state of the particle in the process of surface wave propagation. The numerical simulation of 3D seismic wave field is of great significance in understanding the propagation of seismic wave field in practical medium. In the aspect of programming, distributed shared storage is used to design the program in parallel with MPI OpenMP library, which improves the efficiency of program calculation and the utilization of hardware.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P631.4

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