The role of multiple-point statistics and model selection in quantitative hydrogeophysical studies of the critical zone

Abstract:

Geophysical data are routinely used to provide qualitative insights about the main lithologies and the distribution of soil moisture in the critical zone. Quantitative hydrogeophysical inferences of critical zone properties and processes are much more challenging because of the multitude of interacting physical, biological and chemical gradients that may affect the geophysical measurement response. In this context, it is essential to incorporate the geophysical data within a wider modeling framework that centers on a conceptual model that describes the properties and processes under study together with appropriate boundary conditions. Based on recent groundwater applications, I describe how it is now possible to build geologically meaningful realizations of subsurface structure using multiple-point statistics (MPS) and to make uncertainty estimates. I will demonstrate conditioning of MPS simulations to geophysical tomograms, inclusion of summary statistics derived from MPS simulations within a Markov chain Monte Carlo (MCMC) inversion, and full MPS MCMC inversion based on fast (speed-up of 40 times) model proposal algorithms that we have adapted from computer vision. For future applications in the critical zone, I suggest that MPS simulations should be used to derive and perturb primary lithological properties and that biological, chemical, and hydrological state variables (given appropriate boundary conditions) are subsequently simulated using domain-specific algorithms. The geophysical data (an individual snap shot or time-series) are then used to guide the model update of the primary properties (and nuisance parameters such as petrophysical parameters) that in turn influence the predicted state variables and their associated fluxes. Instead of classical parameter estimation, I argue that it is often more appropriate to focus on model selection, in which alternative conceptual models of the subsurface are compared and ranked given the available data.