Geostastical modeling of space-time dynamics calcite dissolution at the nanoscale

We investigate the intricate patterns associated with space-time dynamics displayed by (i) surface topography (Z) and (ii) reaction rates (R) resulting from direct nano-scale imaging of calcite-water interfaces subject to dissolution. The analysis rests on a space-time variogram modeling approach. The latter has been suggested as promising in unveiling major patterns exhibited by hydrogeological quantities across large scale aquifer systems. Transferability of the associated theoretical and operational framework to interpret nano-scale geochemical scenarios is here assessed for the first time. We do so upon taking advantage of recent high-resolution experiments attained through Atomic Force Microscopy (AFM) and targeting the evolution of the interface between a calcite crystal and water as driven by mineral dissolution processes. Upon relying on the ensuing large data-set, key variability patterns are identified through (i) efficient sampling of the spatial domain via quasi-random Sobol sequences and (ii) the use of a Harmonic Covariance Estimator (HCE) to model the space-time variogram of Z. The resulting (sample) space-time variogram exhibits visibly periodic oscillations at specific spatial and temporal lags. These patterns highlight the interaction taking place between the spatial structure and temporal dynamics in hydrogeological processes. We also explore the theoretical bases of the relationship between the variograms of Z and R. Corresponding results offer valuable insights into the spatial and temporal correlation of calcite dissolution dynamics. Our findings enable one to link space-time dynamics of crystal topography and the ensuing dissolution rates to corresponding traits of space-time variograms. Hence, they constitute the basis for potential applications associated with the possibility of providing estimates of the way these complex processes evolve at nano-scale resolutions, thus driving chemical weathering of minerals constituting the Earth’s interior.