none 10.1190/1.3496001 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 46221855 5981 2025121114342792500 10.1190 2025-12-11T19:34:42Z 2010-12-28T18:34:52Z 17 Geophysics 1942-2156 0016-8033 11 2010 01 01 2010 75 6 Majken C. Looms 1University of Copenhagen, Department of Geography and Geology, Copenhagen, Denmark. E-mail: mcl@geo.ku.dk; ln@geo.ku.dk; khj@geo.ku.dk. Thomas M. Hansen 2Formerly University of Copenhagen; presently Technical University of Denmark, Center for Energy Resources Engineering, Lyngby, Denmark. E-mail: thomas.mejer.hansen@gmail.com. Knud S. Cordua 2Formerly University of Copenhagen; presently Technical University of Denmark, Center for Energy Resources Engineering, Lyngby, Denmark. E-mail: thomas.mejer.hansen@gmail.com. Lars Nielsen 1University of Copenhagen, Department of Geography and Geology, Copenhagen, Denmark. E-mail: mcl@geo.ku.dk; ln@geo.ku.dk; khj@geo.ku.dk. Karsten H. Jensen 1University of Copenhagen, Department of Geography and Geology, Copenhagen, Denmark. E-mail: mcl@geo.ku.dk; ln@geo.ku.dk; khj@geo.ku.dk. Andrew Binley 3Lancaster University, Lancaster Environment Centre, Lancaster, U. K. E-mail: a.binley@lancaster.ac.uk. Abstract High-resolution tomographic images obtained from crosshole geophysical measurements have the potential to provide valuable information about the geostatistical properties of unsaturated-zone hydrologic-state variables such as moisture content. Under drained or quasi-steady-state conditions, the moisture content will reflect the variation of the physical properties of the subsurface, which determine the flow patterns in the unsaturated zone. Deterministic least-squares inversion of crosshole ground-penetrating-radar (GPR) traveltimes result in smooth, minimum-variance estimates of the subsurface radar wave velocity structure, which may diminish the utility of these images for geostatistical inference. We have used a linearized stochastic inversion technique to infer the geostatistical properties of the subsurface radar wave velocity distribution using crosshole GPR traveltimes directly. Expanding on a previous study, we have determined that it is possible to obtain estimates of global variance andmean velocity values of the subsurface as well as the correlation lengths describing the subsurface velocity structures. Accurate estimation of the global variance is crucial if stochastic realizations of the subsurface are used to evaluate the uncertainty of the inversion estimate. We have explored the full potential of the geostatistical inference method using several synthetic models of varying correlation structures and have tested the influence of different assumptions concerning the choice of covariance function and data noise level. In addition, we have tested the methodology on traveltime data collected at a field site in Denmark. There, inferred correlation structures indicate that structural differences exist between two areas located approximately 10 m apart, an observation confirmed by a GPR reflection profile. Furthermore, the inferred values of the subsurface global variance and the mean velocity have been corroborated with moisture-content measurements, obtained gravimetrically from samples collected at the field site. 11 2010 01 01 2010 10 29 2010 J29 J41 10.1190/1.3496001 https://pubs.geoscienceworld.org/geophysics/article/75/6/J29/299325/Geostatistical-inference-using-crosshole-ground https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/75/6/J29/3226550/gsgpy_75_6_J29.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/75/6/J29/3226550/gsgpy_75_6_J29.pdf http://geophysics.geoscienceworld.org/cgi/doi/10.1190/1.3496001 Water Resources Research Alumbaugh 38 1309 2002 10.1029/2001WR000754 Estimating moisture contents in the vadose zone using cross-borehole ground penetrating radar: A study of accuracy and repeatability GPR methods for hydrogeological studies Annan 129 2005 Hydrogeophysics 6th International Geostatistics Congress Asli 64 2000 Direct inversion of gravity data by cokriging Characterization of heterogeneity in unsaturated sandstone using borehole logs and cross-borehole tomography Binley 129 2004 Aquifer characterization Water Resources Research Binley 37 2639 2001 10.1029/2000WR000089 High-resolution characterization of vadose zone dynamics using cross-bore-hole radar Geophysics Constable 52 289 1987 10.1190/1.1442303 Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data Vadose Zone Journal Cordua 7 1 263 2008 10.2136/vzj2007.0008 Accounting for correlated data errors during inversion of cross-borehole ground penetrating radar data Journal of Applied Geophysics Cordua 68 1 71 2009 10.1016/j.jappgeo.2008.12.002 Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data Water Resources Research Dafflon 45 9 W09407 2009 10.1029/2008WR007646 Use of high-resolution geophysical data to characterize heterogeneous aquifers: Influence of data integration method on hydrological predictions Geophysical Prospecting Davis 37 5 531 1989 10.1111/j.1365-2478.1989.tb02221.x Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy Geophysical