基于有限体积法的二维大地电磁各向异性数值模拟

为了计算带任意地形的各向异性介质中二维大地电磁响应,本文在非结构化网格的基础上,采用有限体积法,开发了二维大地电磁各向异性正演模拟的新算法.首先,从Maxwell方程出发,推导二维各向异性介质中大地电磁场的边值问题;然后,采用三角网格自动生成技术对求解区域进行非结构化网格剖分,进而构建节点中心控制体积单元,利用有限体积方法,得到求解边值问题的大型稀疏线性方程组;最后,利用Pardiso精确地计算了大地电磁响应值.三个各向异性模型的计算结果表明,本文开发的有限体积算法,不仅能够高精度求解带任意地形的大地电磁电导率各向异性问题,而且对于同一模型,该方法的计算消耗和精度都与有限单元法相当.因此,有限体积法是处理电磁法各向异性问题的一种有效方法.

     

一种优化的频率域三维声波有限差分模拟方法

为提高频率域有限差分（FD,finite-difference）正演模拟技术的计算精度和效率,基于旋转坐标系统的优化差分格式被广泛应用,但是只应用于正方形网格的情况.基于平均导数法（ADM）的优化差分格式,应用于正方形和长方形网格模拟.这些频率域有限差分算子,各自具有不同的差分格式和对应的优化系数求解表达式.本文基于三维声波方程发展了一种新的优化方法,只要给定FD模板形式,可直接构造频散方程,求取FD模板上各节点的优化系数.此方法的优点在于频率域FD算子的优化系数对应各个节点,可扩展优化其他格式.运用此优化方法,计算得到了不同空间采样间距比情况下27点和7点格式的优化系数.数值实验表明,优化27点格式与ADM 27点格式具有相同的精度,优化7点格式比经典的7点格式具有更小的数值频散.

     

复电阻率法二维有限元数值模拟

伴随着复电阻率法的广泛应用,发展精确和快速的正演和反演算法成为复电阻率法研究的重点.本文采用基于三角单元剖分的有限单元法进行了复电阻率二维数值模拟研究.为了提高计算速度,对无穷远边界进行了近似处理.整个正演计算过程分为两步,首先采用有限单元法计算四个不同频率的视复电阻率数据,然后对前一步得到的视复电阻率数据采用递推算法计算视Cole-Cole参数.采用这种正演算法与一维正演的结果进行了对比,验证了本文方法的正确性.设计了两个二维极化模型,数值模拟结果表明视复电阻率和Cole-Cole视参数等值线断面图对于异常目标体都有比较明显的反映.     

用于声波正演模拟的时空域高精度交错网格有限差分方法

地震正演模拟是逆时偏移和全波形反演中的核心问题之一,因为它们都需要高效、高精度地模拟波场正向和反向传播。为了提高数值模拟的精度,人们广泛采用高阶有限差分方法,但是大多数方法仅在空间上具有更高的精度,在时间上只有二阶精度。首先系统介绍时空域高精度交错网格有限差分方法的基本原理,然后利用模型验证方法的有效性,结果表明:时空域高精度交错网格有限差分方法拥有比常规交错网格有限差分方法更低的数值频散。      

二维声波方程速度反演的一种方法

从二维声波方程出发,用最小二乘－正则化方法,利用平面波垂直入射时的反射地震记录,成功地反演出地下介质的速度．同时给出数值模拟结果．计算结果表明该方法具有较高的精度和较好的稳定性,是求解波动方程反问题行之有效的方法．     

二维频率空间域粘声波正演模拟研究

地球介质本身的非弹性导致大地吸收效应,黏滞性影响波场的所有频率成分且对高频成分的影响更大,从而降低了地震记录和地震成像的垂向分辨率.通常使用经验公式描述吸收衰减.在时间域模拟吸收衰减需大量的计算机内存、计算效率较低,模拟Q值非常困难;而频率空间域可以通过引入复速度和Q值,使用任意的经验公式而进行粘滞介质的数值模拟.本文...     

二维声波方程速度反演的一种方法

从二维声波方程出发，用最小二乘－正则化方法，利用平面波垂直入射时的反射地震记录，成功地反演出地下介质的速度．同时给出数值模拟结果．计算结果表明该方法具有较高的精度和较好的稳定性，是求解波动方程反问题行之有效的方法．     

