非均质含水层中渗流与溶质运移研究进展*

  • 覃荣高 ,
  • 曹广祝 ,
  • 仵彦卿
展开
  • 1.上海交通大学环境科学与工程学院, 上海 200240
    2.昆明理工大学国土资源与工程学院地球科学系, 云南 昆明 650093

覃荣高(1982-),男,广西来宾人,讲师,主要从事地下水污染物迁移模拟方面的研究. E-mail: qinronggao@126.com

收稿日期: 2013-08-05

  修回日期: 2013-11-12

  网络出版日期: 2014-01-10

基金资助

国家自然科学基金面上项目“非均质含水层中有机污染物迁移机理研究”(编号:41272261)资助.

Review of Study on Groundwater Flow and Solute Transport in Heterogeneous Aquifer

  • Ronggao Qin ,
  • Guangzhu Cao ,
  • Yanqing Wu
Expand
  • 1.School of Environmental Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
    2. Department of Earth Sciences, Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China
仵彦卿(1957-), 男, 陕西咸阳人, 教授, 主要从事地下水污染模拟与修复方面的研究. E-mail: wuyanqing@sjtu.edu.cn

Received date: 2013-08-05

  Revised date: 2013-11-12

  Online published: 2014-01-10

摘要

含水层的非均质性控制着地下水渗流和溶质迁移特性, 准确定量化描述非均质含水层中的渗流和溶质迁移问题受到广泛关注, 已成为地球科学领域中的研究热点。首先从非均质含水层地下水流和溶质迁移理论模型、矩分析、多尺度进行系统综述, 指出尺度转换在目前水文地质研究中主要解决的问题以及存在的问题;其次从非均质含水层场地试验、不确定性以及速度连通性等方面分析了该方向的研究进展;最后指出地球物理反演含水层非均质性、随机理论与随机模拟软件开发、尺度转换及速度连通性的不确定性问题、非均质性与水文地质条件关系研究4个方面是该领域今后的主要研究方向。

本文引用格式

覃荣高 , 曹广祝 , 仵彦卿 . 非均质含水层中渗流与溶质运移研究进展*[J]. 地球科学进展, 2014 , 29(1) : 30 -41 . DOI: 1001-8166(2014)01-0030-12

Abstract

Natural aquifer heterogeneity controls the groundwater flow and solute transport, and how to accurately quantify the flow and solute transport in heterogeneous aquifers has received wide attention by many scholars, and has become a hot research topic in earth science. Theoretically, a systematic review is given by the following aspect: flow and solute transport model, moment analysis, multiscale analysis. The resolved and remained issues for scale conversion in hydrogeology research are pointed out. Secondly, recent advances of heterogeneous field test, uncertainty and velocity connectivity are analyzed. Finally, the geophysical inversion of aquifer heterogeneity, stochastic theory and development of stochastic simulation software, scale conversion and uncertainty of velocity connectivity, and the relationship between heterogeneity and hydrogeological condition on the major four aspects of the future research direction is pointed out.

