Hierarchical Bayesian Model for Estimating the Spatiotemporal Distribution of Geochemical Processes Associated with In-Situ Remediation Using Geophysical Datatsets

Understanding the spatial and temporal distribution of biogeochemical responses to in-situ remediation treatments is useful for assessing treatment efficacy. However, some geochemical properties are difficult to measure directly and wellbore measurements typically only provide a sparse sampling of a highly heterogeneous system. We present a hierarchical Bayesian state-space approach to model the temporal and spatial dependence of the biogeochemical processes as functions of geochemical and geophysical properties. We specifically focus on predicting the volume of evolved precipitates associated with remediation treatments using measurable aqueous geochemical samples and crosshole geophysical data. We expect that the spatiotemporal distribution of the transformations will progress systematically and will be impacted by the initial, in-situ heterogeneity. We represent the spatial structure using a process convolution model with spatially dependent kernel parameters. This flexible model allows the processes to be non-stationary and can accommodate directional flow. Implementation uses Gibbs and Slice Sampling MCMC-based algorithms. The developed statistical model is demonstrated using synthetic data based on the Uranium-contaminated DOE Rifle Integrated Field Study Site in Colorado.