A conditioned Latin hypercube sampling design methodology for ground-truthing transient EM resistivity models

Abstract

Translating 3D resistivity models of the subsurface to relevant hydrogeological parameters such as sediment texture requires applying a rock physics transform that is ideally calibrated using co-located 1D sediment texture logs. It is difficult to select optimal logging sites in the model that span the range of observed resistivity values using expert opinion alone. Instead, we demonstrate a methodology for selecting logging sites using conditioned Latin hypercube sampling (cLHS), a maximally stratified sampling design methodology. cLHS employs simulated annealing to select sampling sites that minimize an objective function by reproducing the statistics of the resistivity model. We implement numerous preprocessing steps to isolate desirable regions within the model for logging, and we use principal component analysis to reduce the dimensionality of the model to aid the convergence of the simulated annealing procedure while preserving the majority of the model variance. Additionally, we impose an additional objective function condition to penalize the selection of sites in the resistivity model that exhibit a high degree of lateral variance. This condition is used to increase the likelihood that the sediment texture logs acquired at the selected sites correlate well with the resistivity model. We tested our approach on a resistivity model obtained using a towed transient EM system in an almond orchard in California’s Central Valley, comparing our selected sets of logging sites against the five cone penetrometer testing logs originally acquired at the site, as well as randomly selected logging sites. The sample sets selected with cLHS were consistently able to reproduce the statistics of the resistivity model and did so more effectively than the true sampling locations or the random sampling locations.