一种新水平跳点网格计算特性的对比分析

提出了一个新的水平跳点网格(LE网格), 这种网格将h放置在格点上, u, v同时放置在x方向和y方向格点中间. 采用一种推导频散关系的通用方法, 研究在该LE网格上与Arakawa A—E网格上描述惯性重力波产生误差的情况, 分为可分辨和不可分辨两种情况, 采用二阶中央差或四阶紧致差分格式从频率和群速两个方面进行了对比分析. 结果表明不论可分辨或不可分辨, 还是采用二阶中央差或四阶紧致差分格式, 在频率和群速两方面, LE网格描述惯性重力波产生的误差均较Arakawa A—E网格要小, 同时也表明只有LE网格和Arakawa C网格采用差分精度较高的紧致差分格式时, 模拟惯性重力波的精度才会提高, 而其他的4种网格(Arakawa A, B, D, E)当差分精度提高以后, 模拟惯性重力波的精度反而下降.     

一种新水平网格的Rossby波计算特性

提出了一个新的水平跳点网格（LE网格）,这种网格将h放置在格点上,u,v同时放置在x方向和y方向格点中间.并采用一种推导频散关系的通用方法,研究在该LE网格上与Arakawa A E网格上描述Rossby波产生误差的情况,分可分辨和不可分辨两种情况.采用二阶中央差或四阶紧致差分格式从频率和群速度两个方面进行对比分析,结果表明不论在可分辨或不可分辨情况下,还是采用二阶中央差或四阶紧致差分格式,在频率和群速度两方面,LE网格在描述Rossby波产生的误差均较Arakawa A E网格要小,同时也表明不论在可分辨还是不可分辨的情况下,采用高精度的四阶紧致差分格式,LE网格和Arakawa A_E网格在描述Rossby波时产生的频率误差和x、y方向群速度误差并非必然减少.     

基于新的差分结构的时-空域高阶有限差分波动方程数值模拟方法

传统的高阶有限差分波动方程数值模拟方法采用高阶差分算子近似空间偏导数,能有效抑制空间频散.然而,传统的有限差分法仅采用二阶差分算子近似时间偏导数,这使得地震波场沿时间外推的精度较低.当采用较大的时间采样间隔,传统的有限差分法模拟波场会出现明显的时间频散,甚至不稳定.本文基于新的差分结构和中心网格剖分,发展了一种空间任意偶数阶精度、时间四阶和六阶精度的时空域有限差分方法.基于对离散后的频散关系进行泰勒展开,本文推导了时空域高阶有限差分算子的差分系数.相速度分析表明时间四阶、六阶精度的差分方法能显著地减小传统时间二阶精度差分方法的时间频散.在相同的精度下与传统差分法比较,本文发展的时间四阶、六阶有限差分方法的计算效率比传统方法高.均匀和非匀均介质中的波场数值模拟实验进一步证实本文研究的时空高阶有限差分方法的优越性.     

各向异性介质弹性波传播的三维不规则网格有限差分方法

提出一种新的三维空间不规则网格有限差分方法,模拟具有地形构造的非均匀各向异性介质中弹性波传播过程. 该方法通过具有二阶时间精度和四阶空间精度的不规则交错网格差分算子来近似一阶弹性波动方程,与多重网格不同,无需在精细网格和粗糙网格间进行插值,所有网格点上的计算在同一次空间迭代中完成. 针对具有复杂物性参数和复杂几何特征的地层结构,使用精细不规则网格处理粗糙界面、断层和空间界面等复杂几何构造, 理论分析和数值算例表明,该方法不但节省了大量计算机内存和计算时间,而且具有令人满意的稳定性和精度.     

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,系统推导出了两类非坐标轴网格点构建三维Laplace差分算子的方法,进而提出了一种利用坐标轴网格点和非坐标轴网格点共同构建三维Laplace差分算子的混合网格有限差分方法,并利用时空域频散关系和泰勒展开建立差分系数方程,推导出了差分系数的通解.相比常规高阶和时空域高阶差分格式的2阶差分精度,时空域混合网格差分离散波动方程理论上能够达到任意偶数阶差分精度,模拟精度显著提高,同时稳定性更强.频散分析表明:相比常规高阶和时空域高阶差分格式,在计算效率基本相同时,时空域混合网格差分格式能更有效地减小数值频散,减弱数值各向异性,模拟精度更高;在模拟精度基本相当时,混合网格差分格式能采用更大的时间采样间隔,计算效率更高.数值模拟实例进一步验证了混合网格差分格式在提高模拟精度和计算效率方面的先进性,也验证了其普遍适用性.     

