非均质多孔介质多尺度模型及其在地下水模拟中的应用
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摘要
基于区域大量的密集分布的钻孔岩性数据，实现多尺度、多精度需求与数据联合驱动的地下水流和溶质运移数值模拟，可为解决区域地下水资源问题、环境问题、生态问题以及地下水灾害问题等提供理论支持。然而，由于含水介质的非均质性，含水层水文地质参数具有空间变异性和尺度效应，导致地下水流和溶质运移模拟的结果往往会与实际有较大的偏离。本文基于较高密度的钻孔岩性数据建立多尺度非均质多孔介质模型，根据建立的多孔介质模型获取水文地质参数场，并将参数场应用于地下水数值模拟中的研究十分有意义。
本文主要开展了以下研究：以大量的密集分布钻孔岩性数据为基础，分析了含水介质的非均质性，利用Voronoi图方法实现了钻孔数据的密度和面积分布概况的分析；提出了针对密集分布钻孔数据尺度综合方法；研究了多孔介质的转移概率地质统计随机模拟，提出了侧向转移概率计算方法；分析了侧向转移概率对模拟结果的影响；对比分析了尺度综合虚拟钻孔与原始钻孔建立的转移概率地质统计三维随机模型；基于尺度综合虚拟钻孔和真实钻孔的多尺度多孔介质模拟和确定-随机耦合模拟；基于多孔介质随机模型的水文地质参数提取；分析了基于转移概率地统计模拟提取参数的稳定性与实现个数的关系；并将建立的多孔介质模型与地下水流和溶质运移数值模型结合，应用于地下水数值模拟，从而为区域地下水管理和分析提供支持，得出以下主要结论和成果：
（1）基于密集分布钻孔岩性数据，得出了实例研究区含水介质的的两个主方向空间变异相关距离分别为5500m和12000m；提出了对密集分布钻孔岩性数据进行尺度综合生成虚拟钻孔的方法，生成的虚拟钻孔较好地反映了含水介质大尺度上的结构性特征。基于尺度综合虚拟钻孔建立的含水介质随机模型，可以较好的反映含水介质粗尺度上的总体分布特征，在强非均质区域模拟结果表现为连续等效介质。
（2）侧向转移概率对模拟结果的影响分析显示，如果侧向与垂向介质平均长度比值估计过小，导致介质分布随机性强，不具有连续性；如果某种介质比值估计过大，则导致该介质水平方向上连续性过强，本文提出的基于垂向分层平面连续地质类型假设的侧向转移概率计算方法，可以有效的根据钻孔数据得到侧向转移率矩阵，并且模拟效果较好。开发了基于GIS的集钻孔等数据管理与转移概率地统计建模与一体的程序。
（3）转移概率地统计模拟结果评估显示，在弱非均质或者相对均质区域，模拟结果可以较好的还原区域含水介质的介质类型分布，而在非均质性较强的区域，模拟结果难以还原真实的介质分布；由此，针对大尺度含水介质模拟，提出了基于多尺度钻孔数据转移概率地统计模拟的方法，即耦合弱非均质区的正常尺度综合钻孔和强非均质区更细尺度的尺度综合钻孔进行模拟，使得模拟结果在强非均质区域可以更好地还原含水介质真实分布。
（4）基于尺度综合虚拟钻孔和实际钻孔，利用转移概率地统计可以有效地创建多尺度多孔介质模型；将建立的确定性水文地质结构模型与结构体内的随机模型相结合，实现了多孔介质的确定-随机耦合模拟，模拟的多孔介质模型即具有大尺度的结构性又具有小尺度的随机性特征。
（5）转移概率地统计模拟各结点的稳定性与钻孔密度和分布，模拟区域的非均质性强弱等因素有关，在弱非均质区域，转移概率地统计的模拟结果趋于稳定较快，每次模拟结果相同的可能性大；而在强非均质区域，模拟结果趋于稳定慢，每次模拟结果随机性强；在数据稀少区域，每次模拟结果的随机性更强，但是随着实现数的增加，各介质所占比例趋于稳定。
（6）将多尺度多孔介质模型与大尺度地下水流和多尺度溶质运移数值模拟结合应用的实例显示，大尺度地下水流数值模拟使用基于尺度综合虚拟钻孔进行转移概率地统计模拟提取的渗透系数，小尺度溶质运移模拟使用实际钻孔进行转移概率地统计模拟提取的渗透系数，在地下水数值模拟中是可行的，转移概率地统计生成的条件化的随机模型体现了渗透系数的空间变异性，改变了局部水头分布和水流方向，其模拟结果往往更接近实际情况。
本文创新点体现在：（1）创新了基于密集分布钻孔岩性数据进行尺度综合生成虚拟钻孔的方法；（2）提出了基于垂向分层平面连续地质类型假设的侧向转移概率计算方法；（3）基于尺度综合虚拟钻孔和实际钻孔，利用转移概率地统计方法实现了多孔介质多尺度随机模拟。
Numerical simulation of groundwater flow and solute transport based on relative high densitydrilling lithology data of a region, which is jointly driven by multi-scale, different accuracyrequirements and data, can provide theoretical support for solving issues of regional groundwaterresources, environmental problems, ecological problems, and groundwater disasters. However, dueto the heterogeneity of aquifer medium, hydrogeological parameters of aquifer arespatial variabilityand scale effect, which result in there is a large deviation between groundwater flow and solutetransport simulation results with the actual situation. Therefore, it is very meaningful thatestablishing multi-scale heterogeneous porous medium model based on high density drillinglithology data to obtain hydrogeological parameters field, and applying parameter field to numericalsimulation of groundwater.
This paper carried out the following researches. The heterogeneity of aquifer medium wasanalysed based on high density drillings lithology data. Voronoi diagram method was employed toanalyze the density and distribution of drilling data. A scale generalization approach for high densityboreholes data was proposed. The stochastic simulation of transition probabilities geostatistics wasresearched in this paper, and a method for computing lateral transition probabilities was proposed.The relationship of lateral transition probabilities and simulation result was analyzed, and theestablished three-dimensional stochastic models with scale generalization virtual boreholes andoriginal boreholes were compared. Simulation of multiscale porous medium model based on scalegeneralization virtual drillings and real drillings and deterministic-stochastic coupled simulationwere realized. Hydrogeological parameters were extracted from stochastic model of porous medium.The relationship of the stability of the extracted parameters with realization number in transitionprobabilities geostatistical simulation was analyzed. Porous medium model with numerical model ofgroundwater flow and solute transport was combined, which can provide support for regionalgroundwater management and multi-scale numerical simulation of groundwater. The mainconclusions and results are as follows:
(1) Based on the high density drilling lithology data, the spatial correlation distance of the twomain directions for the instance study area of the aquifer were obtained; A scale generalizationapproach for high density boreholes data was proposed to generate virtual drillings, and thegenerated virtual drillings can better reflect the large-scale structural characteristics of aquifermedium. Stochastic model based on scale generalization virtual drillings can shows the overalldistribution characteristics of aquifer medium, and the simulation result in strong heterogeneousregion are shown as continuous equivalent material.
(2) The analysis of lateral transition probabilities shows if the ratio of mean lens length of thelateral to vertical is estimated too small, it will lead to a strong random materials distribution in thesimulation result, which is uncontinuity. If the estimated ratio is too big, it will lead to too strongcontinuity materials in horizontal direction.The proposed method based on vertical stratification andthe hypothesis of continuous geological type in plane for computing lateral transition probabilitiescan effectively obtain lateral transition rate matrix, and can get better simulation result. A programbased on GIS which can manage drilling data and conduct transition probabilities geostatistics wasdeveloped.
