An equal area conversion model for rasterization of vector polygons

Vector-raster conversion is one of the classic research topics in the field of Geographical Information Systems (GIS). The algorithms commonly used in GIS are devoted to maintaining the vector polygons’ shape characteristics, but neglect the gain and loss of a polygon’s area, which is another important attribute. This paper proposes an equal-area conversion model based on an area compensation optimization principle. According to the topological relationship among polygons and boundary grids, a neighborhood compensation principle was adopted to assign the attributes of boundary grids and a global optimization algorithm was developed to minimize area distortion in the whole data set. Two experiments were designed and the results indicated that this algorithm not only guaranteed the area error is as small as possible, but also has the advantage as being adaptive to polygon shape and spatial structure.

     

最大准则优化技术在贴体网格中的应用

贴体网格在地质数值模拟中具有广阔的应用前景,为解决贴体网格生成时边界离散问题,提出了最大长度准则和最大面积准则,把曲线逼近和曲面网格优化问题转化为数学优化问题,为求解该问题,提出了改进的单粒子优化算法.试验表明,最大长度准则和最大面积准则的优化效果好于常规方法;以改进的单粒子优化算法求解该问题时,计算效率是智能单粒子优化算法的30倍左右（节点量为200）,从而实现最大长度准则和最大面积准则在贴体网格生成中的应用.针对最大面积准则优化曲面网格不能控制网格步长的情况,提出了限定步长的网格优化算法,使网格步长合理化,并通过实例验证了该算法的有效性.研究成果提供了生成贴体网格时边界优化准则和求解方法,对今后复杂边界的贴体网格生成具有重要意义.     

多孔弹性波方程的多尺度波场模拟

本文研究了二维多孔弹性波方程的多尺度波场数值模拟方法.该多尺度方法可采用较粗的网格计算,同时又能反映细尺度上物性参数的变化信息.文中详细阐述了多尺度模拟方法与算法,并推导了相应的计算格式.基本思想是建立粗细两套网格,在粗网格上,基于有限体积方法计算更新波场;在细网格上,计算多尺度基函数,这基于有限元方法通过求解一个局部化问题得到.对含有随机分布散射体的多孔介质模型进行了数值计算,计算中应用了完全匹配层(PML)吸收边界条件,数值结果验证了本文方法和算法的正确性和有效性.     

基于改进声波方程和MCPML边界的频率域高精度正演模拟

数值频散和边界反射是频率域模拟时需要解决的两个重要问题.然而,受计算效率和分解阻抗矩阵时的内存占用量的制约,提高有限差分算子长度或增加有限差分网格数目均不是提高频率域模拟精度的最优解决方案.本文首先分析了数值频散产生的理论机制,在此基础上,推导了一种"波数补偿"的声波方程表达式来压制数值频散,并给出其物理意义,有效地改善了数值频散问题,提高了模拟精度;在边界问题上,本文采用多轴卷积完全匹配层(MCPML)边界条件代替传统的完全匹配层(PML)边界条件,快速吸收边界内的残余能量,压制边界反射.结合改进声波方程和MCPML边界条件,给出了一种高精度的频率域声波方程有限差分格式.数值模拟结果表明,在不增加计算量和内存占用量的前提下,本文研究的方法、正演精度高、波场模拟清晰、无干扰反射,是一种可靠高效的频率域模拟方法.     

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。     

扇形边界条件下的龙门山壳幔电性结构特征

沿甘肃碌曲-四川龙门山-重庆合川布设了长周期大地电磁剖面,对龙门山及邻区进行了壳幔电性结构探测,采用更直观合理的扇形边界条件下的反演算法对长周期大地电磁资料进行二维反演.该剖面电性结果揭示了自北西向南东岩石圈深部的若尔盖壳幔高阻块体、松潘壳幔低阻带、龙门山壳幔高阻块体和川中壳幔高阻块体电性结构特征;龙门山逆冲推覆构造带下方的龙门山壳幔高阻体显示为向北西延伸的楔形构造,推断龙门山及松潘-甘孜地块由于受青藏高原东缘和上扬子地块双向挤压,松潘-甘孜地块地壳物质向龙门山逆冲推覆,中下地壳至上地幔向下向南东俯冲,呈现上扬子地块西缘壳幔高阻楔形体插入青藏高原东缘的态势;初步认为上扬子地块西缘深部以松潘壳幔韧性剪切带作为中新生代以来的边界.     

