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

Authors: Osterman, Gordon; LESCH, SCOTT - Riverside Public Utilities; Bradford, Scott

Submitted to: Computers and Geosciences
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/23/2024
Publication Date: 3/26/2024
Citation: Osterman, G.K., Lesch, S., Bradford, S.A. 2024. A conditioned Latin hypercube sampling design methodology for ground-truthing transient EM resistivity models. Computers and Geosciences. 187. Article 105582. https://doi.org/10.1016/j.cageo.2024.105582.
DOI: https://doi.org/10.1016/j.cageo.2024.105582

Interpretive Summary: Interpreting geology from subsurface 3D electrical resistivity models requires drilling sediment texture logs to ground-truth the resistivity model. Logs are expensive, so we want to extract the maximum value from each one for interpreting the resistivity model. We have developed a data-driving sampling design procedure to select logging sites that will match the statistics (mean, standard deviation) of the sampled resistivity model. We test this procedure on a resistivity model from California's Central Valley with co-located sediment texture logs, selected by expert opinion. We show that our sampling design methodology can represent the resistivity model better than random sampling and better than the random or true samples. This approach has potential to improve sampling selection, and thus the geological interpretation, for the growing number of resistivity model being acquired across the Central Valley.

Technical Abstract: Translating 3D resistivity models to relevant hydrogeological parameters such as sediment texture requires applying a rock physics transform, ideally calibrated using co-located sediment texture logs. It is difficult to select optimal logging sites that span the range of observed resistivity values using expert opinion alone, so we select sites use conditioned Latin hypercube sampling (cLHS), a maximally stratified sampling design methodology. cLHS employs simulated annealing to select sites that minimize an objective function by reproducing the statistics of the resistivity model. We implement a range of preprocessing steps as well as principal component analysis to reduce the size of the model, which helps 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 imposed to increase the likelihood that the selected soundings correlate well with the 1D sediment texture logs. 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 sample sets against the five cone penetrometer testing logs that were acquired at the site, as well as randomly selected sampling sites. The sample set selected with cLHS was able to reproduce the statistics of the resistivity model and did so more effectively than the true sampling locations or the random sampling locations.