摘要
透地通信系统是应用于煤炭安全生产和灾后救援的一种安全可靠的通信系统,在其设计和开发过程中,复杂地层中的电磁场传播特性研究是一项重要的基础工作。采用解析方法研究无线电波在大地媒质中传播问题时,只能计算简化模型中的反射和透射系数;而采用试验研究方法也只能获取某个特定区域的电磁场传播特性参数值。随着计算机技术的发展,采用数值计算来研究电磁场问题成为一个热点;尽管电磁场数值计算在很多领域有成功应用,但在研究透地通信复杂地层中的电磁场传播特性时,也是在简化模型条件下开展仿真研究的;由于简化模型把整个地层媒质近似地等效为均匀媒质,对研究区域的地层的电磁参数取平均值来获取参数值,因此忽略了不同层系地层的差异性,与实际的地层电磁参数分布有较大出入,从而导致计算结果与实际地层中的电磁场传播存在偏差。本文通过对地层三维建模、空间插值和电磁场数值计算的吸收和分析,利用改进的Kriging空间插值技术实现了基于钻孔数据的突变型地层媒质电磁参数分布估计和媒质建模,并采用时域有限差分(FDTD)实现了透地通信的电磁场仿真;进一步,为了解决透地通信电磁场仿真在计算大型地层区域和网格数量大时存在计算速度慢的问题,本文对三维地层媒质建模和FDTD进行了系列的并行化研究;最后,在系统分析电磁场仿真过程的基础上实现了透地通信电磁场仿真的系统集成。本文的研究成果为复杂地层中的电磁场传播特性分析提供了一条新的有效途径,主要研究工作如下:
(1)阐述了大地媒质的特性和无线电波传播一般理论,研究了媒质中的电磁参数对无线电波传播的影响;依据大地媒质不同的平行分层结构,采用解析方法推导出了无线电波在大地多层突变型媒质中的反射和透射系数。在建立大地媒质简化模型的基础上,分析了均匀平面波在自由空间和理想大地分界面上的反射和透射现象。
(2)提出了基于钻孔数据的地层媒质参数分布估计方法。采用Kriging作为地层建模的空间插值技术,并针对Kriging的相关模型参数的多变量寻优选取问题,利用遗传微粒群算法的全局优化能力克服了对参数优化中对初始点设置的依赖,快速稳定的实现参数求解;建立了地层媒质的Kriging模型,并通过kriging插值计算获取突变型地层媒质中的电磁参数分布状况。
(3)将Kriging媒质建模技术与FDTD相结合,提出了适用于研究复杂地层中电磁场传播的电磁场仿真方法。采用Kriging插值对地层媒质建模的方法克服了简化模型条件下忽略地层差异性的问题,通过对Yee网格中属于不同层系的格点赋予对应的电磁参数值来反映复杂地层的媒质特点,详细描述了复杂地层中的电磁场传播过程。
(4)为解决Kriging插值算法在建立网格数量大和地层层数多时计算量大和计算时间长的问题,提出了一种具有动态调整并行粒度策略的并行Kriging插值算法,该算法根据CPU与地层层数之间的数量关系动态调整并行计算的粒度,优先使用粗粒度的并行计算策略,同时利用中粒度并行算法平衡负载。
(5)为了提高并行FDTD的计算效率,研究了仿真过程中的区域分割及电磁场值通信方式、负载平衡、进程拓扑结构、数据传送等技术,将媒质建模和FDTD两个并行计算模块有机结合形成了透地通信电磁场并行仿真系统。
Through-the-earth communication system is a safe and reliable communication system used in minecoal production and disaster relief, which is designed and developed based on the basic research of electromagnetic (EM) propagation in the complex stratum media. When analytical methods is used to study the radio wave propagation in the earth medium, only the reflection and transmission coefficients can be calculated in a simplified model.And test method can be used to provide some EM propagation parameters in a particular region only. With the development computer technology, the research of EM issues by numerical calculation becomes a hotspot. Although the EM numerical calculation was successfully applied to many areas of EM problem, it is also carried out to research the EM propagation in a complex stratum based on the simplified stratum model. Because the whole stratum media is approximation to the homogeneous medium in the simplified model, the EM parameters are get by averaging the value of parameters of study region with ignoring the difference of the stratum, and there are errors between the computing result in simplified model and the EM transmission in the real world. This thesis achieves the estimation of the EM parameters distribution in stratum and the modeling of stratum media using an improved Kriging interpolation based on the borehole data by absorbing and analyzing the 3D stratum modeling, spatial interpolation and EM numerical computation, and uses the finite difference time domain (FDTD) to simulate the process of EM transmission in the real world stratum. Furthermore, this thesis makes a thorough study on the parallel computing in the stratum media modeling and FDTD in order to improve the computing speed for large area with a plenty of layers and Yee grids. Finally, an integration system is developed by analyzing the process of EM simulation.The study results provide an advance and effective way to studying the propagation characteristics in a complex stratum media ,these studis are as follows:
The characteristics of the stratum and wireless wave theory are presented, the EM parameters of stratum media tied closely to transmission of the radio wave are analyzed. Based on the model of parallel multi-layer stratum, the mathematic expressions of reflection and transmission coeficients of the radio wave transmitting through the multi-layer stratum medium are deduced.
