Estimating the spatiotemporal distribution of geochemical parameters associated with biostimulation using spectral induced polarization data and hierarchical Bayesian models

We developed a hierarchical Bayesian model to estimate the spatiotemporal distribution of aqueous geochemical parameters associated with in-situ bioremediation using surface spectral induced polarization (SIP) data and borehole geochemical measurements collected during a bioremediation experiment at a uranium-contaminated site near Rifle, Colorado (USA). The SIP data were first inverted for Cole-Cole parameters, including chargeability, time constant, resistivity at the DC frequency, and dependence factor, at each pixel of two-dimensional grids using a previously developed stochastic method. Correlations between the inverted Cole-Cole parameters and the wellbore-based groundwater chemistry measurements indicative of key metabolic processes within the aquifer (e.g., ferrous iron, sulfate, uranium) were established and used as a basis for petrophysical model development. The developed Bayesian model consists of three levels of statistical submodels: (1) data model, providing links between geochemical and geophysical attributes, (2) process model, describing the spatial and temporal variability of geochemical properties in the subsurface system, and (3) parameter model, describing prior distributions of various parameters and initial conditions. The unknown parameters were estimated using Markov chain Monte Carlo methods. By combining the temporally distributed geochemical data with the spatially distributed geophysical data, we obtained the spatiotemporal distribution of ferrous iron, sulfate, and sulfide, and their associated uncertainty information. The obtained results can be used to assess the efficacy of the bioremediation treatment over space and time and to constrain reactive transport models.