黏声波方程波场模拟的通用格式自适应系数频域有限差分方法

黏声波方程常被用于描述地下介质的黏弹性及波的传播现象,频域有限差分(finite difference frequency domain, FDFD)方法是黏声波和黏弹性波波场模拟的常用工具.目前FDFD黏声波模拟常用的二阶五点方法和优化九点方法在一个波长内的网格点数小于4时误差较大.通过令FDFD系数随一个波长内的网格点数自适应从而提高FDFD方法的精度,本文针对黏声波波场模拟发展了一种适用于不同空间采样间隔之比的通用格式自适应系数FDFD方法.同时,为了验证自适应系数FDFD方法对一般黏声波模型的有效性,本文针对三个典型的黏声波模型,分别采用解析解和基于高阶FDFD的参考解验证了所提出方法的有效性.本方法的FDFD格式通过在传统的二阶FDFD格式的基础上引入相关校正项得到,其中校正项按网格点与中心点的距离进行分类选取,同时校正项对应的自适应FDFD系数不仅和空间采样间隔之比相关,还和一个波长内的采样点数相关.所需的自适应FDFD系数可通过声波方程的数值频散关系和查找表高效给出.数值频散分析表明,在空间采样间隔相等或不等的情况下,以相速度误差不超过1%为标准,通用格式自适应系数FDF...     

二维地震波场的组合型紧致有限差分数值模拟

地震波场数值模拟在地球物理勘探和地震学中具有重要的支撑作用.本文将组合型紧致差分格式用于声波和弹性波方程的数值模拟中.根据泰勒级数展开和声波方程,建立了位移场时间四阶离散格式,并将组合型紧致差分格式用于位移场空间导数的求取,然后对该差分格式进行了精度分析、误差分析、频散分析和稳定性分析.理论研究结果表明：①该差分格式为时间四阶、空间六阶精度,与常规七点六阶中心差分和五点六阶紧致差分相比,具有更小的截断误差和更高的模拟精度;②每个波长仅需要5.6个采样点,且满足稳定性条件的库郎数为0.792,可以使用粗网格和较大时间步长进行计算.所以该方法具有占用内存少、计算效率高和低数值频散等优势.最后,本文进行了二维各向同性完全弹性介质的声波和弹性波方程的数值模拟,实验结果表明本文提出的方法具有更高的计算精度,能够大幅度的节约计算量和内存需求,对于三维大尺度模型问题具有更好的适应性.     

基于第二代小波自适应网格的二维声波方程波传模拟

本文利用第二代小波多尺度分解和快速变换的特点,构造自适应计算网格.对初始计算网格上的数值解进行第二代小波变换,得到数值解对应的小波系数空间.小波系数的大小表示相邻网格上数值变化率,小波系数大的区域网格点上的数值解变化梯度大.当小波系数大于等于预设的阈值时,在小波系数对应的网格点周围插入新的计算网格点,通过阈值可以实现网格的细化,得到多尺度下层层嵌套的细化自适应网格;由有限差分法得到相应网格点的空间导数.比较数值算例得到的波场快照和计算时间,验证了该方法的有效性.     

有限元算法在声波方程数值模拟中的频散分析

针对有限元算法在地震波数值模拟中的数值频散问题,利用集中质量矩阵双线性插值有限元算法,推导了二维声波方程的频散函数.在此基础上采用定量分析方法,对比分析了网格纵横长度比变化时的入射方向、空间采样间隔、地震波频率以及地层速度对数值频散的影响.数值算例和模型正演结果表明：当采用集中质量矩阵双线性插值有限元算法时,为了有效地压制数值频散,在所使用震源子波的峰值频率对应的波长内,采样点数目应不少于20个;减小网格长度的纵横比可以有效地抑制入射角(波传播方向与z轴的夹角)较小的地震波的数值频散;地震波频率越高,传播速度越慢,频散越严重,尤其是当相速度与其所对应的频率比值小于2倍空间采样间隔时,不仅会出现严重的数值频散,还会出现假频现象.     

Two-dimensional finite volume method for dam-break flow simulation

A numerical model based upon a second-order upwind ceil-center f＇mite volume method on unstructured triangular grids is developed for solving shallow water equations. The assumption of a small depth downstream instead of a dry bed situation changes the wave structure and the propagation speed of the front which leads to incorrect results. The use of Harten-Lax-vau Leer （HLL） allows handling of wet/dry treatment. By usage of the HLL approximate Riemann solver, also it make possible to handle discontinuous solutions. As the assumption of a very small depth downstream oftbe dam can change the nature of the dam break flow problem which leads to incorrect results, the HLL approximate Riemann solver is used for the computation of inviscid flux functions, which makes it possible to handle discontinuous solutions. A multidimensional slope-limiting technique is applied to achieve second-order spatial accuracy and to prevent spurious oscillations. To alleviate the problems associated with numerical instabilities due to small water depths near a wet/dry boundary, the friction source terms are treated in a fully implicit way. A third-order Runge-Kutta method is used for the time integration of semi-discrete equations. The developed numerical model has been applied to several test cases as well as to real flows. The tests are tested in two cases： oblique hydraulic jump and experimental dam break in converging-diverging flume. Numerical tests proved the robustness and accuracy of the model. The model has been applied for simulation of dam break analysis of Torogh in Iran. And finally the results have been used in preparing EAP （Emergency Action Plan）.     