Simultaneous identification of parameter,initial condition,and boundary condition in groundwater modelling

In this paper, we perform an inverse method to simultaneously estimate aquifer parameters, initial condition, and boundary conditions in groundwater modelling. The parameter estimation is extended to a complete inverse problem that makes the calibrated groundwater flow model more realistic. The adjoint state method, the gradient search method, and the least square error algorithm are combined to build the optimization procedure. Horizontal two‐dimensional groundwater flow in a confined aquifer is exemplified to demonstrate the correlation between unknowns, the contribution of observation, as well as the suitability of applying the inverse method. The correlation analysis shows the connection between storage coefficient and initial condition. Besides, transmissivity and boundary conditions are also highly correlated. More observations at different location and time are necessary to provide sufficient information. A time series of unsteady head is requested for estimation of storage coefficient and initial condition. Observation near boundary is very effective for boundary condition estimation. The observation at pumping well mostly contributes to the estimation of transmissivity. According to all observations, it is possible to identify parameters, initial condition, and boundary condition simultaneously. Furthermore, the results not only illustrate the traditional assumption of known boundary condition but also initial condition, which may cause an incorrect estimation. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A NEW MATHEMATICAL MODEL FOR2-D FLOW

A new mathematical model for 2-D flow is formulated with accurate satisfac tion of boundary conditions in conjunction with square or any grids,so that it may also yield accurate results when the domain of computation is in the shape of a strip as occurring in rivers. The basic equations are split into three sets of compo- nent equations of which two sets may be transformed to the same form. This model is a part or a model devised for 2-D flows with sediment.     

倾斜各向异性地层中多分量电磁波测井响应三维时域有限差分（FDTD）算法

利用三维时域有限差分技术（FDTD）研究建立倾斜各向异性地层中多分量电磁测井响应的数值模拟算法.首先,利用Yee氏交错差分格式和线性内插公式对各向异性介质中时域Maxwell方程进行离散化,得到各向异性介质中各个交错节点上电磁场的时域递推公式,同时将面积加权平均与旋转矩阵技术相结合确定各个网格节点的等效电导率张量,此外,单轴各向异性吸收边界条件（UPML）被用于降低求解区域外边界反射.在此基础上,利用单频正弦磁偶源计算时域电磁场空间分布以及特殊的双方程算法（2E2U）从数值结果中快速提取电磁场幅度和相位,确定多分量电磁测井仪器的三维响应.最后,通过数值结果证明该算法的有效性,并系统考察不同层厚、地层倾角以及侵入带半径等变化对多分量电磁测井响应的影响.     

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.     

基于GIS的当雄同震InSAR形变场分析

InSAR技术对同震形变的量测达到了厘米级的精度,但在数据后处理和结果分析方面仍然存在明显的不足。采用可对空间信息进行存储、管理及分析等功能的GIS,对InSAR数据获取的2008年10月6日16时30分西藏自治区当雄县MW6.3地震的同震形变场进行分析。结果表明:(1)GIS可对多源数据进行有效管理;(2)可以确定当雄地震的震中位置;(3)可获取沉降区的最大形变量;(4)可确定主要的形变区间;(5)可将形变结果进行三维展示。GIS可有效地弥补InSAR数据后处理、数据分析及成果展示方面的不足。     

波动方程三维吸收边界分解与拟合深度偏移方法

在偏移问题中引入吸收边界条件，既可以消除由人工边界激发的虚假反射，从而提高剖面质量。又可以减少计算工作量．本文讨论了三维吸收边界条件方程，提出了求解具有吸收边界条件的三维波动方程偏移定解问题的分解与拟合方法。理论分析与合成记录及野外实际地震资料处理结果表明，本文方法为一有效的三维吸收边界深度偏移方法。     

Multiscale island injection genetic algorithms for groundwater remediation

Genetic algorithms have been shown to be powerful tools for solving a wide variety of water resources optimization problems. Applying these approaches to complex, large-scale water resources applications can be difficult due to computational limitations, especially when a numerical model is needed to evaluate different solutions. This problem is particularly acute for solving field-scale groundwater remediation design problems, where fine spatial grids are often needed for accuracy. Finer grids usually improve the accuracy of the solutions, but they are also computationally expensive. In this paper we present multiscale island injection genetic algorithms (IIGAs), in which the optimization algorithms have different multiscale populations working on different islands (groups of processors) and periodically exchanging information. This new approach is tested using a field-scale pump-and-treat design problem at the Umatilla Army Depot in Oregon, USA. The performance of several variations of this approach is compared with the results of a simple genetic algorithm. The new approach found the same solution as much as 81% faster than the simple genetic algorithm and 9–53% faster than other previously formulated multiscale strategies. These findings indicate substantial promise for multiscale IIGA approaches to improve solution of complex water resources applications at the field scale.     