(3) The simulation result of transition probabilities geostatistics was assessed, which shows themodel can better restore materials distribution of aquifer medium in weak heterogeneous orhomogeneous area, but difficult to restore the true materials distribution in strong heterogeneousregion. Thus the simulation method based on multi-scale virtual boreholes data was proposed, whichis combining the normal scale generalization boreholes in weak heterogeneous area and finer scalegeneralization boreholes in strong heterogeneous area to simulate.The simulation results can betterrestore the actual distribution of aquifer medium in a strong heterogeneous region.
(4) Multi-scale porous medium model based on scale generalization virtual drillings and actualdrillings can effectively established with transition probabilities geostatistics. Hydrogeologicalstructure model and the stochastic models in the structures were combined to establishdeterministic-stochastic porous medium model. The final model has large-scale structuralcharacteristic and small-scale random characteristic.
(5) The stabilities of nodes in transition probabilities geostatistical model are related withdrillings’ density and distribution, the strength of heterogeneity of the simulation area, and otherfactors. In weak heterogeneity area the result of realizations with increasing number is faster to tendto be stable, and the probability of the same result in the same node in different realization is higher,but slower to tend to be stable and random of that in strong heterogenous area. There is a morerandomness simulation results in the area of sparse data. However, the proportion of each material ata node tends to be stable with the increase in realization number.
(6) The instances of combining multi-scale porous medium model with groundwater flow andsolute transport numerical simulation show it is feasible that numerical simulation of large-scalegroundwater flow uses hydraulic conductivity values extracted from transition probabilitiesgeostatistical model based on scale generalization virtual boreholes, and small-scale solute transportsimulation uses hydraulic conductivity values extracted from the model based on actual boreholes.The conditional stochastic model reflects the spatial variability of hydraulic conductivity, which maychange the local head distribution and flow direction, and make the simulation results often closer tothe actual situation.
This innovations are reflected in:(1) proposing scale generalization method for generatingvirtual boreholes based on high density boreholes lithology data;(2) proposing the method forcomputing lateral transition probabilities based on vertical stratification and the hypothesis ofcontinuous geological type in plane;(3) realizing multi-scale porous medium simulation withtransition probabilities geostatistics based on scale generalization virtual drillings and actualdrillings.
本文主要开展了以下研究：以大量的密集分布钻孔岩性数据为基础，分析了含水介质的非均质性，利用Voronoi图方法实现了钻孔数据的密度和面积分布概况的分析；提出了针对密集分布钻孔数据尺度综合方法；研究了多孔介质的转移概率地质统计随机模拟，提出了侧向转移概率计算方法；分析了侧向转移概率对模拟结果的影响；对比分析了尺度综合虚拟钻孔与原始钻孔建立的转移概率地质统计三维随机模型；基于尺度综合虚拟钻孔和真实钻孔的多尺度多孔介质模拟和确定-随机耦合模拟；基于多孔介质随机模型的水文地质参数提取；分析了基于转移概率地统计模拟提取参数的稳定性与实现个数的关系；并将建立的多孔介质模型与地下水流和溶质运移数值模型结合，应用于地下水数值模拟，从而为区域地下水管理和分析提供支持，得出以下主要结论和成果：
（1）基于密集分布钻孔岩性数据，得出了实例研究区含水介质的的两个主方向空间变异相关距离分别为5500m和12000m；提出了对密集分布钻孔岩性数据进行尺度综合生成虚拟钻孔的方法，生成的虚拟钻孔较好地反映了含水介质大尺度上的结构性特征。基于尺度综合虚拟钻孔建立的含水介质随机模型，可以较好的反映含水介质粗尺度上的总体分布特征，在强非均质区域模拟结果表现为连续等效介质。
（2）侧向转移概率对模拟结果的影响分析显示，如果侧向与垂向介质平均长度比值估计过小，导致介质分布随机性强，不具有连续性；如果某种介质比值估计过大，则导致该介质水平方向上连续性过强，本文提出的基于垂向分层平面连续地质类型假设的侧向转移概率计算方法，可以有效的根据钻孔数据得到侧向转移率矩阵，并且模拟效果较好。开发了基于GIS的集钻孔等数据管理与转移概率地统计建模与一体的程序。
（3）转移概率地统计模拟结果评估显示，在弱非均质或者相对均质区域，模拟结果可以较好的还原区域含水介质的介质类型分布，而在非均质性较强的区域，模拟结果难以还原真实的介质分布；由此，针对大尺度含水介质模拟，提出了基于多尺度钻孔数据转移概率地统计模拟的方法，即耦合弱非均质区的正常尺度综合钻孔和强非均质区更细尺度的尺度综合钻孔进行模拟，使得模拟结果在强非均质区域可以更好地还原含水介质真实分布。
（4）基于尺度综合虚拟钻孔和实际钻孔，利用转移概率地统计可以有效地创建多尺度多孔介质模型；将建立的确定性水文地质结构模型与结构体内的随机模型相结合，实现了多孔介质的确定-随机耦合模拟，模拟的多孔介质模型即具有大尺度的结构性又具有小尺度的随机性特征。
（5）转移概率地统计模拟各结点的稳定性与钻孔密度和分布，模拟区域的非均质性强弱等因素有关，在弱非均质区域，转移概率地统计的模拟结果趋于稳定较快，每次模拟结果相同的可能性大；而在强非均质区域，模拟结果趋于稳定慢，每次模拟结果随机性强；在数据稀少区域，每次模拟结果的随机性更强，但是随着实现数的增加，各介质所占比例趋于稳定。
（6）将多尺度多孔介质模型与大尺度地下水流和多尺度溶质运移数值模拟结合应用的实例显示，大尺度地下水流数值模拟使用基于尺度综合虚拟钻孔进行转移概率地统计模拟提取的渗透系数，小尺度溶质运移模拟使用实际钻孔进行转移概率地统计模拟提取的渗透系数，在地下水数值模拟中是可行的，转移概率地统计生成的条件化的随机模型体现了渗透系数的空间变异性，改变了局部水头分布和水流方向，其模拟结果往往更接近实际情况。
本文创新点体现在：（1）创新了基于密集分布钻孔岩性数据进行尺度综合生成虚拟钻孔的方法；（2）提出了基于垂向分层平面连续地质类型假设的侧向转移概率计算方法；（3）基于尺度综合虚拟钻孔和实际钻孔，利用转移概率地统计方法实现了多孔介质多尺度随机模拟。
Numerical simulation of groundwater flow and solute transport based on relative high densitydrilling lithology data of a region, which is jointly driven by multi-scale, different accuracyrequirements and data, can provide theoretical support for solving issues of regional groundwaterresources, environmental problems, ecological problems, and groundwater disasters. However, dueto the heterogeneity of aquifer medium, hydrogeological parameters of aquifer arespatial variabilityand scale effect, which result in there is a large deviation between groundwater flow and solutetransport simulation results with the actual situation. Therefore, it is very meaningful thatestablishing multi-scale heterogeneous porous medium model based on high density drillinglithology data to obtain hydrogeological parameters field, and applying parameter field to numericalsimulation of groundwater.