结合边界条件的截断高阶隐式有限差分方法(英文)

有限差分方法广泛应用于求解许多科技领域所涉及的偏微分方程,高阶显式有限差分方法通常用来提高求解精度,已经提出的高阶隐式有限差分方法和截断高阶显式有限差分方法可用来进一步提高模拟精度而不增加计算量。本文首先计算了针对常规网格上的一阶导数和二阶导数、交错网格上的一阶导数的有限差分系数,发现高阶隐式有限差分系数中存在一些小的系数。频散分析结果表明:忽略这些小的差分系数能够近似维持有限差分的精度,但是显著减小了计算量。然后,引入镜像对称边界条件来提高隐式有限差分方法的精度和稳定性,采用混合吸收边界条件来减小来自模型边界所不需要的反射。最后,给出了针对均匀和非均匀介质模型的弹性波模拟例子,表明了本文方法的优点。     

时间-空间高阶精度矩形交错网格隐式有限差分声波正演模拟

有限差分方法因其操作简单、计算消耗低而成为地震勘探领域中最为常用的数值模拟方法之一,然而用离散的显式差分算子数值逼近地震波动方程中的连续导数容易导致数值频散,并且基于正方形网格离散形式的有限差分方法对不同地质模型的适应性较低.针对一阶变密度声波方程的数值模拟,本文发展了一种适用于矩形网格离散形式的时间高阶空间隐式有限差分格式,可以有效压制时间和空间频散,同时灵活的网格剖分增强了其应用的广泛性.基于本文矩形交错网格时间高阶空间隐式有限差分格式的时空域频散关系和变量替换的思想,首先采用泰勒级数展开方法求解不同方向的非轴上时间差分系数及轴上空间差分系数,使本文差分格式可以获得任意偶数阶时间和空间精度.为了进一步提高本文差分格式在更大波数区域的空间模拟精度,我们采用线性优化方法来求取新的轴上空间差分系数用于一阶变密度声波方程的波场迭代求解中.频散、稳定性分析及数值模拟算例表明：相比于传统十字形空间域隐式有限差分格式,本文矩形交错网格时间高阶空间隐式有限差分格式在精度、稳定性和效率方面均具有优势.     

地震波数值模拟中差分阶数的边界效应

提出了声波正演数值模拟中计算网格间差分阶数(精度)的不衔接而引起的边界反射效应问题,采用不同中心网格有限差分法求解声波波动方程来验证.数值实例分析表明,同差分阶数间不存在任何边界效应,而当差分阶数较低且网格间差分阶数递变较大时,边界效应显著,通过缩小差分网格间的递变阶数并提高相应的离散阶数,可以有效压制该边界效应,并保...     

横向各向同性介质地震波场数值模拟研究

地震波场数值模拟是理解地震波在地下介质中的传播特点,帮助解释观测数据的有效手段,而提高计算精度和运算效率是所有波场数值模拟方法研究所追求的目标.有限差分技术是求解波动方程计算效率最高、应用最为广泛的方法之一.但传统的有限差分技术计算过程中的数值频散问题影响了该技术的计算精度与计算效率.本文通过交错网格高阶有限差分技术与通量校正传输方法（Flux|corrected transport method,FCT）相结合, 对横向各向同性介质（Transverse isotropic medium,TI）一阶速度|应力弹性波动方程组进行了数值求解研究.波场快照数值模拟结果表明,本文研究的数值模拟方法与波动方程二阶有限差分方法、交错网格四阶有限差分方法相比,在压制网格数值频散方面有明显的优势,计算精度提高,而且可以利用较大的空间步长,提高计算效率.     

基于广义旋转法双九点格式标量波方程数值模拟

前人虽然基于传统旋转法提出了四阶精度最优17点差分格式,用于提高频率域地震波场数值模拟精度,但其仅适用于等网格间距的情形.这大大限制了该格式的使用范围.为了进一步提高17点有限差分格式的数值精度并将其推广到矩形网格,本文基于二阶精度有限差分算子利用广义旋转法提出了双九点格式,由于其差分格点与前人17点格式在分布上一样,所以也可称为二阶精度最优17点格式,但由差分格式构造原理上来讲,称其为双九点格式更妥.前人四阶精度17点格式仅为本文等网格间距情形时的特殊情况,本文方法单位波长网格点数仅需要2.2个即可.本文格式在继承传统旋转法良好几何旋转性质的同时,拥有平均导数方法适用于矩形网格的特点,和平均导数法所得的广义17点格式相比,本文格式数值精度更高,数值频散抑制性能和差分算子对称性更好.同时,本文双九点格式方法和思想对于后人借助传统九点格式的构造方法将其扩展到17点格式求解各类波动方程具有十分重要的意义.     

