THE EXTENT OF THE FLOW AREA OF HYDROTHERMAL SYSTEMS: ESTIMATES FROM HEAT FLOW AND RADIOCARBON AGES

The surface area involved in thermal groundwater systems is difficult to estimate. Here we describe a simple method to make such estimates. Assumptions include: 1) terrestrial heat flow is the only heat source, and 2) terrestrial heat flow is steady state. The heat carried to a springs H = Q.c.r.(T_spring-T_surface), where H is the heat discharged at the spring, Q is spring discharge (m³s^-1), c is specific heat capacity of water (J.kg^-1K^-1), r is water density (kgm^-3), T_spring is mean annual spring temperature (^oC), and T_surface is mean annual surface temperature (i.e., annual air temperature). The minimum extent of the deep flow area is S_min = H/q, where S_min is the minimum flow area (km²), and q is the undisturbed terrestrial heat flow (Wm^-2). In other words we are looking for an aerial extent such that all terrestrial heat flow is consumed by water heating. In reality, only small part of the terrestrial heat flow is transported by groundwater, whereas most is conducted to the ground surface as residual heat flow. Therefore, the real flow area will be least several times higher than S_min. Groundwater typically transports 7-20% of the heat flux. When residual heat flow can be measured (i.e., in boreholes) S_real = H/(q- q_residual) where S_real is the estimation of a real flow area (km²) and q_residual is the residual terrestrial heat flow (Wm^-2). Results calculated using the above equations were compared to results based on thermal spring discharge rates and groundwater ¹⁴C ages in the Idaho Batholith.