This paper carried out the following researches. The heterogeneity of aquifer medium wasanalysed based on high density drillings lithology data. Voronoi diagram method was employed toanalyze the density and distribution of drilling data. A scale generalization approach for high densityboreholes data was proposed. The stochastic simulation of transition probabilities geostatistics wasresearched in this paper, and a method for computing lateral transition probabilities was proposed.The relationship of lateral transition probabilities and simulation result was analyzed, and theestablished three-dimensional stochastic models with scale generalization virtual boreholes andoriginal boreholes were compared. Simulation of multiscale porous medium model based on scalegeneralization virtual drillings and real drillings and deterministic-stochastic coupled simulationwere realized. Hydrogeological parameters were extracted from stochastic model of porous medium.The relationship of the stability of the extracted parameters with realization number in transitionprobabilities geostatistical simulation was analyzed. Porous medium model with numerical model ofgroundwater flow and solute transport was combined, which can provide support for regionalgroundwater management and multi-scale numerical simulation of groundwater. The mainconclusions and results are as follows:
(1) Based on the high density drilling lithology data, the spatial correlation distance of the twomain directions for the instance study area of the aquifer were obtained; A scale generalizationapproach for high density boreholes data was proposed to generate virtual drillings, and thegenerated virtual drillings can better reflect the large-scale structural characteristics of aquifermedium. Stochastic model based on scale generalization virtual drillings can shows the overalldistribution characteristics of aquifer medium, and the simulation result in strong heterogeneousregion are shown as continuous equivalent material.
(2) The analysis of lateral transition probabilities shows if the ratio of mean lens length of thelateral to vertical is estimated too small, it will lead to a strong random materials distribution in thesimulation result, which is uncontinuity. If the estimated ratio is too big, it will lead to too strongcontinuity materials in horizontal direction.The proposed method based on vertical stratification andthe hypothesis of continuous geological type in plane for computing lateral transition probabilitiescan effectively obtain lateral transition rate matrix, and can get better simulation result. A programbased on GIS which can manage drilling data and conduct transition probabilities geostatistics wasdeveloped.
(3) The simulation result of transition probabilities geostatistics was assessed, which shows themodel can better restore materials distribution of aquifer medium in weak heterogeneous orhomogeneous area, but difficult to restore the true materials distribution in strong heterogeneousregion. Thus the simulation method based on multi-scale virtual boreholes data was proposed, whichis combining the normal scale generalization boreholes in weak heterogeneous area and finer scalegeneralization boreholes in strong heterogeneous area to simulate.The simulation results can betterrestore the actual distribution of aquifer medium in a strong heterogeneous region.
(4) Multi-scale porous medium model based on scale generalization virtual drillings and actualdrillings can effectively established with transition probabilities geostatistics. Hydrogeologicalstructure model and the stochastic models in the structures were combined to establishdeterministic-stochastic porous medium model. The final model has large-scale structuralcharacteristic and small-scale random characteristic.
(5) The stabilities of nodes in transition probabilities geostatistical model are related withdrillings’ density and distribution, the strength of heterogeneity of the simulation area, and otherfactors. In weak heterogeneity area the result of realizations with increasing number is faster to tendto be stable, and the probability of the same result in the same node in different realization is higher,but slower to tend to be stable and random of that in strong heterogenous area. There is a morerandomness simulation results in the area of sparse data. However, the proportion of each material ata node tends to be stable with the increase in realization number.
(6) The instances of combining multi-scale porous medium model with groundwater flow andsolute transport numerical simulation show it is feasible that numerical simulation of large-scalegroundwater flow uses hydraulic conductivity values extracted from transition probabilitiesgeostatistical model based on scale generalization virtual boreholes, and small-scale solute transportsimulation uses hydraulic conductivity values extracted from the model based on actual boreholes.The conditional stochastic model reflects the spatial variability of hydraulic conductivity, which maychange the local head distribution and flow direction, and make the simulation results often closer tothe actual situation.
This innovations are reflected in:(1) proposing scale generalization method for generatingvirtual boreholes based on high density boreholes lithology data;(2) proposing the method forcomputing lateral transition probabilities based on vertical stratification and the hypothesis ofcontinuous geological type in plane;(3) realizing multi-scale porous medium simulation withtransition probabilities geostatistics based on scale generalization virtual drillings and actualdrillings.
引文
[1] Jha, M.K., Chowdhury, A., Chowdary, V.M., et al. Groundwater management and development byintegrated remote sensing and geographic information systems: prospects and constraints[J].Water Resources Management,2007,(21):427–467.
[2]中国地下水科学战略研究小组.中国地下水科学的机遇与挑战[M].北京:科学出版社,2009.
[3] Wu, Q., Liu, Y.Z., Liu, D.H., et al. Prediction of Floor Water Inrush: The Application of GIS-BasedAHP Vulnerable Index Method to Donghuantuo Coal Mine, China[J]. Rock Mechanics and RockEngineering,2011,44(5):591-600.
[4] Wang, Y., Yang, W.F., Li, M., et al. Risk assessment of floor water inrush in coal mines based onsecondary fuzzy comprehensive evaluation[J]. International Journal of Rock Mechanics andMining Sciences,2012,52:50-55.
[5] Wu, Q., Xu, H., and Pang, W. GIS and ANN coupling model: an innovative approach to evaluatevulnerability of karst water inrush in coalmines of north China[J]. Environmental Geology,2008,54(5):937-943.
[6] Bonacci, O. and Roje-Bonacci, T. Water losses from the Ricice reservoir built in the Dinaric karst[J].Engineering Geology,2008,99(3-4):121-127.
[7] Garcia-Lopez, S., Benavente, J., Cruz-Sanjulian, J.J., et al. Conjunctive use of water resources as analternative to a leaky reservoir in a mountainous, semiarid area (Adra River basin, SE Spain)[J].Hydrogeology Journal,2009,17(7):1779-1790.
[8] Farhadian, H., Aalianvari, A., and Katibeh, H. Optimization of analytical equations of groundwaterseepage into tunnels: A case study of Amirkabir tunnel[J]. Journal of the Geological Society ofIndia,2012,80(1):96-100.
[9] Li, X.B., Zhang, W., Li, D.Y., et al. Influence of underground water seepage flow on surrounding rockdeformation of multi-arch tunnel[J]. Journal of Central South University of Technology,2008,15(1):69-74.
[10] Xu, Y.S., Ma, L., Du, Y.J., et al. Analysis of urbanisation-induced land subsidence in Shanghai[J].Natural Hazards,2012,63(2):1255-1267.
[11] Tang, Y.Q., Ren, X.W., Chen, B., et al. Study on land subsidence under different plot ratios throughcentrifuge model test in soft-soil territory[J]. Environmental Earth Sciences,2012,66(7):1809-1816.
[12] Chalupova, D., Havlikova, P., and Jansky, B. Water quality of selected fluvial lakes in the context ofthe Elbe River pollution and anthropogenic activities in the flood plain[J]. EnvironmentalMonitoring and Assessment,2012,184(10):6283-6295.
[13] Qian, J.Z., Zhan, H.B., Wu, J.F., et al. What can be learned from sequential multi-well pumping testsin fracture-karst media? A case study in Zhangji, China[J]. Hydrogeology Journal,2009,17(7):1749-1760.
[14]廖华胜,李连侠, LI, S.G.地下水非平稳随机模型及空间变异性与非均匀性相互关系研究的展望[J].水利学报,2004,(10):13-21.
[15]肖朝明,张征,鞠硕华,等.水环境模拟中多孔介质场空间变异性研究方法述评[J].安全与环境学报,2004,(03):88-92.
[16] Chang, C.M. and Yeh, H.D. Nonstationary stochastic analysis of flow in a heterogeneous unconfinedaquifer subject to spatially-random periodic recharge[J]. Journal of Hydrology,2010,395(3-4):163-168.
[17]薛禹群,叶淑君,谢春红,等.多尺度有限元法在地下水模拟中的应用[J].水利学报,2004,(07):7-13.
[18] Li, S.G., Liu, Q., and Afshari, S. An object-oriented hierarchical patch dynamics paradigm (HPDP)for modeling complex groundwater systems across multiple-scales[J]. Environmental Modelling&Software,2006,21(5):744-749.
