A latent Gaussian approach for modeling geological sequences: model, inference and conditional simulation

The prediction of the soil contamination in a environmental risk area is a problem of relevant public interest. Very often a proper analysis requires a preliminary geological study. Indeed, understanding the distributions of permeable and impermeable layers under the risk area is necessary in order to estimate the risk that a pollutant could reach a sensible location, like the aquifers. The data available in this sort of studies come from cores drilled at several locations. The data are geological sequences summarized by a vector of thicknesses of dierent sediments or categories. A 3D reconstruction of the soil characteristics starting from this data requires to specify a spatial model for categorical data. In this talk we present a new spatial model based on the assumption that there ex- ists a sequence of categories (parent sequence), which is compatible with all observed sequences in the sense that each observed sequence can be obtained from the parent se- quence by deleting one or more categories of the parent sequence. The parent sequence can be extracted from the empirical data or dened according the prior knowledge of a scientist about the geological deposition. The thickness of each category are modeled as truncated Gaussian random variables that are spatially correlated. This choice allows the possibility that the parent sequence is not completely observed. We will therefore cast the estimation procedure of the model parameters within a Bayesian framework using an MCMC algorithm for sampling all possible sequences. We will illustrated the relative merits of our modeling procedure by means of sim- ulated and real examples. In particular we will show how we can simulate a 3D recon- struction conditionally on the observed data.