Computational properties of a new horizontal staggered grid

On variable configuration in the horizontal direction, Winninghoff[1] had some discussions in the 1960s. Subsequently, according to the thoughts of Winning- hoff, Liu Yudi[2―9] has widely and deeply studied al- most all the existing horizontal grids from the fre- quency and group velocity of inertia gravity and Rossby waves. Results show that although Arakawa C grid is the best one among all existing horizontal grids, it also has some shortcomings. For example, there is still an “average…     

Reconstructing the gravity gradient anomaly field from surveys with wide line spacing using equivalent source processing: an error analysis

When anomalous gravity gradient signals provide a large signal‐to‐noise ratio, airborne and marine surveys can be considered with wide line spacing. In these cases, spatial resolution and sampling requirements become the limiting factors for specifying the line spacing, rather than anomaly detectability. This situation is analysed by generating known signals from a geological model and then sub‐sampling them using a simulated airborne gravity gradient survey with a line spacing much wider than the characteristic anomaly size. The data are processed using an equivalent source inversion, which is used subsequently to predict and grid the field in‐between the survey lines by means of forward calculations. Spatial and spectral error analysis is used to quantify the accuracy and resolution of the processed data and the advantages of acquiring multiple gravity gradient components are demonstrated. With measurements of the full tensor along survey lines spaced at 4 × 4 km, it is shown that the vertical gravity gradient can be reconstructed accurately over a bandwidth of 2 km with spatial root‐mean square errors less than 30%. A real airborne full‐tensor gravity gradient survey is presented to confirm the synthetic analysis in a practical situation.     

Propagation of Kelvin waves along irregular coastlines in finite-difference models

In this paper, we examine the behavior of internal Kelvin waves on an f-plane in finite-difference models using the Arakawa C-grid. The dependence of Kelvin wave phase speed on offshore grid resolution and propagation direction relative to the numerical grid is illustrated by numerical experiments for three different geometries: (1) Kelvin wave propagating along a straight coastline; (2) Kelvin wave propagating at a 45° angle to the numerical grid along a stairstep coastline with stairstep size equal to the grid spacing; (3) Kelvin wave propagating at a 45° angle to the numerical grid along a coarse resolution stairstep coastline with stairstep size greater than the grid spacing. It can be shown theoretically that the phase speed of a Kelvin wave propagating along a straight coastline on an Arakawa C-grid is equal to the analytical inviscid wave speed and is not dependent on offshore grid resolution. However, we found that finite-difference models considerably underestimate the Kelvin wave phase speed when the wave is propagating at an angle to the grid and the grid spacing is comparable with the Rossby deformation radius. In this case, the phase speed converges toward the correct value only as grid spacing decreases well below the Rossby radius. A grid spacing of one-fifth the Rossby radius was required to produce results for the stairstep boundary case comparable with the straight coast case. This effect does not appear to depend on the resolution of the coastline, but rather on the direction of wave propagation relative to the grid. This behavior is important for modeling internal Kelvin waves in realistic geometries where the Rossby radius is often comparable with the grid spacing, and the waves propagate along irregular coastlines.©1998 Published by Elsevier Science Limited. All rights reserved     

一种时空域优化的高精度交错网格差分算子与正演模拟

如何有效压制数值频散是有限差分正演模拟研究中的关键问题之一.近年来,许多学者对二阶声波方程的差分算子开展了大量的优化工作,在压制频散方面取得不错的效果.一阶压强-速度方程广泛用于研究地震波在地下变密度模型中传播规律,目前针对一阶方程的优化工作大多只是在空间差分算子上展开.本文在前人研究的基础上,推导出一阶声波方程中压强场与偏振速度场之间的解析关系,据此在传统交错网格基础上给出一种高精度的显式时间递推格式,该递推格式将时间差分与空间差分算子结合在一起,并采用共轭梯度法得到精确时间递推匹配系数,实现时空差分算子的同时优化.在编程实现算法的基础上,通过频散分析与三个典型模型测试表明:本文方法能够较为有效地压制时间频散与空间频散,提高数值计算精度;同时对复杂模型也有很好适用性.     