An improved Kriging interpolation is adopted to setup a stratified stratum medium model and estimate the distribution of the electromagnetic parameters in the mutant stratum media. In Kriging interpolation algorithm, the determination of parameters of a correlation model is a key issue to construct the regression model, the computing accuracy rely on the initialization when using the conventional numerical optimization methods such as pattern search method when computing the parameters, which result in the instability of the optimization solution,a modified binary particle swarm optimization (GPSO), independent of the initialization of parameters, is presented to compute the global optimums of correlation model parameters, the experimental results show that the proposed GPSO significantly improves the search efficacy and stability compared to the exiting optimization algorithm. By this interpolation method, the high precise media model and electromagnetic parameters can be provided during the electromagnetic numerical computing.
A through-the-earth EM simulation approach integrated with stratum media modeling by Kriging and FDTD is proposed. The issue of ignoring the difference of the stratum in the simplified model is overcome by using the Kriging to model the strum media, the EM features of stratum media are reflected by assigning the values of EM parameters to each Yee grid belong to the different stratum, the radio wave's propagation process in complex stratum is carefully described using the proposed EM simulation approach.
In order to improve the computing speed of spatial interpolation used for stratified stratum, and to achieve the load balancing within the different number of stratum layers and computing nodes , a novel parallel Kriging interpolation with multi-granularity is developed based on the strategy of dynamic adjustment of the parallel granularity. In this algorithm, according to the quantitative relationship between the number of CPUs with this of stratum layer, the parallel granularity is adaptively adjusted, in which the coarse granularity Kriging interpolation is priority used while the medium granularity Kriging is adopted to balance the computing load.
In order to improve the computing efficiency of the parallel FDTD based on MPI, the technologies such as space decomposition, load balace, topologic configuration and data transmission are carefully analyzed and improved. Finally, the parallel media modeling and parallel FDTD are combinated to form an integrative parallel EM simulation system for studying the through-the-earth communication.