参考文献

[1] Qiu J. China faces up to groundwater crisis[J]. Nature, 2010, 466(7 304): 308.
[2] Zheng C, Liu J. China’ s “Love Canal” moment?[J]. Science, 2013, 340(6 134): 810.
[3] Freeze R A. A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media[J]. Water Resources Research, 1975, 11(5): 725-741.
[4] Dagan G. Stochastic modeling of groundwater flow by unconditional and conditional probabilities. II. The solute transport[J]. Water Resources Research, 1982, 18(4): 835-848.
[5] Dagan G. Solute transport in heterogeneous porous formations[J]. Journal of Fluid Mechanics, 1984, 145: 151-177.
[6] Gelhar L W, Axness C L. Three-dimensional stochastic analysis of macrodispersion in aquifers[J]. Water Resources Research, 1983, 19(1): 161-180.
[7] Molz F J, Rajaram H, Lu S L. Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions[J]. Reviews of Geophysics, 2004, 42(1): RG1002, doi:10.1029/2003RG000126.
[8] Berkowitz B, Scher H, Silliman S E. Anomalous transport in laboratory-scale, heterogeneous porous media[J]. Water Resources Research, 2000, 36(1): 149-158.
[9] Cushman J H, Ginn T R. Fractional advection-dispersion equation: A classical mass balance with convolution-Fickian flux[J]. Water Resources Research, 2000, 36(12): 3 763-3 766.
[10] Benson D A, Schumer R, Meerschaert M M, et al. Fractional dispersion, levy motion, and the MADE tracer tests[J]. Transport in Porous Media, 2001, 42(1/2): 211-240.
[11] Rubin S, Dror I, Berkowitz B. Experimental and modeling analysis of coupled non-Fickian transport and sorption in natural soils[J]. Journal of Contaminant Hydrology, 2012, 132: 28-36.
[12] Cortis A, Gallo C, Scher H, et al. Numerical simulation of non-Fickian transport in geological formations with multiple-scale heterogeneities[J]. Water Resources Research, 2004, 40(4): w04209, doi:10.1029/2003WR002750.
[13] Berkowitz B, Cortis A, Dentz M, et al. Modeling non-Fickian transport in geological formations as a continuous time random walk[J]. Reviews of Geophysics, 2006, 44(2): RG2003, doi:10.1029/2005RG000178.
[14] Neuman S P, Tartakovsky D M. Perspective on theories of non-Fickian transport in heterogeneous media[J]. Advances in Water Resources, 2009, 32(5): 670-680.
[15] Li T Y, Yorke J A. Period three implies chaos[J]. The American Mathematical Monthly, 1975, 82(10): 985-992.
[16] Tel T, Karolyi G, Pentek A, et al. Chaotic advection, diffusion, and reactions in open flows[J]. Chaos, 2000, 10(1): 89-98.
[17] Sposito G. Chaotic solute advection by unsteady groundwater flow[J]. Water Resources Research, 2006, 44(6): W06D03, doi:10.1029/2005WR004518.
[18] Mays D C, Neupauer R M. Plume spreading in groundwater by stretching and folding[J]. Water Resources Research, 2012, 48(7), doi: 10.1029/2011WRO11567.
[19] Trefry M G, Lester D R, Metcalfe G, et al. Toward enhanced subsurface intervention methods using chaotic advection[J]. Journal of Contaminant Hydrology, 2012, 127(1/4): 15-29.
[20] Lester D R, Trefry M G, Metcalfe G, et al. Comment on “Plume spreading in groundwater by stretching and folding” by D. C. Mays and R. M. Neupauer[J]. Water Resources Research, 2013, 49(2): 1 189-1 191.
[21] Mays D C, Neupauer R M. Reply to comment by D. R. Lesteret al. on “Plume spreading in groundwater by stretching and folding”[J]. Water Resources Research, 2013, 49(2): 1 192-1 194.
[22] Aris R. On the dispersion of a solute in a fluid flowing through a tube[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1956, 235(1 200): 67-77.
[23] Freyberg D L. A natural gradient experiment on solute transport in a sand aquifer. II. Spatial moments and the advection and dispersion of nonreactive tracers[J]. Water Resources Research, 1986, 22(13): 2031-2046.
[24] Roberts P V, Goltz M N, Mackay D M. A natural gradient experiment on solute transport in a sand aquifer. III. Retardation estimates and mass balances for organic solutes[J]. Water Resources Research, 1986, 22(13): 2047-2058.