[19] Afshari, S., Mandle, R., and Li, S.G. Hierarchical patch dynamics modeling of near-well dynamics incomplex regional groundwater systems[J]. Journal of Hydrologic Engineering,2008,13(9):894-904.
[20] He, X.G. and Ren, L. Finite volume multiscale finite element method for solving the groundwaterflow problems in heterogeneous porous media[J]. Water Resources Research,2005,41(10):W10417.
[21] Shi, L.S., Yang, J.Z., and Zeng, L.Z. Application of multiscale finite element method in theuncertainty qualification of large-scale groundwater flow[J]. Stochastic Environmental Researchand Risk Assessment,2012,26(3):393-404.
[22] Gelhar, L.W. ed. Stochastic subsurface hydrology[M]. Prentice Hall: Englewood cliffs,1993.
[23]杨金忠,蔡树英,黄冠华,等.多孔介质中水分及溶质运移的随机理论[M].北京:科学出版社,2000.
[24] Bakr, A.A., Gelhar, L.W., Gutjahr, A.L., et al. Stochastic analysis of spatial variability in subsurfaceflows. I. Comparison of one-and three-dimensional flows[J]. Water Resources Research,1978,14(2):263-71.
[25] Hoeksema, R.J. and Kitanidis, P.K. Analysis of the spatial structure of properties of selectedaquifers[J]. Water Resources Research,1985,21(4):563-72.
[26] Feinerman, E., Dagan, G., and Bresler, E. Statistical inference of spatial random functionshydrology[J]. Water Resources Research,1986,22(6):935-42.
[27] Gelhar, L.W. Stochastic subsurface hydrology from theory to applications[J]. Water ResourcesResearch,1986,22(9):135S-45S.
[28] Dagan, G. Time-dependent macrodispersion for solute transport in anisotropic heterogeneousaquifers[J]. Water Resources Research,1988,24(9):1491-15001500.
[29] Neuman, S.P. Universal scaling of hydraulic conductivities and dispersivities in geologic media[J].Water Resources Research,1990,26(8):1749-58.
[30] Molz, F.J. and Boman, G.K. Further evidence of fractal structure in hydraulic conductivitydistributions[J]. Geophysical Research Letters,1995,22(18):2545-8
[31] Molz, F.J., Rajaram, H., and Lu, S.L. Stochastic fractal-based models of heterogeneity in subsurfacehydrology: Origins, applications, limitations, and future research questions[J]. Reviews ofGeophysics,2004,42(1): RG1002.
[32] Li, S.G. and McLaughlin, D. A nonstationary spectral method for solving stochastic groundwaterproblems: unconditional analysis[J]. Water Resources Research,1991,27(7):1589-605.
[33] Li, S.G. and McLaughlin, D. Using the Nonstationary Spectral Method to Analyze Flow ThroughHeterogeneous Trending Media[J]. Water Resources Research,1995,31(3):541-551.
[34] Li, S.G., McLaughlin, D., and Liao, H.S. A computationally practical method for stochasticgroundwater modeling[J]. Advances in Water Resources,2003,26(11):1137-1148.
[35] Li, S.G., Liao, H.S., and Ni, C.F. Stochastic modeling of complex nonstationary groundwatersystems[J]. Advances in Water Resources,2004,27(11):1087-1104.
[36] Chang, C.M. and Yeh, H.D. Using the nonstationary spectral method to analyze asymptoticmacrodispersion in uniformly recharged heterogeneous aquifers[J]. Journal of Hydrology,2008,350(1-2):93-99.
[37] Ni, C.F., Li, S.G., Liu, C.J., et al. Efficient conceptual framework to quantify flow uncertainty inlarge-scale, highly nonstationary groundwater systems[J]. Journal of Hydrology,2010,381(3-4):297-307.
[38] Ni, C.F., Lin, C.P., Li, S.G., et al. Efficient approximate spectral method to delineate stochastic wellcapture zones in nonstationary groundwater flow systems[J]. Journal of Hydrology,2011,407(1-4):184-195.
[39] Ni, C.F., Lin, C.P., Li, S.G., et al. Quantifying flow and remediation zone uncertainties for partiallyopened wells in heterogeneous aquifers[J]. Hydrology and Earth System Sciences,2011,15(7):2291-2301.
[40] Wu, J.C., Hu, B.X., and Zhang, D.X. Applications of nonstationary stochastic theory to solutetransport in multi-scale geological media[J]. Journal of Hydrology,2003,275(3-4):208-228.
[41] Hu, B.X. Stochastic study of solute transport in a nonstationary medium[J]. Ground Water,2006,44(2):222-233.
[42] Wu, J.C. and Hu, B.X. Numerical method of moments for solute transport in a nonstationary flowfield conditioned on hydraulic conductivity and head measurements[J]. StochasticEnvironmental Research and Risk Assessment,2007,21(6):665-682.
[43] Dagan, G. Statistical Theory of Groundwater Flow and Transport: Pore to Laboratory, Laboratory toFormation, and Formation to Regional Scale[J]. Water Resources Research,1986,22(9):120S-134S.
[44] Dirk, S.M., Douglas A., C., Douglas S., C., et al. Scale dependency of hydraulic conductivity inheterogeneous media[J]. Ground Water,1999,37(6):904-919.
[45]何宗宜,胡胜华,阮依香,等.基于分形理论的水系要素制图综合研究[J].测绘科技情报,2001(Z2):26-31.
[46]樊硕,武文波,马明舟.基于分形理论的线状地物要素自动综合算法实现[J].测绘科学,2009(S1):97-98.
[47]李含璞.基于小波变换的DEM多尺度综合研究[D].兰州:兰州大学,2006.
[48]王明常,谷兰英,王宇,等.小波变换理论的线状要素制图综合研究[J].吉林大学学报(地球科学版),2005(S1):147-150.
[49]王家耀,邓红艳.基于遗传算法的制图综合模型研究[J].武汉大学学报(信息科学版),2005(07):565-569.
[50]王家耀,成毅.空间数据的多尺度特征与自动综合[J].海洋测绘,2004(04):1-3.
[51] Gomez, C. Multi-scale topographic analysis of Merbabu and Merapi volcanoes using waveletdecomposition[J]. Environmental Earth Sciences,2012,67(5):1423-1430.
[52] Guo, W.L., Yang, Q.K., Wang, H.J., et al. DEM multi-scale representation based on waveletmultiresolution analysis[J]. Journal of Food Agriculture&Environment,2012,10(3-4):1346-1349.
[53] Kalbermatten, M., Van De Ville, D., Turberg, P., et al. Multiscale analysis of geomorphological andgeological features in high resolution digital elevation models using the wavelet transform[J].Geomorphology,2012,138(1):352-363.
[54]于浩,杨勤科,张晓萍,等.基于小波多尺度分析的DEM数据综合研究[J].测绘科学,2008(03):93-95+115.
[55] Marseguerra, M., Patelli, E., and Zio, E. Groundwater contaminant transport in presence of colloids.I. A stochastic nonlinear model and parameter identification[J]. Annals of Nuclear Energy,2001,28(8):777-803.
[56] Carle, S. and Fogg, G. Transition probability-based indicator geostatistics[J]. Mathematical Geology,1996,28(4):453-476.
[57] Carle, S.F. T-PROGS: Transition Probability Geostatistical Software(Version2.1)[R]. HydrologicSciences Graduate Group, University of California, Davis,1999.
[58] Zhang, Y. and Fogg, G.E. Simulation of multi-scale heterogeneity of porous media and parametersensitivity analysis[J]. Science in China Series E-Technological Sciences,2003,46(5):459-474.