引文
[1] Viggh, M. Modes in lossy stratified media with application to underground propagation of radio waves[J]. IEEE Transactions on Antennas and Propagation , 1963, 11(3): 318-323
[2] GEYER, R. G. . Theory and experiments relating to electromagnetic fields of buried sources with consequences to communication and location[C]. in Proc. Through-the-earth electromagnetic workshop, Aug. 15-17, 1973: 20-33
[3] Olsen, R. G. , Farstad, A. J. Electromagnetic direction finding experiments for location of trapped miners[J]. IEEE Tran. on Geoscience Electronics, 1973, 11(4): 178-185
[4] Farstad, A. J. Electromagnetic location experiments in a deep hardrock mine[J]. BuMines Open File Rept. 28-72, 1973
[5] Wait, J. R, and Spies, K. P. Electromagnetic field of a small loop buried in a stratifeid earth[J]. IEEE Transactions on Antennas and Propagation, 1971, 21(5): 717-718
[6] Wait, J. R. Criteria for locating an oscillating magnetic dipole buried in the earth. Proc[J]. IEEE, June, 1971, 59: 1003-1035
[7] Wait, J. R. Electromagnetic induction technique for locating a buried source[J]. IEEE Trans. Geosci. Electron. , 1971, 9: 95-98
[8] Wait, J. R. Locating an oscillating magnetic dipole in the earth[J]. Electron. Letts. , 1972, 8(6): 404-406
[9] Wait, J. R, Spies, K. P. Low-frequency impedance of a circular loop over a conducting ground[J]. Electron. Letts. , 1974, 10: 248
[10] Wait, J. R, Hill, D. A. Field of a horizontal loop of arbitary shape buried in two layer earth[J]. Radio Sci. , 1980, 15(5): 903-912
[11] Large, D. B, Ball, L. and Farstad, A. J. Radio transmission to and from underground coal mines-theory and measurement[J]. IEEE Transactions on Communications , 1973, 21(3): 194-202
[12] Murphy, J. N, Parkinson, H. E. Underground mine communications[C]. Proceedings of the IEEE, 1978, Jan. , 1978, 66(1): 26– 50
[13] (苏)奥戈罗德涅丘克(И.Ф.Огороднейчук)著,吴荣光,虞梦先译.矿井低频无线通讯[M].北京:煤矿工业出版,1981
[14] Gogoi, A. K, Raghuram, R. Analysis of VLF loop antennas on the Earth surface for underground mine communication[C]. Antennas and Propagation Society International Symposium, 1996(2): 962-965
[15] Gogoi, A. K. , Raghuram, R. Variation of field strength in underground mine area on the size of VLF loop antennas laid on the Earth surface[C]. Antennas and Propagation Society International Symposium, 1997, July , 1997(3): 1792-1795
[16] Ayuso, N. , Cuchi, J. A. , etc. . Through-the-earth magnetic field propagation: modelling and experimental validation[C]. Antennas and Propagation Society International Symposium 2006, IEEE, July 2006, pp. 680– 683
[17] Barkand, T. D. , Damiano, N. W. , Shumaker, W. A. Through-the-Earth, Two-Way, Mine Emergency, Voice Communication Systems[C]. Industry Applications Conference, 2006. 41st IAS Annual Meeting. Conference Record of the 2006 IEEE, Oct. 2006, 2: 955– 958
[18]司徒梦天.解决地下通信技术难题的方案及关键设备[J].中国工程科学, 2001, 3(7): 64~69
[19]张清毅,朱建铭.透地通信信道特性的研究[J].电波科学学报, 1999, 1(14): 36-40
[20]陶晋宜.甚低频电磁波穿透地层无线通信系统天线装置的研究[J].太原理工大学学报, 1999, 30(2): 139-144
[21]陶晋宜.甚低频电磁波穿透地层无线通信系统若干问题的探讨[J].太原理工大学学报, 2000, 31(6): 47-50
[22]向新,罗奕,易克初等.穿透岩层地下电流场通信信道分析[J].煤田地质与勘探, 2005, 33(4): 77-79
[23] Umashankar. K, Taflove . A. ComputationalEleetromagnetics[J]. ArtechHouse,1993
[24] H. S. Chang, K. K. Mei. Scattering of eleetromgnetic waves by buried and partly buried bodies of revolution[J]. IEEE Trans. Geoseience and Remote Sensing, 1984, GE-23: 596-605