求解声波方程的辛可分Runge-Kutta方法

本文基于声波方程的哈密尔顿系统,构造了一种新的保辛数值格式,简称NSPRK方法.该方法在时间上采用二阶辛可分Runge-Kutta方法,空间上采用近似解析离散算子进行离散逼近.针对本文发展的新方法,我们给出了NSPRK方法在一维和二维情况下的稳定性条件、一维数值频散关系以及二维数值误差,并在计算效率方面与传统辛格式和四阶LWC方法进行了比较.最后,我们将本文方法应用于声波在三层各向同性介质和异常体模型中的波传播数值模拟.数值结果表明,本文发展的NSPRK方法能有效压制粗网格或具有强间断情况下数值方法所存在的数值频散,从而极大地提高了计算效率,节省了计算机内存.     

2.5D finite-difference solution of the acoustic wave equation

The finite‐difference method applied to the full 3D wave equation is a rather time‐consuming process. However, in the 2.5D case, we can take advantage of the medium symmetry. By taking the Fourier transform with respect to the out‐of‐plane direction (the symmetry axis), the 3D problem can be reduced to a repeated 2D problem. The third dimension is taken into account by a sum over the corresponding wave‐vector component. A criterion for where to end this theoretically infinite sum derives from the stability conditions of the finite‐difference schemes employed. In this way, the computation time of the finite‐difference calculations can be considerably reduced. The quality of the modelling results obtained with this 2.5D finite‐difference scheme is comparable to that obtained using a standard 3D finite‐difference scheme.     

三维波动方程时空域混合网格有限差分数值模拟方法

常规高阶和时空域高阶有限差分方法广泛应用于三维标量波动方程的数值模拟,这两种差分方法仅利用笛卡尔坐标系中的坐标轴网格点构建三维Laplace差分算子,相应的差分离散波动方程本质上仅具有2阶差分精度,模拟精度低.本文将三维笛卡尔坐标系中非坐标轴网格点分为两类:坐标平面内的非坐标轴网格点和坐标平面外的非坐标轴网格点,系统推...     

流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法

本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的.     

Determining finite difference weights for the acoustic wave equation by a new dispersion‐relationship‐preserving method

Numerical simulation of the acoustic wave equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse‐time migration. With finite‐difference methods, the discretization of temporal and spatial derivatives in wave equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed wavenumber points within a wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the wave velocity. This new dispersion‐relationship‐preserving method relatively uniformly reduces the numerical dispersion over a large‐frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.     

Train-induced wave propagation in layered soils using finite/infinite element simulation

In this paper, the transmissibility of soils for vibrations induced by trains moving at different speeds is studied. The 2.5 D finite/infinite element approach adopted herein allows us to consider the load-moving effect of the train in the direction normal to the two-dimensional profile of the soils considered, and, therefore, to obtain three-dimensional responses for the soils using only plane elements. The moving train is simulated by a sequence of moving wheel loads that may vibrate with certain frequency. Two train speeds are considered, one is smaller and the other is greater than the Rayleigh wave speed of the layered soils, to represent the effects of speed in the sub-critical and super-critical ranges. In order to evaluate the effect of each parameter on the ground response induced by moving trains, parametric studies are conducted for the following parameters: the shear wave speed, damping ratio and stratum depth of the supporting soils, and the moving speed and vibration frequency of the traveling trains. Conclusions concerning the mechanism of wave propagation in layered soils are drawn from the parametric studies, which should prove useful to practicing engineers.     

Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators

We present a numerical method of simulating seismic wave propagation on unstructured 2D grids. The algorithm is based on the velocity–stress formulation of the elastic wave equation and therefore uses a staggered grid approach. Unlike finite-element or spectral-element methods, which can also handle flexible unstructured grids, we use explicit differential operators for the calculation of spatial derivatives in each time step. As shown in previous work, three types of these operators are used, and their particular performance is analysed and compared with standard explicit finite-difference operators on regular quadratic and hexagonal grids. Our investigations are especially focused on the influence of grid irregularity, sampling rate (i.e. gridpoints per wavelength) and numerical anisotropy on the accuracy of numerical seismograms. The results obtained from the various methods are therefore compared with analytical solutions. The algorithm is then applied to a number of models that are difficult to handle using (quasi-)regular grid methods. Such alternative techniques may be useful in modelling the full wavefield of bodies with complex geometries (e.g. cylindrical bore-hole samples, 2D earth models) and, because of their local character, they are well suited for parallelization.