[59] Sivakumar, B., Halter, T., and Zhang, H. A fractal investigation of solute travel time in aheterogeneous aquifer: transition probability/Markov chain representation[J]. EcologicalModelling,2005,182(3-4):355-370.
[60] Rubin, Y., Lunt, I.A., and Bridge, J.S. Spatial variability in river sediments and its link with riverchannel geometry[J]. Water Resources Research,2006,42(6), W06D16, doi:10.1029/2005WR004853.
[61] Zhang, H., Harter, T., and Sivakumar, B. Nonpoint source solute transport normal to aquifer beddingin heterogeneous, Markov chain random fields[J]. Water Resources Research,2006,42(6),W06403, doi:10.1029/2004WR003808.
[62] Lee, S.Y., Carle, S.F., and Fogg, G.E. Geologic heterogeneity and a comparison of two geostatisticalmodels: Sequential Gaussian and transition probability-based geostatistical simulation[J].Advances in Water Resources,2007,30(9):1914-1932.
[63] He, Y., Hu, K.L., Li, B.G., et al. Comparison of Sequential Indicator Simulation and TransitionProbability Indicator Simulation Used to Model Clay Content in Microscale Surface Soil[J]. SoilScience,2009,174(7):395-402.
[64] Blessent, D., Therrien, R., and Lemieux, J.M. Inverse modeling of hydraulic tests in fracturedcrystalline rock based on a transition probability geostatistical approach[J]. Water ResourcesResearch,2011,47, doi:10.1029/2011WR011037.
[65] Engdahl, N.B., Vogler, E.T., and Weissmann, G.S. Evaluation of aquifer heterogeneity effects onriver flow loss using a transition probability framework[J]. Water Resources Research,2010,46,doi:10.1029/2009WR007903.
[66] Sakaki, T., Frippiat, C.C., Komatsu, M., et al. On the value of lithofacies data for improvinggroundwater flow model accuracy in a three-dimensional laboratory-scale synthetic aquifer[J].Water Resources Research,2009,45, doi:10.1029/2008WR007229.
[67]何芳,吴吉春.基于马尔可夫链的多元指示地质统计模型[J].水文地质工程地质,2003(05):28-32.
[68]王荣.华北平原地下水数值模拟研究[D].北京:中国地质大学（北京）,2006.
[69]董英.基于随机水文地质结构的华北平原地下水流模拟研究[D].北京:中国地质大学（北京）,2006.
[70]靳萍,邵景力,李长青,等.基于T-PROGS的地下水三维数值模拟及应用[J].水文地质工程地质,2009(04):21-26.
[71]郭飞,葛成,韩宇.嵌入式马尔可夫链的地质属性建模与应用[J].地理与地理信息科学,2012,(01):47-50.
[72] Weissmann, G.S., Carle, S.F., and Fogg, G.E. Three-dimensional hydrofacies modeling based on soilsurveys and transition probability geostatistics[J]. Water Resources Research,1999,35(6):1761–1770.
[73] Maji, R., Sudicky, E.A., Panday, S., et al. Transition probability/Markov chain analyses of DNAPLsource zones and plumes[J]. Ground Water,2006,44(6):853-863.
[74]李军,杨晓娟,张晓龙,等.基于三维马尔可夫链模型的岩性随机模拟[J].石油学报,2012(05):846-853.
[75] Hou, T.Y. and Xiao-Hui, W. A multiscale finite element method for elliptic problems in compositematerials and porous media[J]. Journal of Computational Physics,1997,134(1):169-89.
[76] Ye, S.J. and Wu, J.C. Application of the multiscale finite element method to3-D groundwater flow inheterogeneous porous media[J]. Geochimica Et Cosmochimica Acta,2004,68(11): A465-A465.
[77]蒋小伟.盆地含水系统与地下水流动系统特征[D].北京:中国地质大学(北京),2011.
[78]宫辉力,赵文吉,诸云强.裂隙-岩溶介质空间水流数值仿真与流场优化[J].系统仿真学报,2002,(02):186-188.
[79]吴呈懋.地下水系统孔隙介质尺度效应与异质性地层参数化方法之研究[D].台北:国立台湾大学,2006.
[80]姚磊华.非平稳随机地下水流模拟[J].煤炭学报,2000,(S1):16-21.
[81] Dettinger, M.D. and Wilson, J.L. First order analysis of uncertainty in numerical models ofgroundwater flow. I. Mathematical development[J]. Water Resources Research,1981,17(1):149-61.
[82]姚磊华.地下水水流模型的摄动待定系数随机有限元法[J].水利学报,1999(07):61-65.
[83]李连侠,廖华胜, and刘达.随机地下水非平稳谱方法[J].中国科技论文,2012(05):382-387+394.
[84] Li, S.G., McLaughlin, D., and Liao, H. The Accuracy of Stochastic Perturbation Solutions toSubsurfaceTransport Problems[J]. Advances in Water Resources,2004,27(1):47-56.
[85]孙蓉琳.玄武岩渗透系数尺度效应及顺序指示模拟[D].武汉:中国地质大学,2006.
[86]王家华.克里金地质绘图技术[M].北京:石油工业出版社,1990.
[87]周海燕.空间数据挖掘的研究[D].郑州:中国人民解放军信息工程大学,2003.
[88]李志林,朱庆.数字高程模型[M].武汉:武汉大学出版社,2003.
[89]王仁铎,胡光道.线性地质统计学[M].北京:地质出版社,1988.
[90]胡细宝,孙洪祥.概率论与随机过程[M].北京:北京邮电大学出版社,2001.
[91] Carle, S.F. and Fogg, G.E. Modeling Spatial Variability with One and MultidimensionalContinuous-Lag Markov Chains[J]. Mathematical Geology,1997,28(7):891-918.
[92] Walker, J.R. Application of Transition Probability Geostatistics for Indicator Simulations Involvingthe MODFLOW Model.2002, Provo: Brigham Young University.
[93]董英.基于随机水文地质结构的华北平原地下水流模拟研究[D].北京:中国地质大学(北京),2006.
[94] Proce, C.J., Ritzi, R.W., Dominic, D.F., et al. Modeling Multiscale Heterogeneity and AquiferInterconnectivity[J]. GROUND WATER,2004,42(5):658-670.
[95] Deutsch, C.V. and Journel, A.G. GSLIB, Geostatistical Software Library and User's Guide[R]. NewYork: Oxford University Press,1992.
[96]蒋龙聪,刘江平.模拟退火算法及其改进[J].工程地球物理学报,2007,(02):135-140.
[97]史舟,李艳.地统计学在土壤学中的应用[M].北京:中国农业出版社,2006.
[98] Carle, S.F. Implementation Schemes for Avoiding Artifact Discontinuities in Simulated Annealing[J].Mathematical Geology,1997,29(2):231-244.
[99]吴立新,史文中, Gold, C.3D GIS与3D GMS中的空间构模技术[J].地理与地理信息科学,2003,(01):5-11.
[100]梁煦枫,王文科,曾永刚. GMS在水文地质结构可视化方面的应用[J].东北水利水电,2006,(09):64-67+72.
[101]梁煦枫,王哲,曾永刚.基于GMS的水文地质结构可视化研究——以天山北麓为例[J].地下水,2006,(06):79-82.
[102]谢轶,苏小四,高淑琴.基于GMS支持下的大庆地下水库区水文地质结构可视化模型[J].吉林大学学报(地球科学版),2006,(S1):51-54.
[103]陈刚,徐恒力,陈植华.多孔介质渗透系数的空间尺度效应研究进展[J].地质科技情报,1998,(S2):28-35.