[25] D. A. Hil. Electromagnetic Scattering by Buried Objects of Low Constracst[J]. IEEE Trans. Geoseience and Remote sensing, 1988, GE-26: 195-203
[26] S. Vitebskiy, L. Carin. MoM-Method modeling of Short-Pulse Scattering from and the Resonances of a wire buried inside a lossy dispersive half-space[J]. IEEE Trans. Antenna and Propagation, 1995,AP-43: 1303-1312
[27] S. Vitebskiy, K. Sturgess, L. Carin. Short-pulse planep wave scattering from buried perfectly condueting bodies of Revolution[J]. IEEE Trans. Antenna and Propagation, 1996, AP-44: 143-151
[28] S. Vitebskiy, L. Carin. Resonanees of perfectly conducting wires and bodies of revolution buried in a lossy dispersive half space[J]. IEEE Trans. Antenna and Propagation, 1996, AP-44: 1575-1583
[29] Jinxi Ma, F. P. Dawalibi, W. K. Daily, Analysis of grounding systems in soils with hemispherical layering[J]. IEEE Transactions on Power Delivery, 1993, 8(4): 1773-1781
[30] Jinxi Ma, F. P. Dawlibi. Analysis of grounding systems in soils with cylindrical soil volumes[J]. IEEE Transactions on Power Delivery, 2000, 15 (3): 91(3-918
[31] Jinxi Ma, F. P. D awalibi. Analysis of grounding systemsin soils with finite volumes of different resistivities[J]. IEEE Transactions on Power Delivery, 2002, 1 (2): 596-602
[32]孙结中,刘力.运用等值复数镜像法求解复合分层土壤结构的格林函数[J].中国电机工程学报, 2003, 23(9): 146-151
[33] K. S Yee. Numerieal solution of initial boundary value problems involving Maxwell’s equations in isotropic media[J]. IEEE Transactions on Antenna and Propagation, 1996, AP-14: 302-307
[34] Wang T,晓尘.三维介质中电磁波传播的FDTD模拟[J].勘探地球物理进展, 1997, 20 (1): 97-98
[35] Dcbroux P S.地球物理目标体电磁响应的FDTD法3D模拟[J].勘探地球物理进展, 1997, 20(2): 87-89
[36]王长清,祝西里,陈国华等. Maxwell方程用于电磁脉冲在损耗介质中的传播问题[J].电波科学学报, 1999, 14(1) : 97-101
[37]刘凌志,王建新,刘联会.基于FDTD方法的无线电波透地传输特性的研究[J].现代电子技术, 2004, 10: 55-56
[38]周蔚红,周东明,刘克成.二维FDTD分析土壤及地下管道的时域散射场[J].国防科技大学学报, 2003, 25(6): 53-55
[39] G. Mur. Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic-field equations[J]. IEEE Transactions on Electromagnetic Compatibility, 1981, EMC-23: 377-382
[40]秦臻,胡文宝.用于有耗介质FDTD计算的改进的Mur吸收边界条件[J].江汉石油学院学报, 2004, 26(2): 76-79
[41] J. P. Berenger. A perfectly matched layer for the absorption of electromagnetic waves [J]. Comput. Phys. , 1994, 114: 185-200
[42] J. Fang, Z. Wu. Generalized perfectly matched layer-an extension of Berenger's perfectly matched layer boundary condition[J]. Microwave and Guided Wave Letters, IEEE, 1995, 5(12): 451-453
[43] J. Fang, Z. Wu . Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media[J]. IEEE Transactions on Microwave Theory and Techniques, 1996, 44(12): 2216-2222
[44] Gedney, S. D. An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices[J]. IEEE Transactions on Antennas and Propagation, 1996, 44(12): 1630 - 1639
[45] Pereda, J. A. ; Garcia, O. , et al. . Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics[J]. Microwave and Guided Wave Letters, IEEE 1998, 8(7): 245-247
[46] Lu Ling, Li Ronglin, et al. . A new generalized perfectly matched layer for terminating 3D lossy media[J]. IEEE Transactions on Magnetics, 2002, 38(2): 713-716
[47] L. Cirio, A. Richardson , Odile Picon. Accurate development of the UPML absorbing boundary conditions in a 3D-FDTD algorithm for CPW and microstrip line on silicon substrate. Microwave and Optical Technology Letter, 2005, 44(4): 334-338
