Uncertainty in training image‐based inversion of hydraulic head data constrained to ERT data: Workflow and case study

Abstract

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, most of the studies ignore modeling the prior with realistic geological uncertainty. In this paper, we propose a workflow inspired by a Popper-Bayes philosophy that data should first be used to falsify models, then only be considered for matching. We propose a workflow consisting of three steps: (1) in defining the prior, we interpret multiple alternative geological scenarios from literature (architecture of facies) and site-specific data (proportions of facies). Prior spatial uncertainty is modeled using multiplepoint geostatistics, where each scenario is defined using a training image. (2) We validate these prior geological scenarios by simulating electrical resistivity tomography (ERT) data on realizations of each scenario and comparing them to field ERT in a lower dimensional space. In this second step, the idea is to probabilistically falsify scenarios with ERT, meaning that scenarios which are incompatible receive an updated probability of zero while compatible scenarios receive a nonzero updated belief. (3) We constrain the hydrogeological model with hydraulic head and ERT using a stochastic search method. The workflow is applied to a synthetic and a field case studies in an alluvial aquifer. This study highlights the importance of considering and estimating prior uncertainty (without data) through a process of probabilistic falsification.

Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data

“…The first synthetic benchmark is based on surface ERT measurements inspired by a field case (Hermans et al, 2015a). The background model mimics a heterogeneous alluvial aquifer with a distribution of electrical resistivity ranging from 50 Ωm in loam and clay, located mainly in the upper part of the model, to more than 300 Ωm in sand and gravel located in the bottom part of the aquifer.…”

The Present State and Future Application of Cloud Computing for Numerical Groundwater Modeling

“…The calibration constrained subspace uncertainty analysis method of Tonkin and Doherty (), often referred to as Null Space Monte Carlo (NSMC), has several limitations that could be addressed by more computationally intensive analysis methods: NSMC relies upon an assumption of model linearity about a calibrated model produced by local optimization techniques (PEST). So while it is computationally efficient, it may not be robust in the presence of model nonlinearity, that can produce multiple local minima (Mosegaard and Tarantola ). Due to limitations on what aspects of a model can be represented as an adjustable parameter, and the increasing computational cost of additional parameterization, aspects of model structure, such as model geometry representing uncertain geological features, are fixed during the analysis potentially leading to bias and underprediction of predictive uncertainty (White et al ; Hermans et al ). To optimize model parameter values to reduce observation data misfit and represent models as linear approximations, the PEST/NSMC approach requires parameters that are smoothly varying and differentiable. However, often geology is categorical in nature with sharp contrasts in physical properties with facies changes that are impossible to represent with smooth differentiable parameters (Refsgaard et al ). …”

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer

“…The idea of accounting for uncertainty in such groundwater models constrained by geophysical data is not novel (e.g., Ezzedine et al 1999;Yeh et al 2002;Chen et al 2006). Numerous studies combine the use of electrical resistivity tomography with hydrological modeling, often employing Markov Chain Monte Carlo (MCMC) algorithms in combination with geostatistical methods to quantify prior beliefs on geology (e.g., Huisman et al 2010;Irving and Singha 2010;Hermans et al 2015).…”