[104] Rubin, Y. and Gomez-Hernandez, J.J. A stochastic approach to the problem of upscaling ofconductivity in disordered media: theory and unconditional numerical simulations[J]. WaterResources Research,1990,26(4):691-701.
[105]李竞生,姚磊华.遗传算法在反演三维地下水流模型参数中的应用[J].水文地质工程地质,2002,(05):7-11.
[106]魏连伟,邵景力,张建立,等.模拟退火算法反演水文地质参数算例研究[J].吉林大学学报(地球科学版),2004,(04):612-616.
[107]王佩,朱国荣,江思珉.水文地质参数识别的连续禁忌搜索改进算法[J].水文地质工程地质,2010,37(06):17-21.
[108]陆乐,吴吉春,陈景雅.基于贝叶斯方法的水文地质参数识别[J].水文地质工程地质,2008,(05):58-63.
[109]张俊艳,魏连伟,韩文秀,等.基于RBF神经网络的水文地质参数识别[J].中国工程科学,2004,(08):74-78.
[110]魏连伟,韩文秀,张俊艳,等.基于模拟退火遗传算法的水文地质参数识别[J].天津大学学报,2003,(05):618-621.
[111] Bachu, S. and Cuthiell, D. Effects of core-scale heterogeneity on steady state and transient fluidflow in porous media: numerical analysis[J]. Water Resources Research,1990,26(5):863-74.
[112] Desbarats, A.J. Numerical estimation of effective permeability in sand-shale formations[J]. WaterResources Research,1987,23(2):273-86.
[113]漆力健,廖华胜,苏沛兰.各向异性渗流数值计算中的旋转控制体积法[J].四川大学学报(工程科学版),2008(01):10-15.
[114] Li, S.G. and Liu, Q. Interactive Ground Water (IGW)[J]. Environmental Modelling&Software,2006,21(3):417-418.
[115] Li, S.G. and Liu, Q. Interactive groundwater (IGW): An innovative digital laboratory forgroundwater education and research[J]. Computer Applications in Engineering Education,2004,11(4):179-202.
[2]中国地下水科学战略研究小组.中国地下水科学的机遇与挑战[M].北京:科学出版社,2009.
[3] Wu, Q., Liu, Y.Z., Liu, D.H., et al. Prediction of Floor Water Inrush: The Application of GIS-BasedAHP Vulnerable Index Method to Donghuantuo Coal Mine, China[J]. Rock Mechanics and RockEngineering,2011,44(5):591-600.
[4] Wang, Y., Yang, W.F., Li, M., et al. Risk assessment of floor water inrush in coal mines based onsecondary fuzzy comprehensive evaluation[J]. International Journal of Rock Mechanics andMining Sciences,2012,52:50-55.
[5] Wu, Q., Xu, H., and Pang, W. GIS and ANN coupling model: an innovative approach to evaluatevulnerability of karst water inrush in coalmines of north China[J]. Environmental Geology,2008,54(5):937-943.
[6] Bonacci, O. and Roje-Bonacci, T. Water losses from the Ricice reservoir built in the Dinaric karst[J].Engineering Geology,2008,99(3-4):121-127.
[7] Garcia-Lopez, S., Benavente, J., Cruz-Sanjulian, J.J., et al. Conjunctive use of water resources as analternative to a leaky reservoir in a mountainous, semiarid area (Adra River basin, SE Spain)[J].Hydrogeology Journal,2009,17(7):1779-1790.
[8] Farhadian, H., Aalianvari, A., and Katibeh, H. Optimization of analytical equations of groundwaterseepage into tunnels: A case study of Amirkabir tunnel[J]. Journal of the Geological Society ofIndia,2012,80(1):96-100.
[9] Li, X.B., Zhang, W., Li, D.Y., et al. Influence of underground water seepage flow on surrounding rockdeformation of multi-arch tunnel[J]. Journal of Central South University of Technology,2008,15(1):69-74.
[10] Xu, Y.S., Ma, L., Du, Y.J., et al. Analysis of urbanisation-induced land subsidence in Shanghai[J].Natural Hazards,2012,63(2):1255-1267.
[11] Tang, Y.Q., Ren, X.W., Chen, B., et al. Study on land subsidence under different plot ratios throughcentrifuge model test in soft-soil territory[J]. Environmental Earth Sciences,2012,66(7):1809-1816.
[12] Chalupova, D., Havlikova, P., and Jansky, B. Water quality of selected fluvial lakes in the context ofthe Elbe River pollution and anthropogenic activities in the flood plain[J]. EnvironmentalMonitoring and Assessment,2012,184(10):6283-6295.
[13] Qian, J.Z., Zhan, H.B., Wu, J.F., et al. What can be learned from sequential multi-well pumping testsin fracture-karst media? A case study in Zhangji, China[J]. Hydrogeology Journal,2009,17(7):1749-1760.
[14]廖华胜,李连侠, LI, S.G.地下水非平稳随机模型及空间变异性与非均匀性相互关系研究的展望[J].水利学报,2004,(10):13-21.
[15]肖朝明,张征,鞠硕华,等.水环境模拟中多孔介质场空间变异性研究方法述评[J].安全与环境学报,2004,(03):88-92.
[16] Chang, C.M. and Yeh, H.D. Nonstationary stochastic analysis of flow in a heterogeneous unconfinedaquifer subject to spatially-random periodic recharge[J]. Journal of Hydrology,2010,395(3-4):163-168.
[17]薛禹群,叶淑君,谢春红,等.多尺度有限元法在地下水模拟中的应用[J].水利学报,2004,(07):7-13.
[18] Li, S.G., Liu, Q., and Afshari, S. An object-oriented hierarchical patch dynamics paradigm (HPDP)for modeling complex groundwater systems across multiple-scales[J]. Environmental Modelling&Software,2006,21(5):744-749.
[19] Afshari, S., Mandle, R., and Li, S.G. Hierarchical patch dynamics modeling of near-well dynamics incomplex regional groundwater systems[J]. Journal of Hydrologic Engineering,2008,13(9):894-904.
[20] He, X.G. and Ren, L. Finite volume multiscale finite element method for solving the groundwaterflow problems in heterogeneous porous media[J]. Water Resources Research,2005,41(10):W10417.
[21] Shi, L.S., Yang, J.Z., and Zeng, L.Z. Application of multiscale finite element method in theuncertainty qualification of large-scale groundwater flow[J]. Stochastic Environmental Researchand Risk Assessment,2012,26(3):393-404.
[22] Gelhar, L.W. ed. Stochastic subsurface hydrology[M]. Prentice Hall: Englewood cliffs,1993.
[23]杨金忠,蔡树英,黄冠华,等.多孔介质中水分及溶质运移的随机理论[M].北京:科学出版社,2000.
[24] Bakr, A.A., Gelhar, L.W., Gutjahr, A.L., et al. Stochastic analysis of spatial variability in subsurfaceflows. I. Comparison of one-and three-dimensional flows[J]. Water Resources Research,1978,14(2):263-71.
[25] Hoeksema, R.J. and Kitanidis, P.K. Analysis of the spatial structure of properties of selectedaquifers[J]. Water Resources Research,1985,21(4):563-72.
[26] Feinerman, E., Dagan, G., and Bresler, E. Statistical inference of spatial random functionshydrology[J]. Water Resources Research,1986,22(6):935-42.
[27] Gelhar, L.W. Stochastic subsurface hydrology from theory to applications[J]. Water ResourcesResearch,1986,22(9):135S-45S.
[28] Dagan, G. Time-dependent macrodispersion for solute transport in anisotropic heterogeneousaquifers[J]. Water Resources Research,1988,24(9):1491-15001500.
