An empirical function to estimate the depths of linear hot sources: Laboratory modeling and field measurements of lava tubes

Estimating depths of buried lava tubes is important for determining the thermal budgets and effusion rates of basaltic volcanic systems. This research used a laboratory experiment scaled to a lava tube system to measure the 3D temperature field surrounding a hot viscous fluid flowing through a buried glass tube while varying conditions such as flow rate and temperature. The depth of the glass tube was changed for different experimental runs. Numerical techniques were applied to model the laboratory experiment. The surface thermal distributions from 166 thermal traverses, constrained to a depth to width ratio of 0.6 to 1.6, were analyzed to empirically derive a depth estimation function using regression techniques. This “Linear Anomaly Surface Transect (LAST)” depth function is a scaleable depth estimation technique which can be solved with thermal imaging data alone. The minimum temperature, maximum temperature and width of a Lorentzian distribution fit to a surface thermal transect, are the only inputs required for the LAST function to estimate the depths of the hot source. The input parameters were then applied to non-laboratory situations including the Kuhio lava tube system in Hawai’i. The LAST function produced depth estimates of ∼ 0.3 m for the Kuhio lava tube in Hawai’i, which did not agree with observations on the ground. This is the result of the complex composition and geometry of an actual lava tube where heat transfer is controlled by more than a simple fluid filling a tube, but also by convection of gasses and fluids in a partially filled passage. Though not effective for lava tubes at this time, the model provides promising results for simple cases applied to engineering and underground coal fires.