[48] A. Richardson, L. Cirio, L. Martoglio, and O. Picon, 3D-FDTD characterization ofan original low-loss silicon line, Int J Computation and Math in Electrical and Electron Engine. 2002(21): 624-632
[49] A. C. Cangellaris, D. B. Wright. Analysis of the numerical error caused by the stairstepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena [J]. IEEE Transactions on Antennas and Propagation, 1991, 39(l0): 1518-1525
[50] T. G. Jurgens, A. Taflove. Three-dimensional contour FDTD modeling of scattering form single and multiple bodies[J]. IEEE Transactions on Antennas and Propagation, 1993, 41(12): 1703-1708
[51] S. Dey, R. Mittra. A locally conformal finite difference time domain (FDTD) algorithm for modeling three-dimensional perfectly objects[J]. IEEE Microwave Guide d Wave Lett. , 1997, 7(9): 273-276
[52] S. Dey, R. Mittra. A modified locally conformal FDTD algorithm for modeling three-dimensional perfectly conductingo bjects[J]. IEEE Microwave and Optical Te chnology Letters, 1998, 17(6): 349-352
[53] Fusco M, Smith M V , Gordon L W. A three dimensional algorithm in curvilinear coordinates[J]. IEEE Transactions on Antennas and Propagation, 1991, 39(10): 1463-1471
[54] Ralton Chris J , Schneider John B . Analytical and numericalan alysis of several locally conformal FDTD schemes[J]. IEEET rans. on MTT. 1999, 47(l): 56-65
[55] Wenhua Yu, R. Mittra. A conformal FDTD algorithm modeling perfectly conducting obects with curved shaped surfaces and edges[J]. IEEE Antennas and Propagation Magazine, 2000, 42(5): 28-39
[56] J. F L ee, R . R . Pa landech, R . M ittra. Modeling three-dimensional discontinuities in wave guides using non-orthogonal FDTD algorithm[J]. IEEE Trans. MTT, 1992, 40(2): 346-352
[57] Ycc Kanc S, Chcn Jci Shuan, and Chang Albert II. Conformal FDTD with overlapping grids. IEEE Trans. on A P. 1992, 40(9): 1068-1073
[58] Rongxing Li. Data structures and application issues in (3-D geographic information systems[J]. GEOMATICA. 1994, 48(3): 209-224
[59] R. Li. 3D data structure and application in geological subsurface modeling[C]. International Archives of Photogrammetry and Remote Sensing, 1994, 30:124-131
[60]李清泉,李德仁.三维地理信息系统中的数据结构[J].武汉测绘科技大学学报. 1996, 21(2): 128-133
[61] Li R X. Data structure and application issue in 3D geographic information sysetm. Geomatics, 1994, 48(3): 209-244
[62]吴冲龙,毛小平,李绍虎等.数字盆地与构造一地层格架三维动态模拟技术研究[M].第二届年全国沉积学大会摘要论文集, 2001: 494-500
[63]毛小平,吴冲龙,袁艳斌.三维构造模拟方法一体平衡技术研究[J].地球科学-中国地质大学学报, 1999, 24(6): 505-505
[64]田宜平,袁艳斌,李绍虎等.建立盆地三维构造一地层格架的插值方法[J],地球科学-中国地质大学学报, 2000, 25(2): 191-194
[65]翁正平,吴冲龙,毛小平等.基于平面图的盆地三维构造一地层格架建模技术[J].地球科学-中国地质大学学报, 2001, 26, suppl: 135-135
[66]柳庆武,吴冲龙,李绍虎.基于钻孔资料的三维数字地层格架自动生成技术研究[J].石油实验地质, 2003, 25(5): 501-504
[67]朱合华,郑国平,吴江斌等.基于钻孔信息的地层数据模型研究[J].同济大学学报, 2003, 31(5): 535-539
[68]陈健.三维地层空间信息系统结合三维有限元的研究与实现.武汉:武汉岩土所[博士学位论文], 2001
[69]贺怀建,白世伟,赵新华等.三维地层模型中地层划分的探讨.岩土力学, 2002, 23(5): 637-639
[70] Alna M. L, Nonnan L. J. Buildlng solid models from boreholes and user-defined cross-sectinos. Computer&Geoseiences, 2003, 29: 547-555
[71] Wu Q. , Xu H. An approach to computer modeling and visualization of geological faults in 3D[J]. Computers&Geosciences, 2003, 29(4): 503-509
[72] Wu Q. , Xu H. , Zou X. K. An effective method for 3D geological modeling with multi-source data integration[J]. Computer&Geosciences, 2005, 31(1): 35-43
