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Mass conservative three‐dimensional water tracer distribution from Markov chain Monte Carlo inversion of time‐lapse ground‐penetrating radar data
Author(s) -
Laloy Eric,
Linde Niklas,
Vrugt Jasper A.
Publication year - 2012
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2011wr011238
Subject(s) - ground penetrating radar , markov chain monte carlo , monte carlo method , plume , inversion (geology) , radar , geology , tracer , synthetic data , algorithm , statistical physics , computer science , meteorology , mathematics , statistics , physics , geomorphology , nuclear physics , telecommunications , structural basin
Time‐lapse geophysical measurements are widely used to monitor the movement of water and solutes through the subsurface. Yet commonly used deterministic least squares inversions typically suffer from relatively poor mass recovery, spread overestimation, and limited ability to appropriately estimate nonlinear model uncertainty. We describe herein a novel inversion methodology designed to reconstruct the three‐dimensional distribution of a tracer anomaly from geophysical data and provide consistent uncertainty estimates using Markov chain Monte Carlo simulation. Posterior sampling is made tractable by using a lower‐dimensional model space related both to the Legendre moments of the plume and to predefined morphological constraints. Benchmark results using cross‐hole ground‐penetrating radar travel times measurements during two synthetic water tracer application experiments involving increasingly complex plume geometries show that the proposed method not only conserves mass but also provides better estimates of plume morphology and posterior model uncertainty than deterministic inversion results.