Research Letters Day-Lewis 31 7 L07503 2004 10.1029/2004GL019617 Assessing the resolution-dependent utility of tomograms for geostatistics Journal of Geophysical Research Day-Lewis 110 B8 B08206 2005 10.1029/2004JB003569 Applying petrophysical models to radar travel time and electrical resistivity tomograms: Resolution-dependent limitations Water Resources Research Eppstein 34 1889 1998 10.1029/98WR00776 Efficient three-dimensional data inversion: Soil characterization and moisture monitoring from cross-well ground penetrating radar at a Vermont test site Geophysics Ernst 72 5 J53 2007 10.1190/1.2761848 Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data Near Surface Geophysics Ernst 4 1 19 2006 10.3997/1873-0604.2005028 Realistic FDTD modelling of borehole georadar antenna radiation: Methodology and application Water Resources Research Ferré 32 2 271 1996 10.1029/95WR02576 Spatial averaging of water content by time domain reflectometry: Implications for twin rod probes with and without dielectric coatings Computers & Geosciences Giroux 33 1 126 2007 10.1016/j.cageo.2006.05.014 bh_tomo — A Matlab borehole georadar 2D tomography package Geophysics Gloaguen 72 5 J43 2007 10.1190/1.2755929 Pseudo-full-waveform inversion of borehole GPR data using stochastic tomography Journal of Applied Geophysics Gloaguen 57 4 242 2005 10.1016/j.jappgeo.2005.01.001 Bore-hole radar velocity inversion using cokriging and cosimulation Goovaerts 1997 10.1093/oso/9780195115383.001.0001 Geostatistics for natural resources evaluation Computers & Geosciences Hansen 34 1 53 2008 10.1016/j.cageo.2007.02.003 VISIM: Sequential simulation for linear inverse problems Geophysics Hansen 71 6 R101 2006 10.1190/1.2345195 Linear inverse Gaussian theory and geostatistics Vadose Zone Journal Hansen 7 1 249 2008 10.2136/vzj2006.0144 Inferring a sub-surface structural covariance model using cross-borehole ground penetrating radar tomography The Leading Edge Hubbard 16 1623 1997 10.1190/1.1437539 Estimation of permeable pathways and water content using tomographic radar data Water Resources Research Hubbard 35 1809 1999 10.1029/1999WR900040 Spatial correlation structure estimation using geophysical and hydrogeological data Geophysics Irving 70 5 K39 2005 10.1190/1.2049349 Effect of antennas on velocity estimates obtained from cross-borehole GPR data Computers & Geosciences Irving 32 9 1247 2006 10.1016/j.cageo.2005.11.006 Numerical modeling of ground-penetrating radar in 2-D using MATLAB Water Resources Research Irving 45 12 W12404 2009 10.1029/2008WR007471 Estimation of the lateral correlation structure of subsurface water content from surface-based ground-penetrating radar reflection images Journel 1978 Mining geostatistics The Leading Edge Knight 16 1576 1997 10.1190/1.1437526 The role of ground penetrating radar and geostatistics in reservoir description Water Resources Research Kowalsky 41 11 W11425 2005 10.1029/2005WR004237 Estimation of field-scale soil hydraulic and dielectric parameters through joint inversion of GPR and hydrological data Water Resources Research Linde 42 12 W12404 2006 10.1029/2006WR005131 Improved hydrogeophysical characterization using joint inversion of crosshole electrical resistance and ground penetrating radar traveltime data Vadose Zone Journal Looms 7 1 227 2008 10.2136/vzj2006.0129 Monitoring unsaturated flow and transport using cross-borehole geophysical methods Technometrics Marquardt 12 591 1970 10.1080/00401706.1970.10488699 Generalized inverses, ridge regression, biased linear estimation and non-linear estimation Menke 1989 Geophysical data analysis: Discrete inverse theory Mathematical Geology Pardo-Igúzquiza 30 1 95 1998 10.1023/A:1021765405952 Maximum likelihood estimation of spatial covariance parameters Computers & Geosciences Pebesma 24 1 17 1998 10.1016/S0098-3004(97)00082-4 Gstat: A program for geostatistical modelling, prediction and simulation Journal of Environmental & Engineering Geophysics Peterson 6 1 1 2001 10.4133/JEEG6.1.1 Pre-inversion corrections and analysis of radar tomographic data Water Resources Research Rea 34 3 329 1998 10.1029/97WR03070 Geostatistical analysis of ground-penetrating radar data: A means of describing spatial variation in the subsurface Geophysics Shamsipour 75 1 I1 2010 10.1190/1.3295745 3D stochastic inversion of gravity data using cokriging and cosimulation Geophysics Squires 57 353 1992 10.1190/1.1443249 The effects of statics on tomographic velocity reconstructions Tarantola 1987 Inverse problem theory — Methods for data fitting and model parameter estimation Reviews of Geophysics and Space Physics Tarantola 20 2 219 1982 10.1029/RG020i002p00219 Generalized nonlinear inverse problems solved using the least squares criterion Water Resources Research Topp 16 574 1980 10.1029/WR016i003p00574 Electromagnetic determination of soil water content: Measurements in coaxial transmission lines Journal of Geophysical Research Zelt 103 7187 1998 10.1029/97JB03536 Three-dimensional seismic refraction tomography: A comparison of two methods applied to data from the Faeroe Basin