[25] Sudicky E A. A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process[J]. Water Resources Research, 1986, 22(13): 2069-2082.
[26] Garabedian S P, LeBlanc D R, Gelhar L W, et al. Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts. 2. Analysis of spatial moments for a nonreactive tracer[J]. Water Resources Research, 1991, 27(5): 911-924.
[27] LeBlanc D R, Garabedian S P, Hess K M, et al. Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts. I. Experimental design and observed tracer movement[J]. Water Resources Research, 1991, 27(5): 895-910.
[28] Goltz M N, Roberts P V. Using the method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives[J]. Water Resources Research, 1987, 23(8): 1 575-1 585.
[29] Govindaraju R S, Das B S. Moment Analysis for Subsurface Hydrologic Applications[M]. London: Springer, 2007.
[30] Dagan G. Statistical theory of groundwater flow and transport pore to laboratory, laboratory to formation, and formation to regional scale[J]. Water Resources Research, 1986, 22(9): 120S-134S.
[31] Koltermann C E, Gorelick S M. Heterogeneity in sedimentary deposits: A review of structure-imitating, process-imitating, and descriptive approaches[J]. Water Resources Research, 1996, 32(9): 2617-2658.
[32] Dentz M, Le Borgne T, Englert A, et al. Mixing, spreading and reaction in heterogeneous media: A brief review[J]. Journal of Contaminant Hydrology, 2011, 120/121: 1-17.
[33] Indelman P, Dagan G. Upscaling of permeability of anisotropic heterogeneous formations: 1. The general framework[J]. Water Resources Research, 1993, 29(4): 917-923.
[34] Wen X H, Gómez-Hernández J J. Upscaling hydraulic conductivities in heterogeneous media: An overview[J]. Journal of Hydrology, 1996, 183(1/2), doi:10.1016/0022-1694(96)03111-3.
[35] Painter S, Cvetkovic V. Upscaling discrete fracture network simulations: An alternative to continuum transport models[J]. Water Resources Research, 2005, 41(2): 1-10.
[36] Gomez-Hernandez J J, Fu J L, Fernandez-Garcia D. Upscaling retardation factors in 2-D porous media[J]. Calibration and Reliability in Groundwater Modelling: From Uncertainty to Decision Making, 2006, 304: 130-136.
[37] Fernndez-Garcia D, Gómez-Hernndez J J. Impact of upscaling on solute transport: Traveltimes, scale dependence of dispersivity, and propagation of uncertainty[J]. Water Resources Research, 2007, 43(2): W02423, doi:10.1029/2005WR004727.
[38] Fernandez-Garcia D, Llerar-Meza G, Gomez-Hernandez J J. Upscaling transport with mass transfer models: Mean behavior and propagation of uncertainty[J]. Water Resources Research, 2009, 45: W10411, doi:10.1029/2009WR007764.
[39] Fiori A, Dagan G, Jankovic I. Upscaling of steady flow in three-dimensional highly heterogeneous formations[J]. Multiscale Modeling & Simulation, 2011, 9(3): 1 162-1 180.
[40] Li L, Zhou H, Gómez-Hernndez J J. Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media[J]. Advances in Water Resources, 2011, 34(4): 478-489.
[41] Frippiat C, Holeyman A. A comparative review of upscaling methods for solute transport in heterogeneous porous media[J]. Journal of Hydrology, 2008, 362(1/2): 150-176.
[42] Dagan G, Fiori A, Jankovic I. Upscaling of flow in heterogeneous porous formations: Critical examination and issues of principle[J]. Advances in Water Resources, 2013, 51: 67-85.
[43] Mackay D M, Freyberg D L, Roberts P V, et al. A natural gradient experiment on solute transport in a sand aquifer. I. Approach and overview of plume movement[J]. Water Resources Research, 1986, 22(13): 2 017-2 029.
[44] Curtis G P, Roberts P V, Reinhard M. A natural gradient experiment on solute transport in a sand aquifer. IV. Sorption of organic solutes and its influence on mobility[J]. Water Resources Research, 1986, 22(13), doi:10.1029/WR022i013p02017.
