Magnitude and geometry of reactive fluid flow from direct inversion of spatial patterns of geochemical alteration

Time-integrated equations governing tracer mass-balance provide a framework for interpreting spatial patterns of mineralogical, elemental, and isotopic alteration in rocks caused by reactive fluid flow, and linear inverse theory allows quantitative estimates of the magnitude and three-dimensional (3D) geometry of fluid flow. We demonstrate the inverse technique with a simple model system that involves fluid advection and fluid-rock oxygen isotope exchange only. Analytic forward models of reactive transport enable patterns of isotope alteration to be calculated exactly, and inversions of the resulting spatial patterns of synthetic isotope composition demonstrate the effectiveness of our approach. For a field application of the inverse method, we consider regional metamorphic rocks from the Waits River Formation, southeastern Vermont, that expose a mineralogical and stable isotopic record of reactive fluid flow over an area of ≈120 km2. Spatial patterns of prograde changes in whole-rock CO2, δ18O, and δ13C allow a direct inversion for the magnitude and 3D geometry of reactive flow at the time of final prograde mineral reaction. Consistency tests suggest that the inverse estimate is primarily controlled by patterns of CO2 changes, and resolution tests indicate that the smallest features in the inverse flux field that can be reliably detected have an east-west dimension of ≈5 km and a north-south dimension of ≈14 km. The regionally-averaged time-integrated fluid flux vector returned by the inversion has a magnitude of 2.2×104 mol fluid/cm2 rock, trends 255° in the horizontal plane, and is directed upward at 32° from the horizontal. The geometry of terrain-scale reactive flow was largely controlled by regional structure. Reactive fluids that entered the study area appear to have been tectonically-driven horizontally from the east at a depth ≈0.5 to 2.0 km beneath the present level of exposure.