地震波传播有限差分模拟的人工边界问题

在用有限差分法模拟地震波传播中，差分网格人工边界的反射问题是至关的。本文简要介绍了几种消除人工边界反射的方法及其主要优缺点，联立这些不同的吸收边界条件于实际的有限差分计算可以给出好的结果。     

Numerically modelling groundwater in an arid area with ANN‐generated dynamic boundary conditions

Groundwater is sensitive to the climate change and agricultural activities in arid and semi‐arid areas. Over the past several decades, human activities, such as groundwater extraction for irrigation, have resulted in aquifer overdraft and disrupted the natural equilibrium in these areas. Regional groundwater simulation is important to determine appropriate groundwater management policies, and numerical simulation has become the most popular method. However, most groundwater models were developed with static boundary conditions. In this research, the Minqin oasis, an arid region located in northwest China, was selected as the study area. An artificial neural network (ANN) was developed to simulate effects of weather conditions, agricultural activities and surface water on groundwater level in a dynamic boundary of the domain. Subsequently, a groundwater numerical model, named ANN‐FEFLOW model, was developed, with a dynamic boundary condition defined by the ANN model. The verifying results showed that the model has higher precision, with a root mean square error (RMSE) of 0·71 m, relative error (RE) of 17·96% and R² of 0·84 relative to the great groundwater change. Furthermore, the groundwater model has higher precision than the conventional groundwater model with static boundary condition, particularly in the area near the dynamic boundary. This study demonstrated that dynamic boundaries can improve the precision of the regional groundwater model in an arid area and that ANN can provide higher accuracy prediction capability for groundwater levels with dynamic boundary. Copyright © 2010 John Wiley & Sons, Ltd.     

波前构建法中网格点相对定位及属性计算研究

针对波前构建法射线追踪中非规则的波前四边形网格与规则的矩形网格节点之间的相对定位问题,采用矢量叉积判断方法从四个方面较详细的讨论了规则的矩形网格节点与非规则的波前四边形的相对位置关系,并针对四种不同的位置关系采用不同的插值算法进行其属性的转换计算,误差分析及计算实例表明本文所采用的网格定位方法以及属性转换的插值算法从理论到实际应用都是正确的、切实可行的.     

有限元模拟中边界条件对计算结果的影响

本文从总电位法和异常电位法两个方面,分别就直流电法有限元中所采用的三类边界条件对计算结果的影响进行了分析,为采用合适的边界条件及选取最佳边界距离来提高正演精度提供了基础.结果表明,混合边界条件精度最高,可大大缩小求解区域而不影响计算精度,其次是Dirichlet边界条件精度较高,但测点越靠边界误差会越大,必须取足够大的边界区域,齐次边界条件的误差比较大,但如果采用非二极装置,通过电位差计算得到的视电阻率,由于无穷远边界对电位差的影响基本消除,视电阻率计算误差与混合边界条件下的接近,在反演中,为了节省计算时间,经常使用齐次边界条件进行有限元正演.     

Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores

Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with small-scale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference (FD) method of Biot’s poroelastic equations, with an arbitrary even-order (2L) accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer (CPML) absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultrasonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thicknesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Q _sc values between the numerical and experimental ultrasonic S waveforms for a cylindrical rock sample demonstrate that the boundary reflection may contribute around one-third of the ultrasonic coda attenuation observed in laboratory experiments.     

Ray tracing based on Fermat's principle in irregular grids1

A new method to trace rays in irregular grids based on Fermat's principle of minimum time is introduced. Besides the usual transmitted and reflected waves, refracted, diffracted and converted waves can also be simulated. The proposed algorithm is fast and stable, and respects the reciprocity principle between source and receiver better than procedures adopting the shooting method. It is particularly suited to form part of a traveltime inversion procedure. The use of irregular grids allows adaptation of the earth discretization to the available acquisition geometry and ray distribution, to obtain more stable and reliable tomographic images.