[45] Hess K M, Wolf S H, Celia M A. Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts. 3. Hydraulic conductivity variability and calculated macrodispersivities[J]. Water Resources Research, 1992, 28(8): 2 011-2 027.
[46] Boggs J M, Young S C, Beard L M, et al. Field study of dispersion in a heterogeneous aquifer: 1. Overview and site description[J]. Water Resources Research, 1992, 28(12): 3 281-3 291.
[47] Adams E E, Gelhar L W. Field study of dispersion in a heterogeneous aquifer, 2. Spatial moments analysis[J]. Water Resources Research, 1992, 28(12): 3 293-3 307.
[48] Rehfeldt K R, Boggs J M, Gelhar L W. Field study of dispersion in a heterogeneous aquifer: 3. Geostatistical analysis of hydraulic conductivity[J]. Water Resources Research, 1992, 28(12): 3309-3324.
[49] Boggs J M, Adams E E. Field study of dispersion in a heterogeneous aquifer: 4. Investigation of adsorption and sampling bias[J]. Water Resources Research, 1992, 28(12): 3325-3336.
[50] Vereecken H, Dring U, Hardelauf H, et al. Analysis of solute transport in a heterogeneous aquifer: The Krauthausen field experiment[J]. Journal of Contaminant Hydrology, 2000, 45(3/4): 329-358.
[51] Vereecken H, Kemna A, Tillmann A, et al. Hydrogeophysical Characterization of Subsurface Solute Transport at the Krauthausen Test Site: Experiments and Numerical Modelling[M]. Berlin:Spring, 2005.
[52] Vanderborght J, Vereecken H. Analyses of locally measured bromide breakthrough curves from a natural gradient tracer experiment at Krauthausen[J]. Journal of Contaminant Hydrology, 2001, 48(1/2): 23-43.
[53] Feehley C E, Zheng C, Molz F J. A dual-domain mass transfer approach for modeling solute transport in heterogeneous aquifers: Application to the Macrodispersion Experiment (MADE) site[J]. Water Resources Research, 2000, 36(9): 2 501-2 515.
[54] Zheng C, Bianchi M, Gorelick S M. Lessons learned from 25 years of research at the MADE site[J]. Ground Water, 2011, 49(5): 649-662.
[55] Liu G, Zheng C, Gorelick S M. Limits of applicability of the advection-dispersion model in aquifers containing connected high-conductivity channels[J]. Water Resources Research, 2004, 40(8): W08308, doi:10.1029/2003WR002735.
[56] Liu G S, Chen Y, Zhang D X. Investigation of flow and transport processes at the MADE site using ensemble Kalman filter[J]. Advances in Water Resources, 2008, 31(7): 975-986.
[57] Sudicky E A, Illman W A, Goltz I K, et al. Heterogeneity in hydraulic conductivity and its role on the macroscale transport of a solute plume: From measurements to a practical application of stochastic flow and transport theory[J]. Water Resources Research, 2010, 46: W01508, doi:10.1029/2008WR007558.
[58] Refsgaard J C, Christensen S, Sonnenborg T O, et al. Review of strategies for handling geological uncertainty in groundwater flow and transport modeling[J]. Advances in Water Resources, 2012, 36: 36-50.
[59] Carle S F, Fogg G E. Transition probability-based indicator geostatistics[J]. Mathematical Geology, 1996, 28(4): 453-476.
[60] Zhang Tuanfeng, Caers J.Multiple-point geostatistics: A quantitative vehicle for integrating geologic analogs into multiple reservoir models[M]∥Michael Grammer G, Paul M, Eberli G P, eds.Integration of Outcrop and Modern Analogs in Reservoir Modeling: AAPG Memoir 80. Oklahoma:American Association of Petroleum Geologists, 2004.
[61] Zhang Y, Person M, Paola C, et al. Geostatistical analysis of an experimental stratigraphy[J]. Water Resources Research, 2005, 41(11): W11416, doi:10.1029/2004WR003756.
[62] Lee S Y, Carle S F, Fogg G E. Geologic heterogeneity and a comparison of two geostatistical models: Sequential gaussian and transition probability-based geostatistical simulation[J]. Advances in Water Resources, 2007, 30(9): 1 914-1 932.
[63] Hu L Y, Chugunova T. Multiple-point geostatistics for modeling subsurface heterogeneity: A comprehensive review[J]. Water Resources Research, 2008, 44(11): W11413, doi:10.1029/2008WR006993.
