Estimation of field‐scale soil hydraulic and dielectric parameters through joint inversion of GPR and hydrological data

[1] A method is described for the joint use of time-lapse ground-penetrating radar (GPR) travel times and hydrological data to estimate field-scale soil hydraulic parameters. We build upon previous work to take advantage of a wide range of cross-borehole GPR data acquisition configurations and to accommodate uncertainty in the petrophysical function, which relates soil porosity and water saturation to the effective dielectric constant. We first test the inversion methodology using synthetic examples of water injection in the vadose zone. Realistic errors in the petrophysical function result in substantial errors in soil hydraulic parameter estimates, but such errors are minimized through simultaneous estimation of petrophysical parameters. In some cases the use of a simplified GPR simulator causes systematic errors in calculated travel times; simultaneous estimation of a single correction parameter sufficiently reduces the impact of these errors. We also apply the method to the U.S. Department of Energy (DOE) Hanford site in Washington, where time-lapse GPR and neutron probe (NP) data sets were collected during an infiltration experiment. We find that inclusion of GPR data in the inversion procedure allows for improved predictions of water content, compared to predictions made using NP data alone. These examples demonstrate that the complimentary information contained in geophysical and hydrological data can be successfully extracted in a joint inversion approach. Moreover, since the generation of tomograms is not required, the amount of GPR data required for analyses is relatively low, and difficulties inherent to tomography methods are alleviated. Finally, the approach provides a means to capture the properties and system state of heterogeneous soil, both of which are crucial for assessing and predicting subsurface flow and contaminant transport.

[1]  A. Ward,et al.  A combined parameter scaling and inverse technique to upscale the unsaturated hydraulic parameters for heterogeneous soils , 2004 .

[2]  A. Sahuquillo,et al.  Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—I. Theory , 1997 .

[3]  S. Friedman,et al.  Relationships between the Electrical and Hydrogeological Properties of Rocks and Soils , 2005 .

[4]  A. Binley,et al.  Vadose zone flow model parameterisation using cross-borehole radar and resistivity imaging , 2001 .

[5]  Ali Fares,et al.  Dual Field Calibration of Capacitance and Neutron Soil Water Sensors in a Shrinking–Swelling Clay Soil , 2004 .

[6]  Magnus Persson,et al.  Predicting the Dielectric Constant-Water Content Relationship Using Artificial Neural Networks , 2002 .

[7]  D. Or,et al.  Temperature effects on soil bulk dielectric permittivity measured by time domain reflectometry: A physical model , 1999 .

[8]  R. Luebbers,et al.  The Finite Difference Time Domain Method for Electromagnetics , 1993 .

[9]  Andrés Sahuquillo,et al.  Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data 2. Demonstration on a synthetic aquifer , 1997 .

[10]  K. Pruess,et al.  TOUGH2 User's Guide Version 2 , 1999 .

[11]  Andrew Binley,et al.  High‐resolution characterization of vadose zone dynamics using cross‐borehole radar , 2001 .

[12]  Marcel G. Schaap,et al.  Laboratory Measurements of the Unsaturated Hydraulic Properties at the Vadose Zone Transport Field Study Site , 2003 .

[13]  F. Day‐Lewis,et al.  Assessing the resolution‐dependent utility of tomograms for geostatistics , 2004 .

[14]  Marnik Vanclooster,et al.  Electromagnetic Inversion of GPR Signals and Subsequent Hydrodynamic Inversion to Estimate Effective Vadose Zone Hydraulic Properties , 2004 .

[15]  D. McLaughlin,et al.  A Reassessment of the Groundwater Inverse Problem , 1996 .

[16]  O. H. Jacobsen,et al.  A laboratory calibration of time domain reflectometry for soil water measurement including effects of bulk density and texture , 1993 .

[17]  Y. Rubin.  Applied Stochastic Hydrogeology , 2003 .

[18]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[19]  P. R. Heller,et al.  A Catalog of Vadose Zone Hydraulic Properties for the Hanford Site , 2001 .

[20]  Budiman Minasny,et al.  Microwave dielectric behavior of wet soils , 2006 .

[21]  J. Sethian,et al.  3-D traveltime computation using the fast marching method , 1999 .

[22]  G. P. de Loor,et al.  Dielectric Properties of Heterogeneous Mixtures Containing Water , 1968 .

[23]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[24]  J. Robertsson,et al.  Finite‐difference modeling of electromagnetic wave propagation in dispersive and attenuating media , 1998 .

[25]  Robert R. Stewart,et al.  Exploration seismic tomography : fundamentals , 1991 .

[26]  David L. Alumbaugh,et al.  Estimating moisture contents in the vadose zone using cross‐borehole ground penetrating radar: A study of accuracy and repeatability , 2002 .

[27]  M. G. Marietta,et al.  Pilot Point Methodology for Automated Calibration of an Ensemble of Conditionally Simulated Transmissivity Fields: 2. Application , 1995 .

[28]  Rosemary Knight,et al.  Determining water content and saturation from dielectric measurements in layered materials , 1999 .

[29]  David A. Casper,et al.  Simulation of ground-penetrating radar waves in a 2-D soil model , 1996 .

[30]  M. Eppstein,et al.  Efficient three‐dimensional data inversion: Soil characterization and moisture Monitoring from cross‐well ground‐penetrating radar at a Vermont Test Site , 1998 .

[31]  Susan S. Hubbard,et al.  Ground‐penetrating‐radar‐assisted saturation and permeability estimation in bimodal systems , 1997 .