Tube wave modeling by the finite-difference method with varying grid spacing

A finite-difference approach of aP-SV modeling scheme is applied to compute seismic wave propagation in heterogeneous isotropic media, including fluid-filled boreholes. The discrete formulation of the equation of motion requires the definition of the material parameters at the grid points of the numerical mesh. The grid spacing is chosen as coarse as possible with respect to the accurate representation of the shortest wavelength. If we assume frequencies lower than 250 Hz then the grid spacing is usually chosen in the range of a few meters. One encounters difficulties because of the large-scale difference between the grid spacing and the size of the borehole, usually several centimeters.These difficulties can be overcome by a grid refinement technique. This technique provides the construction of grids with varying grid spacing. The grid spacing in the vicinity of the borehole is chosen such that the borehole is properly represented. An example demonstrates the accuracy of this technique by comparisons with other methods. Unlike many analytical methods, the FD method can handle complex subsurface geometries. Further numerical examples of walk-awayVSP configurations show tube wave propagation within fluid-filled boreholes of realistic diameters.     

地震波传播的三维伪谱和高阶有限差分混合方法并行模拟

基于交错网格伪谱法和高阶精度有限差分方法,发展了模拟非均匀介质地震波传播的三维伪谱和有限差分混合算法.该方法在两个水平方向利用交错网格伪谱算子计算空间微分,保留了该方法高效、高精度的优势,在垂直方向采用交错网格高阶精度有限差分算子实现空间微分计算．利用有限差分方法的局部性特征,将三维计算区域在垂直方向上划分为一系列子区域,并分配给不同的处理器,实现了在并行计算机集群上的三维并行计算．通过模拟算例,与离散波数法比较,检验了该算法的精度．为了检验该方法的实用性,在64个处理器上,对三维沉积盆地模型进行了67108864个网格点的并行计算,模拟的波场主频率为1.25Hz,讨论了沉积盆地深度对三维沉积盆地地面运动的影响．      

The first airborne scalar gravimetry system based on SINS/DGPS in China

China has developed an airborne gravimetry system based on SINS/DGPS named SGA-WZ,the first system in which a strapdown inertial navigation system(SINS)has been used for airborne gravimetry in China.This gravity measurement system consists of a strap-down inertial navigation system and a differential global positioning system(DGPS).In April 2010,a flight test was carried out in Shandong Province of China to test the accuracy of this system.The test was designed to assess the repeatability and accuracy of the system.Two repeated flights and six grid flights were made.The flying altitude was about 400 m.The average flying speed was about 60 m/s,which corresponds to a spatial resolution of 4.8 km when using 160-s cutoff low-pass filter.This paper describes the data processing of the system.The evaluation of the internal precision is based on repeated flights and differences in crossover points.Gravity results in this test from the repeated flight lines show that the repeatability of the repeat lines is 1.6 mGal with a spatial resolution of 4.8 km,and the internal precision of grid flight data is3.2 mGal with a spatial resolution of 4.8 km.There are some systematic errors in the gravity results,which can be modeled using trigonometric function.After the systematic errors are compensated,the precision of grid flight data can be better than1 mGal.     

A hybrid absorbing boundary condition for elastic staggered‐grid modelling

We recently proposed an efficient hybrid scheme to absorb boundary reflections for acoustic wave modelling that could attain nearly perfect absorptions. This scheme uses weighted averaging of wavefields in a transition area, between the inner area and the model boundaries. In this paper we report on the extension of this scheme to 2D elastic wave modelling with displacement‐stress formulations on staggered grids using explicit finite‐difference, pseudo‐implicit finite‐difference and pseudo‐spectral methods. Numerical modelling results of elastic wave equations with hybrid absorbing boundary conditions show great improvement for modelling stability and significant absorption for boundary reflections, compared with the conventional Higdon absorbing boundary conditions, demonstrating the effectiveness of this scheme for elastic wave modelling. The modelling results also show that the hybrid scheme works well in 2D rotated staggered‐grid modelling for isotropic medium, 2D staggered‐grid modelling for vertically transversely isotropic medium and 2D rotated staggered‐grid modelling for tilted transversely isotropic medium.