[64] Huysmans M, Dassargues A. Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)[J]. Hydrogeology Journal, 2009, 17(8): 1 901-1 911.
[65] Huysmans M, Dassargues A. Modeling the effect of clay drapes on pumping test response in a cross-bedded aquifer using multiple-point geostatistics[J]. Journal of Hydrology, 2012, 450/451: 159-167.
[66] Mariethoz G, Renard P, Straubhaar J. The direct sampling method to perform multiple-point geostatistical simulations[J]. Water Resources Research, 2010, 46: W11536, doi:10.1029/2008WR007621.
[67] Comunian A, Renard P, Straubhaar J. 3D multiple-point statistics simulation using 2D training images[J]. Computers & Geosciences, 2012, 40: 49-65.
[68] Neuman S P, Wierenga P J. A Comprehensive Strategy of Hydrogeologic Modeling and Uncertainty Analysis for Nuclear Facilities and Sites [Electronic Resource] Prepared by S.P. Neuman and P.J. Wierenga[M]. Washington DC: Division of Systems Analysis and Regulatory Effectiveness, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 2003.
[69] Dagan G, Neuman S P. Subsurface Flow and Transport: A Stochastic Approach[M]. Cambridge:Cambridge University Press, 2005.
[70] Rubin Y. Applied Stochastic Hydrogeology[M]. New York: Oxford University Press, 2003.
[71] Li H, Zhang D. Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods[J]. Water Resources Research, 2007, 43(9): W09409, doi:10.1029/2006WR005673.
[72] Graham W, McLaughlin D. Stochastic analysis of nonstationary subsurface solute transport: 2. Conditional moments[J]. Water Resources Research, 1989, 25(11): 2 331-2 355.
[73] Graham W, McLaughlin D. Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments[J]. Water Resources Research, 1989, 25(2): 215-232.
[74] Zhang D X, Lu Z M. An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loeve and polynomial expansions[J]. Journal of Computational Physics, 2004, 194(2): 773-794.
[75] Yang J, Zhang D, Lu Z. Stochastic analysis of saturated-unsaturated flow in heterogeneous media by combining Karhunen-Loeve expansion and perturbation method[J]. Journal of Hydrology, 2004, 294(1/3): 18-38.
[76] Liu G, Lu Z, Zhang D. Stochastic uncertainty analysis for solute transport in randomly heterogeneous media using a Karhunen-Loève-based moment equation approach[J]. Water Resources Research, 2007, 43(7): W07427, doi:10.1029/2003WR005193.
[77] Diggle P, Lophaven S. Bayesian geostatistical design[J]. Scandinavian Journal of Statistics, 2006, 33(1): 53-64.
[78] Nowak W, de Barros F P J, Rubin Y. Bayesian geostatistical design: Task-driven optimal site investigation when the geostatistical model is uncertain[J]. Water Resources Research, 2010, 46(3): W03535, doi:10.1029/2009WR008312.
[79] Werth C J, Cirpka O A, Grathwohl P. Enhanced mixing and reaction through flow focusing in heterogeneous porous media[J]. Water Resources Research, 2006, 42(12): W12414, doi:10.1029/2005WR004511.
[80] Rubin Y, Gómez-Hernández J J. A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations[J]. Water Resources Research, 1990, 26(4): 691-701.
[81] Zhang D, Shi L, Chang H, et al. A comparative study of numerical approaches to risk assessment of contaminant transport[J]. Stochastic Environmental Research and Risk Assessment, 2010, 24(7): 971-984.
[82] Neuman S P. Blueprint for perturbative solution of flow and transport in strongly heterogeneous composite media using fractal and variational multiscale decomposition[J]. Water Resources Research, 2006, 42(6): W06D04, doi:10.1029/2005WR004315.
[83] Fernndez-Garcia D, Snchez-Vila X, Guadagnini A. Reaction rates and effective parameters in stratified aquifers[J]. Advances in Water Resources, 2008, 31(10): 1 364-1 376.
[84] Salamon P, Fernandez-Garcia D, Gomez-Hernandez J J. A review and numerical assessment of the random walk particle tracking method[J]. Journal of Contaminant Hydrology, 2006, 87(3/4): 277-305.