[32]  J. Philip.  Horizontal redistribution with capillary hysteresis , 1991 .

[33]  J. J. Peterson.  Pre-inversion Corrections and Analysis of Radar Tomographic Data , 2001 .

[34]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[35]  Yoram Rubin,et al.  Forward modeling of ground‐penetrating radar data using digitized outcrop images and multiple scenarios of water saturation , 2001 .

[36]  G. Gee,et al.  Water-Retention of Fractal Soil Models Using Continuum Percolation Theory: Tests of Hanford Site Soils , 2002 .

[37]  T. Caldwell.  Core Sampling in Support of the Vadose Zone Transport Field Study , 2001 .

[38]  K. Williams,et al.  High resolution imaging of vadose zone transport using crosswell radar and seismic methods , 2000 .

[39]  George A. McMechan,et al.  Ray‐based synthesis of bistatic ground‐penetrating radar profiles , 1995 .

[40]  T. Caldwell,et al.  Sampling of Borehole WL-3A through -12 in Support of the Vadose Zone Transport Field Study , 2001 .

[41]  Karsten Pruess,et al.  Fluid Flow , Heat Transfer , and Solute Transport at Nuclear Waste Storage Tanks in the Hanford Vadose Zone , 2002 .

[42]  Marcel G. Schaap,et al.  On the effective measurement frequency of time domain reflectometry in dispersive and nonconductive dielectric materials , 2005 .

[43]  G. E. Archie.  The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[44]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[45]  Ari Sihvola,et al.  Electromagnetic mixing formulas and applications , 1999 .

[46]  S. Gorelick,et al.  Estimating lithologic and transport properties in three dimensions using seismic and tracer data , 1996 .

[47]  C. G. Gardner,et al.  High dielectric constant microwave probes for sensing soil moisture , 1974 .

[48]  Stefan Finsterle,et al.  Inversion of tracer test data using tomographic constraints , 2006 .

[49]  Dale F. Rucker,et al.  Parameter estimation for soil hydraulic properties using zero-offset borehole radar: Analytical method , 2004 .

[50]  W. Jury,et al.  The spatial variability of water and solute transport properties in unsaturated soil: I. Analysis of property variation and spatial structure with statistical models , 1987 .

[51]  R. Schulin,et al.  Calibration of time domain reflectometry for water content measurement using a composite dielectric approach , 1990 .

[52]  Kamini Singha,et al.  A framework for inferring field‐scale rock physics relationships through numerical simulation , 2005 .

[53]  David Russo,et al.  Statistical analysis of spatial variability in unsaturated flow parameters , 1992 .

[54]  L. W. De Backer,et al.  Statistical Relationship Between Apparent Dielectric-constant and Water-content in Porous-media , 1985 .

[55]  R. Knight,et al.  Modeling the field‐scale relationship between dielectric constant and water content in heterogeneous systems , 2004 .

[56]  Johan Alexander Huisman,et al.  Measuring soil water content with ground penetrating radar , 2003 .

[57]  Interpretation and modeling of a subsurface injection test, 200 East Area, Hanford, Washington , 1994 .

[58]  A. H. Lu,et al.  Field calibration of computer models for application to buried liquid discharges: a status report , 1984 .

[59]  Alan P. Byrnes,et al.  Modeling Dielectric-constant values of Geologic Materials: An Aid to Ground-Penetrating Radar Data Collection and Interpretation , 2001 .

[60]  C. H. Chapman,et al.  Crosshole seismic tomography , 1989 .

[61]  A. P. Annan,et al.  Electromagnetic determination of soil water content: Measurements in coaxial transmission lines , 1980 .

[62]  John E. Peterson,et al.  Applications of algebraic reconstruction techniques to crosshole seismic data , 1985 .

[63]  David J. Daniels,et al.  Surface-Penetrating Radar , 1996 .

[64]  A. P. Annan,et al.  Measuring Soil Water Content with Ground Penetrating Radar: A Review , 2003 .

[65]  R. E. Williams,et al.  A geostatistical methodology to assess the accuracy of unsaturated flow models , 1996 .

[66]  G. Gee,et al.  Vadose Zone Transport Field Study: Soil Water Content Distributions by Neutron Moderation , 2000 .

[67]  J. Harris,et al.  Coupled seismic and tracer test inversion for aquifer property characterization , 1993 .

[68]  S. Finsterle,et al.  Estimating flow parameter distributions using ground-penetrating radar and hydrological measurements , 2004 .

[69]  Anderson L. Ward,et al.  Vadose Zone Transport Field Study: Status Report , 2001 .

[70]  A. P. Annan,et al.  Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy , 1989 .

[71]  S. Friedman.  A saturation degree‐dependent composite spheres model for describing the effective dielectric constant of unsaturated porous media , 1998 .

[72]  S. Jones,et al.  A Review of Advances in Dielectric and Electrical Conductivity Measurement in Soils Using Time Domain Reflectometry , 2003 .

[73]  A. Binley,et al.  Final Report, FY 2001 200 East Vadose Test Site Hanford Washington Electrical Resistance Tomography , 2001 .

[74]  A. Alharthi,et al.  Soil water saturation: Dielectric determination , 1987 .

[75]  M. J. Fayer,et al.  Re-evaluation of a subsurface injection experiment for testing flow and transport models , 1995 .

[76]  A. P. Annan.  GPR Methods for Hydrogeological Studies , 2005 .