Bayesian modeling of non-stationary, univariate, spatial data for the Earth sciences

Some Earth science data, such as geochemical measurements of element concentrations, are non-stationary—the mean and the standard deviation vary spatially. It is important to estimate the spatial variations in both statistics because such information is indicative of geological and other Earth processes. To this end, an estimation method is formulated as a Bayesian hierarchical model. The method represents the spatially varying mean and the spatially varying standard deviation with basis functions; this formulation implicitly accounts for a spatially varying covariance function. A unique advantage of this method is that it can map the mean, the standard deviation, quantiles, and exceedance probabilities. The method is demonstrated by mapping titanium concentrations, which are measured in the coastal plain of the southeastern United States. Various checks demonstrate that the model fits the data and that the estimated statistics are geologically plausible.