[73]邬伦,刘瑜,张晶等.地理信息系统原理方法和应用[M]].北京:科学出版社, 2001: 184-!85
[74]黄健全,罗明高.胡雪涛.实用地质制图[M].北京:地质出版社, 1998
[75] G. Matheron. Principles of geostatistics. Econ. Geol. , 1963, 58(8): 1246–1266
[76] J. P. Chiles and P. Delfiner. Geostatistics : modeling spatial uncertainty. ser. Wiley Series in Probability and Statistics. New York: Wiley, 1999
[77] Briggs I. C. Machine contouring using minimum cuvratuer[J]. GeoPhysics, 1974, 39(1): 39
[78] Banrett V. Inteprreting multivariatedata[M]. NewYork, 1981: 21
[79] Mulgrew, B. Applying radial basis functions[J]. Signal Processing Magazine, IEEE, 1996, 13(2): 50-65
[80] Rognant, L. , Chassery, J. . M. , et al. . The Delaunay constrained triangulation: the Delaunay stable algorithms[C]. IEEE International Conference on Information Visualization, July, 1999: 147-152
[81] McBratuey, A. B, Whelan, B, M. The potential for site-specifc management of cotton farming systems[C]. Discussion Paper No. l Co-operative Researeh Center for Sustainable CottonProduction, Australia, 1995
[82] Dirk, M. B. Mohanty, B. P , et al. . Spatial varariability of hydraulic properties in a multi-layered soil profile[J]. Soil Science, 1996, 161(3): 167-181
[83]王家华,周叶,高海余.克里金地质绘图技术[M].北京:石油工业出版社, 1999
[84] C. D. Lloyd , P. M. Atkinson. Assessing uncertainty in estimates with ordinary and indicator kriging[J]. Computers & Geosciences, 2001, 27(8): 929-937
[85] Clayton V. Deutsch. Correcting for negative weights in ordinary kriging[J]. Computers & Geosciences, 1996, 22(7): 765-773
[86] James R. Carr . UVKRIG: A FORTRAN-77 program for universal kriging[J]. Computers & Geosciences, 1990, 16(2), 1990
[87] B. Zhang, M. Stein. Kernel Approximations for Universal Kriging Predictors[J]. Journal of Multivariate Analysis, 1993, 44( 2): 286-313
[88] Steve W. Lyon, Arthur J. Lembo, et al. . Defining probability of saturation with indicator kriging on hard and soft data[J]. Advances in Water Resources, 2006, 29(2): 181-193
[89] F. G. Bastante, J. Taboada, et al. . Evaluation of the resources of a slate depositusing indicator kriging[J]. Engineering Geology, 2005, 81(4): 407-418
[90] Eulogio P. I, Mario C. O. KRIGRADI: A cokriging program for estimating the gradient of spatial variables from sparse data[J]. Computers & Geosciences, 2007, 33(4): 497-512
[91] Zhongwei Li, You-Kuan Zhang, et al. . Cokriging estimation of daily suspended sediment loads[J]. Journal of Hydrology, 2006, 327((3-4): 389-398
[92]门明新,宇振荣,许皞.基于地统计学的河北省降雨侵蚀力空间格局研究[J]中国农业科学, 2006, 11
[93]鲁振宇,杨太保,郭万钦.降水空间插值方法应用研究-以黄河源区为例[J].兰州大学学报(自然科学版), 2006, 42(4): 11-14
[94] Guevara-Escobar, E. González-Sosa, et al. . Rainfall interception and distribution patterns of gross precipitation around an isolated Ficus benjamina tree in an urban area[J]. Journal of Hydrology, 2007, 333((2-4): 532-541
[95] Raquel B. , Fernando M. , et al. . Geostatistical modelling of air temperature in a mountainous region of Northern Spain[J] Agricultural and Forest Meteorology, 2007, 146((3-4): 173-188
[96] M. Lopes, G. Avillez, et al.. Groundwater contamination plume monitoring in sealed waste dumps. Engineering Geology, 2006, 85 ( 1-2): 62-66
[97] Hoeksema, R. J. , Clapp, R. B. , et al. . Cokriging model for estimation of water table elevation[J]. Water Resources Research, 1989. 25 (3): 429-438
[98]章光新,邓伟,何岩.洮儿河流域地下水TDS时空变异特征研究[J].水土保持学报, 2005, 19(2): 122-125
