Hydrology of meteoric diagenesis: Residence time of meteoric ground water in island fresh-water lenses with application to aragonite-calcite stabilization rate in Bermuda
The average age of ground water that discharges at the shoreline from an island fresh-water lens is equal to the volume of ground water in the lens divided by the total recharge to the island. This island average residence time, τ 0 is easily calculated by Dupuit-Ghyben-Herzberg analysis (DGH). From estimates of the controlling variables (recharge, hydraulic conductivity, and porosity), it is estimated that τ 0 is usually on the order of 1 to a few tens of years in fresh-water lenses of small (width on the order of 100 to a few thousand meters), strip islands where calcarenite is undergoing early diagenesis. Lateral variation in interstitial velocity and distribution of ground-water age within the lens can be calculated from an approximate theory using DGH potentials and an assumption that discharge is uniformly distributed with depth. Results are within a few percent of those from rigorous flow-net construction. Velocities range laterally through two orders of magnitude. Contours of ground-water age are nearly horizontal over most of the lens; at a depth of about 40% of the depth to the interface, the ground-water age is τ 0 /2, and it equals τ 0 at about 60% of the depth to the interface. Flow-net construction shows that velocities are greatest at the water table and decrease rapidly downward to the value given by DGH. Representative velocities halfway between the ground-water flow divide and the shoreline are 10 to 100 m/yr in these islands. Application of these calculation procedures to Bermuda leads to a revised estimate of ground-water age for water samples that have been used to estimate the rate of aragonite-to-calcite transformation in the fresh-water lenses of that island. This rate is an order of magnitude less than that in lenses in Holocene oolitic cays of the Bahamas. The ratio of stabilization rate to amount of aragonite appears to be about the same in the two settings. The value of the ratio implies a half-life of 6,000-7,000 yr for aragonite-to-calcite transformation in these lenses.