Direct prediction of spatially and temporally varying physical properties from time‐lapse electrical resistance data

Abstract

Time‐lapse applications of electrical methods have grown significantly over the last decade. However, the quantitative interpretation of tomograms in terms of physical properties, such as salinity, temperature or saturation, remains difficult. In many applications, geophysical models are transformed into hydrological models, but this transformation suffers from spatially and temporally varying resolution resulting from the regularization used by the deterministic inversion. In this study, we investigate a prediction‐focused approach (PFA) to directly estimate subsurface physical properties with electrical resistance data, circumventing the need for classic tomographic inversions. First, we generate a prior set of resistance data and physical property forecast through hydrogeological and geophysical simulations mimicking the field experiment. We reduce the dimension of both the data and the forecast through principal component analysis in order to keep the most informative part of both sets in a reduced dimension space. Then, we apply canonical correlation analysis to explore the relationship between the data and the forecast in their reduced dimension space. If a linear relationship can be established, the posterior distribution of the forecast can be directly sampled using a Gaussian process regression where the field data scores are the conditioning data. In this paper, we demonstrate PFA for various physical property distributions. We also develop a framework to propagate the estimated noise level in the reduced dimension space. We validate the results by a Monte Carlo study on the posterior distribution and demonstrate that PFA yields accurate uncertainty for the cases studied.

Impact of petrophysical uncertainty on Bayesian hydrogeophysical inversion and model selection

“…For time-lapse applications, Vasco et al (2014) circumvent the use of an explicit petrophysical model by relating the time at which a significant change in geophysical data occurs to the time of a saturation and/or pressure change within a reservoir or aquifer. Alternative approaches are presented by Hermans et al (2016) and Oware et al (2013).…”

Improving Bayesian Evidential Learning 1D imaging (BEL1D) accuracy through iterative prior resampling

“…The framework is based on Bayesian Evidential Learning (e.g. Scheidt et al, 2018;Hermans et al, 2016).…”

Uncertainty Quantification of Medium‐Term Heat Storage From Short‐Term Geophysical Experiments Using Bayesian Evidential Learning

“…A linear regression model is used to account for residual error in the linear regression between and (Satija & Caers, ). The derivation of for field data according to Hermans et al () is described in supporting information Text S3. It is now straightforward to generate samples in the reduced dimension space.…”

“…Although our field data are part of the prior, it is located in a region poorly sampled. This renders prediction‐focused approaches, and stochastic inversions in general, more challenging than in a densely populated zone (Hermans et al, ).…”

“…As for global sensitivity, BEL is not limited to this specific approach. For a more detailed description, we refer to Hermans et al (2016b) and Satija and Caers (2015).…”