[99] F. Z B, Largueche. Estimating Soil Contamination with Kriging Interpolation Method[J]. American Journal of Applied Sciences , 2006, 3 (6): 1894-1898
[100]颜辉武,祝国瑞,徐智勇等.基于Kriging水文地质层的三维建模与体视化[J].武汉大学学报(信息科学版), 2004(7): 611-614
[101] Buttafuoeo, A. Castrignan, E. Busoni. Studying the spatial structure evolution of soil water content using multivariate geostatistics[J]. Joumal of Hydrology, 2005, 311: 202-218
[102] K. F. Stacey, R. M. Lark, et al. . Using a process model and regression kriging to improve predictions of nitrous oxide emissions from soil[J]. Geoderma, 2006, 13:107-117
[103]李启权,王昌全,李冰等.成都平原土壤中砷的空间分布及污染评价[J].土壤通报, 2005, 24(9): 1546-1549
[104]李子忠,龚元石.农田土壤水分和电导率空间变异性及确定其采样数的方法[J].中国农业大学学报, 2000, 33(5): 59-66
[105] L. Tacher, I. Pomian-Srzednicki, A. Parriaux. Geological uncertainties associated with (3-D subsurface models[J]. Computers & Geosciences, 2006, 32(2): 212-221
[106] W. Yu, Y. Liu, et al. . A robust parallelized conformal finite difference time domain field solver package using the MPI library[J]. IEEE Antennas and Propagation Magazine, 2005, 47(3): 39-59
[107] W. Yu, R. Mittra, W. Yu, Y. Liu, et al. . Parallel finite difference time domain method[J]. Artech House, MA, June 2006
[108] V. Varadarajan and R. Mittra. Finite-Difference Time-Domain (FDTD), analysis using distributed computing[J]. IEEE Microwave and Guided Wave Letters, 1994, 4(5): 144-145
[109] S. Gedney. Finite difference time domain analysis of microwave circuit devices in high performance vector/parallel computers[J]. IEEE Transactions on Microwave Theory and Techniques, 1995, 43(10): 2510-2514
[110] W. J. Buchanan and N. K. Gupta . Parallel processing techniques in EMP propagation using 3D Finite-Difference Time-Domain (FDTD) method[J]. Advances in Engineering Software, 1993, 18(3) 149-159
[111] K. Chew and V. Fusco. A Parallel Implementation of the Finite Difference Time Domain Algorithm[J]. International journal of Numerical Modeling Electronic Networks, Devices and Fields, Vol. 8, 1995, pp. 293-299
[112] C. Guiffaut , K. Mahdjoubi. A parallel FDTD algorithm using the MPI library[J]. IEEE Antennas and Propagation Magazine, 2001, 43(2): 94-103
[113] L. Catarinucci, P. Palazzari, L. Tarricone. A parallel FDTD tool for the solution of large dosimetric problems: an application to the interaction between humans and radiobase antennas,”IEEE Microwave Symposium Digest, 2002, 3: 1755-1758
[114] J. Wang, O. Fujiwara and S. Watanabe, et al. . Computation with a parallel FDTD system of human-body effect on electromagnetic absorption for portabletelephones[J]. IEEE Transactions on Microwave Theory and Techniques, 2004, 52(1): 53-58
[115] Su, M. F. , El-Kady, I. , et al. . A novel FDTD application featuring OpenMP-MPI hybrid parallelization[C]. International Conference on Parallel Processing, 2004. ICPP 2004. 2004, 1: 373-379
[116] Araujo, J. S. ; Santos, R. O, et al. . Analysis of antennas by FDTD method using parallel processing with MPI[C]. Microwave and Optoelectronics Conference, 2003( IMOC 2003). 2003, 2: 1049-1054
[117] Dan Yang, Cheng Liao, et al. . A parallel FDTD algorithm based on domain decomposition method using the MPI library[C]. Proceedings of the Fourth International Conference on Parallel and Distributed Computing, Applications and Technologies, 2003(PDCAT'2003) , 2003: 730-733
