Tomogram-based Appraisal of Geostatistical Models

Abstract:

We propose a framework to compare alternative geostatistical descriptions of a given site. Realizations of each of the considered geostatistical models and their corresponding tomograms (based on inversion of noise-contaminated simulated data) are used as a multivariate training image. The training image is scanned with a direct sampling algorithm to obtain conditional realizations that are not only in agreement with the geostatistical model, but also honor the spatially varying resolution of the site-specific tomogram (see Figure for a comparison of different conditional realizations). Model appraisal is based on the quality of the data predicted by the conditional realizations using measures adapted from model selection theory. The tomogram in this study is obtained by inversion of cross-hole ground-penetrating radar (GPR) first-arrival travel time data acquired at the MAcro-Dispersion Experiment (MADE) site in Mississippi (USA). Heterogeneity descriptions ranging from multivariate Gaussian fields to fields with complex multiple-point statistics inferred from outcrops are considered. Under the assumption that the porosity-permeability relationship inferred from local measurements is valid, we find that conditioned multiGaussian realizations and derivatives thereof can explain the crosshole geophysical data. We also find that the hydrogeological facies detected from local outcrops are representative. However, a training image based on an aquifer analog from Switzerland was found to be in better agreement with the geophysical data than the one based on the local outcrop, which appears to under-represent high permeability zones. These conclusions are only based on the information content in a single resolution-limited tomogram and extending the analysis to transport data and higher resolution surface GPR data might lead to different conclusions (e.g., that discrete facies boundaries are necessary). Our framework makes it possible to identify inadequate geostatistical models, effectively narrowing the space of possible heterogeneity representations.