[29] Neuman, S.P. Universal scaling of hydraulic conductivities and dispersivities in geologic media[J].Water Resources Research,1990,26(8):1749-58.
[30] Molz, F.J. and Boman, G.K. Further evidence of fractal structure in hydraulic conductivitydistributions[J]. Geophysical Research Letters,1995,22(18):2545-8
[31] Molz, F.J., Rajaram, H., and Lu, S.L. Stochastic fractal-based models of heterogeneity in subsurfacehydrology: Origins, applications, limitations, and future research questions[J]. Reviews ofGeophysics,2004,42(1): RG1002.
[32] Li, S.G. and McLaughlin, D. A nonstationary spectral method for solving stochastic groundwaterproblems: unconditional analysis[J]. Water Resources Research,1991,27(7):1589-605.
[33] Li, S.G. and McLaughlin, D. Using the Nonstationary Spectral Method to Analyze Flow ThroughHeterogeneous Trending Media[J]. Water Resources Research,1995,31(3):541-551.
[34] Li, S.G., McLaughlin, D., and Liao, H.S. A computationally practical method for stochasticgroundwater modeling[J]. Advances in Water Resources,2003,26(11):1137-1148.
[35] Li, S.G., Liao, H.S., and Ni, C.F. Stochastic modeling of complex nonstationary groundwatersystems[J]. Advances in Water Resources,2004,27(11):1087-1104.
[36] Chang, C.M. and Yeh, H.D. Using the nonstationary spectral method to analyze asymptoticmacrodispersion in uniformly recharged heterogeneous aquifers[J]. Journal of Hydrology,2008,350(1-2):93-99.
[37] Ni, C.F., Li, S.G., Liu, C.J., et al. Efficient conceptual framework to quantify flow uncertainty inlarge-scale, highly nonstationary groundwater systems[J]. Journal of Hydrology,2010,381(3-4):297-307.
[38] Ni, C.F., Lin, C.P., Li, S.G., et al. Efficient approximate spectral method to delineate stochastic wellcapture zones in nonstationary groundwater flow systems[J]. Journal of Hydrology,2011,407(1-4):184-195.
[39] Ni, C.F., Lin, C.P., Li, S.G., et al. Quantifying flow and remediation zone uncertainties for partiallyopened wells in heterogeneous aquifers[J]. Hydrology and Earth System Sciences,2011,15(7):2291-2301.
[40] Wu, J.C., Hu, B.X., and Zhang, D.X. Applications of nonstationary stochastic theory to solutetransport in multi-scale geological media[J]. Journal of Hydrology,2003,275(3-4):208-228.
[41] Hu, B.X. Stochastic study of solute transport in a nonstationary medium[J]. Ground Water,2006,44(2):222-233.
[42] Wu, J.C. and Hu, B.X. Numerical method of moments for solute transport in a nonstationary flowfield conditioned on hydraulic conductivity and head measurements[J]. StochasticEnvironmental Research and Risk Assessment,2007,21(6):665-682.
[43] Dagan, G. Statistical Theory of Groundwater Flow and Transport: Pore to Laboratory, Laboratory toFormation, and Formation to Regional Scale[J]. Water Resources Research,1986,22(9):120S-134S.
[44] Dirk, S.M., Douglas A., C., Douglas S., C., et al. Scale dependency of hydraulic conductivity inheterogeneous media[J]. Ground Water,1999,37(6):904-919.
[45]何宗宜,胡胜华,阮依香,等.基于分形理论的水系要素制图综合研究[J].测绘科技情报,2001(Z2):26-31.
[46]樊硕,武文波,马明舟.基于分形理论的线状地物要素自动综合算法实现[J].测绘科学,2009(S1):97-98.
[47]李含璞.基于小波变换的DEM多尺度综合研究[D].兰州:兰州大学,2006.
[48]王明常,谷兰英,王宇,等.小波变换理论的线状要素制图综合研究[J].吉林大学学报(地球科学版),2005(S1):147-150.
[49]王家耀,邓红艳.基于遗传算法的制图综合模型研究[J].武汉大学学报(信息科学版),2005(07):565-569.
[50]王家耀,成毅.空间数据的多尺度特征与自动综合[J].海洋测绘,2004(04):1-3.
[51] Gomez, C. Multi-scale topographic analysis of Merbabu and Merapi volcanoes using waveletdecomposition[J]. Environmental Earth Sciences,2012,67(5):1423-1430.
[52] Guo, W.L., Yang, Q.K., Wang, H.J., et al. DEM multi-scale representation based on waveletmultiresolution analysis[J]. Journal of Food Agriculture&Environment,2012,10(3-4):1346-1349.
[53] Kalbermatten, M., Van De Ville, D., Turberg, P., et al. Multiscale analysis of geomorphological andgeological features in high resolution digital elevation models using the wavelet transform[J].Geomorphology,2012,138(1):352-363.
[54]于浩,杨勤科,张晓萍,等.基于小波多尺度分析的DEM数据综合研究[J].测绘科学,2008(03):93-95+115.
[55] Marseguerra, M., Patelli, E., and Zio, E. Groundwater contaminant transport in presence of colloids.I. A stochastic nonlinear model and parameter identification[J]. Annals of Nuclear Energy,2001,28(8):777-803.
[56] Carle, S. and Fogg, G. Transition probability-based indicator geostatistics[J]. Mathematical Geology,1996,28(4):453-476.
[57] Carle, S.F. T-PROGS: Transition Probability Geostatistical Software(Version2.1)[R]. HydrologicSciences Graduate Group, University of California, Davis,1999.
[58] Zhang, Y. and Fogg, G.E. Simulation of multi-scale heterogeneity of porous media and parametersensitivity analysis[J]. Science in China Series E-Technological Sciences,2003,46(5):459-474.
[59] Sivakumar, B., Halter, T., and Zhang, H. A fractal investigation of solute travel time in aheterogeneous aquifer: transition probability/Markov chain representation[J]. EcologicalModelling,2005,182(3-4):355-370.
[60] Rubin, Y., Lunt, I.A., and Bridge, J.S. Spatial variability in river sediments and its link with riverchannel geometry[J]. Water Resources Research,2006,42(6), W06D16, doi:10.1029/2005WR004853.
[61] Zhang, H., Harter, T., and Sivakumar, B. Nonpoint source solute transport normal to aquifer beddingin heterogeneous, Markov chain random fields[J]. Water Resources Research,2006,42(6),W06403, doi:10.1029/2004WR003808.
[62] Lee, S.Y., Carle, S.F., and Fogg, G.E. Geologic heterogeneity and a comparison of two geostatisticalmodels: Sequential Gaussian and transition probability-based geostatistical simulation[J].Advances in Water Resources,2007,30(9):1914-1932.
[63] He, Y., Hu, K.L., Li, B.G., et al. Comparison of Sequential Indicator Simulation and TransitionProbability Indicator Simulation Used to Model Clay Content in Microscale Surface Soil[J]. SoilScience,2009,174(7):395-402.
[64] Blessent, D., Therrien, R., and Lemieux, J.M. Inverse modeling of hydraulic tests in fracturedcrystalline rock based on a transition probability geostatistical approach[J]. Water ResourcesResearch,2011,47, doi:10.1029/2011WR011037.
[65] Engdahl, N.B., Vogler, E.T., and Weissmann, G.S. Evaluation of aquifer heterogeneity effects onriver flow loss using a transition probability framework[J]. Water Resources Research,2010,46,doi:10.1029/2009WR007903.
[66] Sakaki, T., Frippiat, C.C., Komatsu, M., et al. On the value of lithofacies data for improvinggroundwater flow model accuracy in a three-dimensional laboratory-scale synthetic aquifer[J].Water Resources Research,2009,45, doi:10.1029/2008WR007229.