[85] Chunmiao Z. MT3DMS v5.3 A Modular Three-dimensional Multispecies Transport Model for Simulation of Advection, Dispersion Chemical Reactions of Contaminants in Groundwater Systems. Supplemental User’s Guide [Z]. Department of Geological Sciences The University of Alabama Tuscaloosa, Alabama 35487, 2010.
[86] Boso F, Bellin A, Dumbser M. Numerical simulations of solute transport in highly heterogeneous formations: A comparison of alternative numerical schemes[J]. Advances in Water Resources, 2013, 52: 178-189.
[87] Harbaugh A W, Banta E R, Hill M C, et al. MODFLOW-2000, the U.S. Geological Survey Modular Ground-water Model—User Guide to Modularization Concepts and the Ground-Water Flow Process: U.S. Geological Survey Open-File Report 00-92, 121 p. [Z]. 2000: 83-875.
[88] Trefry M G, Muffels C. FEFLOW: A finite-element ground water flow and transport modeling tool[J]. Ground Water, 2007, 45(5): 525-528.
[89] Therrien R R G, McLaren E A, Panday S M. HydroGeoSphere A Three-dimensional Numerical Model Describing Fully-integrated Subsurface and Surface Flow and Solute Transportp[M]. Waterloo, Canada: Groundwater Simulations Group, University of Waterloo, 2012.
[90] Graf T, Therrien R. A test case for the simulation of three-dimensional variable-density flow and solute transport in discretely-fractured porous media[J]. Advances in Water Resources, 2008, 31(10): 1 352-1 363.
[91] Chen Y, Smith L, Beckie R. Modeling of strategies for performance monitoring of groundwater contamination at sites underlain by fractured bedrock[J]. Journal of Contaminant Hydrology, 2012, 134/135: 37-53.
[92] The ParFlow Project Modeling Surface Subsurface Flow on High Performance Computers[Z/OL].[2013-01-20].
[93] Ashby S F, Falgout R D. A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations[J]. Nuclear Science and Engineering, 1996, 124(1): 145-159.
[94] Jones J E, Woodward C S. Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems[J]. Advances in Water Resources, 2001, 24(7): 763-774.
[95] Li S G, Liu Q. Interactive Ground Water (IGW): An innovative digital laboratory for groundwater education and research[J]. Computer Applications in Engineering Education, 2003, 11(4): 179-202.
[96] Li S G, Liu Q. Interactive Ground Water (IGW)[J]. Environmental Modelling & Software, 2006, 21(3): 417-418.
[97] Li S G, Liu Q, 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.
[98] Ni C F, Li S G, Liu C J, et al. Efficient conceptual framework to quantify flow uncertainty in large-scale, highly nonstationary groundwater systems[J]. Journal of Hydrology, 2010, 381(3/4): 297-307.
[99] Renard P, Allard D. Connectivity metrics for subsurface flow and transport[J]. Advances in Water Resources, 2013, 51: 168-196.
100 Knudby C, Carrera J. On the relationship between indicators of geostatistical, flow and transport connectivity[J]. Advances in Water Resources, 2005, 28(4): 405-421.
101 Vassena C, Cattaneo L, Giudici M. Assessment of the role of facies heterogeneity at the fine scale by numerical transport experiments and connectivity indicators[J]. Hydrogeology Journal, 2010, 18(3): 651-668.
102 Bianchi M, Zheng C, Wilson C, et al. Spatial connectivity in a highly heterogeneous aquifer: From cores to preferential flow paths[J]. Water Resources Research, 2011, 47: W05524, doi:10.1029/2009WR008966.
103 Zinn B, Harvey C F. When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields[J]. Water Resources Research, 2003, 39(3), doi:10.1029/2001WR001146.
104 Revil A, Karaoulis M, Johnson T, et al. Review: Some low-frequency electrical methods for subsurface characterization and monitoring in hydrogeology[J]. Hydrogeology Journal, 2012, 20(4): 617-658.
105 Pollock D, Cirpka O A. Fully coupled hydrogeophysical inversion of a laboratory salt tracer experiment monitored by electrical resistivity tomography[J]. Water Resources Research, 2012, 48: W01505, doi:10.1029/2011WR010779.
文章导航

/