Distributed Soil Moisture from Crosshole Ground‐Penetrating Radar Travel Times using Stochastic Inversion

Abstract

Linde, N., and J. A. Vrugt, 2013, Distributed soil moisture from crosshole ground-penetrating radar travel times using stochastic inversion. Vadose Zone Journal. 12, doi:10.2136 2 AbstractGeophysical methods offer several key advantages over conventional subsurface measurement approaches, yet their use for hydrologic interpretation is often problematic.Here, we introduce theory and concepts of a novel Bayesian approach for high-resolution soil moisture estimation using traveltime observations from crosshole Ground Penetrating Radar (GPR) experiments. The recently developed Multi-try DiffeRential Evolution Adaptive Metropolis with sampling from past states, MT-DREAM (ZS) is being used to infer, as closely and consistently as possible, the posterior distribution of spatially distributed vadose zone soil moisture and/or porosity under saturated conditions. Two differing and opposing model parameterization schemes are being considered, one involving a classical uniform grid discretization and the other based on a discrete cosine transformation (DCT). We illustrate our approach using two different case studies involving geophysical data from a synthetic water tracer infiltration study and a real-world field study under saturated conditions. Our results demonstrate that the DCT parameterization yields the most accurate estimates of distributed soil moisture for a large range of spatial resolutions, and superior MCMC convergence rates.In addition, DCT is admirably suited to investigate and quantify the effects of model truncation errors on the MT-DREAM (ZS) inversion results. For the field example, lateral anisotropy needs to be enforced to derive reliable soil moisture variability. Our results also demonstrate that the posterior soil moisture uncertainty derived with the proposed Bayesian procedure is significantly larger than its counterpart estimated from classical smoothnessconstrained deterministic inversions.

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

“…5 b) is in good agreement with the velocity field obtained by Linde et al (2008) and Linde and Vrugt (2013) for the exact same data set.…”

“…This multi-chain method creates proposals on the fly from an historical archive of past states using a mix of parallel direction and snooker updates. We refer the reader to Linde and Vrugt (2013) ; Lochbühler et al (2014) ;; Rosas-Carbajal et al (2013) ; for various geophysical case-studies in which this algorithm is used. For the actual field application, we use a hierarchical Bayesian formulation, in which the data error, σ Y in Eq.…”

“…This latter method approximates the evidence by importance sampling from a Gaussian mixture model fitted to a large sample of posterior solutions generated with the DREAM (ZS) algorithm ( Laloy and Vrugt, 2012;Vrugt, 2016;Vrugt et al, 2008 ). Then, we present an application of Bayesian model selection to subsurface modeling using geophysical data from the South Oyster Bacterial Transport Site in Virginia (USA) ( Chen et al, 20 01;20 04;Hubbard et al, 2001;Linde et al, 2008;Linde and Vrugt, 2013 ). These data consist of travel time observations made by crosshole ground-penetrating radar (GPR), and exhibit small measurement errors typical of most near-surface geophysical sensing methods.…”

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

“…A detailed description of this sampling scheme including a proof of ergodicity and detailed balance can be found in the cited references. Various contributions in hydrology and geophysics (amongst others) have demonstrated the ability of DREAM ZS ð Þ to successfully recover high-dimensional target distributions [Laloy et al, , 2013Linde and Vrugt, 2013;RosasCarbajal et al, 2014;Laloy et al, 2014;Lochb€ uhler et al, 2014Lochb€ uhler et al, , 2015.…”

Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion

“…Such methods can be formulated using either a measure theoretic or random variable approach, the first being the most formal and axiomatic definition of probability and preferred by theoreticians, and the latter more easy and practical to use and therefore favored by practitioners. Among these methods, Bayesian inference coupled with Markov chain Monte Carlo (MCMC) simulation has found widespread application and use in GPR inversion [6,[13][14][15][16][17][18][19][20]. This approach results in a posterior parameter distribution and quantifies the uncertainty in the modeling results emerging from the model, observed data, likelihood function and prior distribution.…”