[67]何芳,吴吉春.基于马尔可夫链的多元指示地质统计模型[J].水文地质工程地质,2003(05):28-32.
[68]王荣.华北平原地下水数值模拟研究[D].北京:中国地质大学（北京）,2006.
[69]董英.基于随机水文地质结构的华北平原地下水流模拟研究[D].北京:中国地质大学（北京）,2006.
[70]靳萍,邵景力,李长青,等.基于T-PROGS的地下水三维数值模拟及应用[J].水文地质工程地质,2009(04):21-26.
[71]郭飞,葛成,韩宇.嵌入式马尔可夫链的地质属性建模与应用[J].地理与地理信息科学,2012,(01):47-50.
[72] Weissmann, G.S., Carle, S.F., and Fogg, G.E. Three-dimensional hydrofacies modeling based on soilsurveys and transition probability geostatistics[J]. Water Resources Research,1999,35(6):1761–1770.
[73] Maji, R., Sudicky, E.A., Panday, S., et al. Transition probability/Markov chain analyses of DNAPLsource zones and plumes[J]. Ground Water,2006,44(6):853-863.
[74]李军,杨晓娟,张晓龙,等.基于三维马尔可夫链模型的岩性随机模拟[J].石油学报,2012(05):846-853.
[75] Hou, T.Y. and Xiao-Hui, W. A multiscale finite element method for elliptic problems in compositematerials and porous media[J]. Journal of Computational Physics,1997,134(1):169-89.
[76] Ye, S.J. and Wu, J.C. Application of the multiscale finite element method to3-D groundwater flow inheterogeneous porous media[J]. Geochimica Et Cosmochimica Acta,2004,68(11): A465-A465.
[77]蒋小伟.盆地含水系统与地下水流动系统特征[D].北京:中国地质大学(北京),2011.
[78]宫辉力,赵文吉,诸云强.裂隙-岩溶介质空间水流数值仿真与流场优化[J].系统仿真学报,2002,(02):186-188.
[79]吴呈懋.地下水系统孔隙介质尺度效应与异质性地层参数化方法之研究[D].台北:国立台湾大学,2006.
[80]姚磊华.非平稳随机地下水流模拟[J].煤炭学报,2000,(S1):16-21.
[81] Dettinger, M.D. and Wilson, J.L. First order analysis of uncertainty in numerical models ofgroundwater flow. I. Mathematical development[J]. Water Resources Research,1981,17(1):149-61.
[82]姚磊华.地下水水流模型的摄动待定系数随机有限元法[J].水利学报,1999(07):61-65.
[83]李连侠,廖华胜, and刘达.随机地下水非平稳谱方法[J].中国科技论文,2012(05):382-387+394.
[84] Li, S.G., McLaughlin, D., and Liao, H. The Accuracy of Stochastic Perturbation Solutions toSubsurfaceTransport Problems[J]. Advances in Water Resources,2004,27(1):47-56.
[85]孙蓉琳.玄武岩渗透系数尺度效应及顺序指示模拟[D].武汉:中国地质大学,2006.
[86]王家华.克里金地质绘图技术[M].北京:石油工业出版社,1990.
[87]周海燕.空间数据挖掘的研究[D].郑州:中国人民解放军信息工程大学,2003.
[88]李志林,朱庆.数字高程模型[M].武汉:武汉大学出版社,2003.
[89]王仁铎,胡光道.线性地质统计学[M].北京:地质出版社,1988.
[90]胡细宝,孙洪祥.概率论与随机过程[M].北京:北京邮电大学出版社,2001.
[91] Carle, S.F. and Fogg, G.E. Modeling Spatial Variability with One and MultidimensionalContinuous-Lag Markov Chains[J]. Mathematical Geology,1997,28(7):891-918.
[92] Walker, J.R. Application of Transition Probability Geostatistics for Indicator Simulations Involvingthe MODFLOW Model.2002, Provo: Brigham Young University.
[93]董英.基于随机水文地质结构的华北平原地下水流模拟研究[D].北京:中国地质大学(北京),2006.
[94] Proce, C.J., Ritzi, R.W., Dominic, D.F., et al. Modeling Multiscale Heterogeneity and AquiferInterconnectivity[J]. GROUND WATER,2004,42(5):658-670.
[95] Deutsch, C.V. and Journel, A.G. GSLIB, Geostatistical Software Library and User's Guide[R]. NewYork: Oxford University Press,1992.
[96]蒋龙聪,刘江平.模拟退火算法及其改进[J].工程地球物理学报,2007,(02):135-140.
[97]史舟,李艳.地统计学在土壤学中的应用[M].北京:中国农业出版社,2006.
[98] Carle, S.F. Implementation Schemes for Avoiding Artifact Discontinuities in Simulated Annealing[J].Mathematical Geology,1997,29(2):231-244.
[99]吴立新,史文中, Gold, C.3D GIS与3D GMS中的空间构模技术[J].地理与地理信息科学,2003,(01):5-11.
[100]梁煦枫,王文科,曾永刚. GMS在水文地质结构可视化方面的应用[J].东北水利水电,2006,(09):64-67+72.
[101]梁煦枫,王哲,曾永刚.基于GMS的水文地质结构可视化研究——以天山北麓为例[J].地下水,2006,(06):79-82.
[102]谢轶,苏小四,高淑琴.基于GMS支持下的大庆地下水库区水文地质结构可视化模型[J].吉林大学学报(地球科学版),2006,(S1):51-54.
[103]陈刚,徐恒力,陈植华.多孔介质渗透系数的空间尺度效应研究进展[J].地质科技情报,1998,(S2):28-35.
[104] Rubin, Y. and Gomez-Hernandez, J.J. A stochastic approach to the problem of upscaling ofconductivity in disordered media: theory and unconditional numerical simulations[J]. WaterResources Research,1990,26(4):691-701.
[105]李竞生,姚磊华.遗传算法在反演三维地下水流模型参数中的应用[J].水文地质工程地质,2002,(05):7-11.
[106]魏连伟,邵景力,张建立,等.模拟退火算法反演水文地质参数算例研究[J].吉林大学学报(地球科学版),2004,(04):612-616.
[107]王佩,朱国荣,江思珉.水文地质参数识别的连续禁忌搜索改进算法[J].水文地质工程地质,2010,37(06):17-21.
[108]陆乐,吴吉春,陈景雅.基于贝叶斯方法的水文地质参数识别[J].水文地质工程地质,2008,(05):58-63.
[109]张俊艳,魏连伟,韩文秀,等.基于RBF神经网络的水文地质参数识别[J].中国工程科学,2004,(08):74-78.
[110]魏连伟,韩文秀,张俊艳,等.基于模拟退火遗传算法的水文地质参数识别[J].天津大学学报,2003,(05):618-621.
[111] Bachu, S. and Cuthiell, D. Effects of core-scale heterogeneity on steady state and transient fluidflow in porous media: numerical analysis[J]. Water Resources Research,1990,26(5):863-74.
[112] Desbarats, A.J. Numerical estimation of effective permeability in sand-shale formations[J]. WaterResources Research,1987,23(2):273-86.
[113]漆力健,廖华胜,苏沛兰.各向异性渗流数值计算中的旋转控制体积法[J].四川大学学报(工程科学版),2008(01):10-15.
[114] Li, S.G. and Liu, Q. Interactive Ground Water (IGW)[J]. Environmental Modelling&Software,2006,21(3):417-418.
[115] Li, S.G. and Liu, Q. Interactive groundwater (IGW): An innovative digital laboratory forgroundwater education and research[J]. Computer Applications in Engineering Education,2004,11(4):179-202.