Monitoring Spatio-temporal Dielectric Permittivity Variation in the Shallow Subsurface through Bayesian Inversion of GPR Data
Abstract
A minimum-relative-entropy (MRE) based Bayesian inversion framework is applied to monitor spatio-temporal distribution of dielectric permittivity using tomographic radar first arrival time data from a synthetic, transient infiltration experiment in the shallow subsurface. In this experiment, a spatially correlated random saturated hydraulic conductivity field is generated and used as input to the TOUGH2 flow simulator, which provides realistic distributions of water and dielectric permittivity on a fine grid at several temporal snapshots. For each snapshot, a tomographic GPR simulator is utilized to produce first arrival travel times. In this study, we test the performance of our inverse modeling framework by inverting and monitoring dielectric permittivity variations using these traveltime data. The inverse modeling domain is divided into coarse grid blocks compared to flow simulation grid, in order to reduce the dimension of unknowns. Each unknown parameter is first assigned a minimally subjective probability distribution function (pdf) using the MRE method, then pseudorandom dielectric constant parameter sets are drawn from these pdfs using a quasi-Monte Carlo sampling technique. We then compute first arrival GPR travel times for each parameter set and the corresponding weight based upon the misfit between the calculated model responses and observations. This inversion approach can deal with nonlinearity and nonuniqueness between data and model parameters by incorporating a numerical modeling technique and it can quantify uncertainty in the parameter estimates by treating those estimates as probability distributions rather than deterministic estimates. Moreover, the intermediate inversion results can be used as “memory functions” in the form of MRE pdfs for step-wise inversion. Testing results show that this framework is capable of reproducing estimates of saturation at grid blocks throughout the study area, and that accuracy and precision are improved as more data become available. These outcomes spur ongoing efforts to improve upon this framework including implementing a means of parameter reduction (for example, through use of a pilot point method) and validating the approach using field data from the Chromium-contaminated Hanford 100-D biostimulation study site.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2010
- Bibcode:
- 2010AGUFM.H11K..02T
- Keywords:
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- 1835 HYDROLOGY / Hydrogeophysics;
- 1875 HYDROLOGY / Vadose zone;
- 1894 HYDROLOGY / Instruments and techniques: modeling;
- 3260 MATHEMATICAL GEOPHYSICS / Inverse theory