[118] Omar Ramadan. Three dimensional MPI parallel implementation of the PML algorithm for truncating finite-difference time-domain Grids[J]. Parallel Computing, 2007, 33(2): 109-115
[119]冯峰,逯贵祯,关亚林.用MPI实现FDTD网络并行电磁散射运算[J].微波学报, 2006, 22(2): 11-16
[120]杨利霞,葛德彪,魏兵等. FDTD并行算法研究:电和磁本构参数均为各向异性情形[J].电子学报, 2006, 9: 1703-1707
[121]杨利霞,葛德彪,郑奎松等.电各向异性介质FDTD并行算法的研究[J].电波科学学报, 2006, 21(1): 43-48
[122]张玉,李斌,梁昌洪. PC集群系统中MPI并行FDTD性能研究[J].电子学报, 2005. 9: 1694-1697
[123]张玉,宋健,梁昌洪.并行共形FDTD算法及其在PBG结构仿真中的应用[J].电子学报, 2003, 12A: 2141-2144
[124]张玉,王楠,梁昌洪PC集群MPI并行矩量法分析复杂平台多天线特性.电子学报, 2006, 3: 478-482
[125] Y, Zhang, W. Ding, C. H. Liang. Study on the optimum virtual topology for MPI based parallel conformal FDTD algorithm on PC clusters[J]. Journal of Electromagnetic Waves and Applications, 2005, 19(13): 1817-1831
[126]闫玉波,葛宁,郑美艳等.网络并行FDTD方法分析电大目标电磁散射[J].电子学报, 2003, 6: 821-824
[127]余文华,杨小玲,刘永俊等.并行FDTD和IBM BlueGene/L巨型计算机结合求解电大尺寸的电磁问题[J].电波科学学报, 2006, 21(4): 562-566
[128] K. E. Kerry, K. A. Hawick. Spatial interpolation on distributed, high-performance computers[R]. DHPC Technical Report DHPC-015, Department of Computer Science, University of Adelaide, 1997
[129] K. E. Kerry, K. A. Hawick. Kriging interpolation on high-performance computers[C]. Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking, April 21-23, 1998: 429-438
[130] Albrecht Gebhardt. PVM Kriging with R[C]. Austria: Proceedings of the 3rd International Workshop on Distributed Statistical Computing, 2003
[131] Topp G C. , J. L. Davis, A. P. Anna. Electromagetic determination of soil water content: measurement in coaxial transmission lines[J]. Water Resoures Research, 1980, 16: 574-582
[132] L. M.布列霍夫基赫(前苏联).分层介质中的波[M].北京:科学出版社, 1985
[133]戈鲁.赫兹若格鲁著;周克定等译.电磁场与电磁波[M].机械工业出版社, 2004
[134] Matherton. Prineiples of geo-statistics. Economic Geology, 1963, 58: 1246-1266
[135] Davis, John C. Statistic and data analysis in geology [M]. NewYork: John wiley&Sons, Inc, 2002: 525-529
[136] Lophaven S N, Nielsen H B, Sondergaard J. DACE-A Matlab Kriging toolbox, version 2. 0 [OL]. http : //PPwww1imm1dtu1dk/~hbn/pub1/TR0212. ps
[137] Kennedy, J. , Eberhart, R. C. . Particle swarm optimization, Proc. IEEE Intl [Z]. Conf. on Neural Networks, IEEE Service Center, Piscataway, NJ, 1995, IV: 1942-1948
[138] P. Y. Yin. Genetic particle swarm optimization for polygonal approximation of digital curves. Pattern Recognition and Image Analysis[J], 2006, 16(2): 22(3-233
[139] Eziol Todini1 Influence of parameter estimation uncertainty in Kriging part I—theoretical development [J]. Hydrology and Earth System Sciences , 2001, 5 (2): 215-223
[140]游海龙,贾新章.基于遗传算法Kriging模型构造与优化[J].计算机辅助设计与图形学学报, 2007, 19(1): 64-68
[141] Taflove A, Brodwin M. E. Numerical solution of steady-state EM scattering problems using the time-dependent Maxwell's equations. IEEE Trans. Microwave Theory Tech, 1975, 23: 623-630
[142] W. C. Chew and W H. Weedon,“A 3D perfectly matched medium from modified Maxwell s equatlons with stretched coordinates,”Microwave Opt Techno1 Lett, 1994, 7(13): 599-604
[143] M Gribbons, S K. Lee, and A. C Cangellans,“Modification of Berenger’s perfectly matched layer for the absorption of electromagnellcwaves in layered media,”in Proc llth Annu Review of Progress inApplied Computational Electromagnetics, Monterey, CA, Mar 20-25, 1995: 498-503
[144]陈国良,安虹,陈崚等编著.并行算法实践.北京:高等教育出版社, 2004
[145]都志辉编著.高性能计算并行编程技术-MPI并行程序设计.北京:清华大学出版社, 2001