Planetary heat flow from shallow subsurface measurements: Mars

Abstract

Planetary heat flow probes measure heat flow (depth-resolved temperature and thermal conductivity) to provide insight into the internal state of a planet. The probes have been utilized extensively on Earth, twice on the Moon, and once on the Surface of comet 67P-CG. Mars is an important target for heat flow measurement as heat flow is a critical parameter in Martian thermal history models. Earlier studies indicate that Martian planetary heat flow can be accessed at 5 m below the surface in dry regolith monitored over at least one Martian year. A one Martian year monitoring period is necessary because, in the shallow subsurface, heat flow from the interior is superposed with time varying heat flow contributions, primarily due to insolation. Given that a heat flow probe may not achieve its target depth or monitoring period, this study investigates how the depth (2–5 m), duration (0–1 Martian year) and quality of measurements influence the accuracy of planetary heat flow. An inverse model is used to show that, in the preceding scenarios, the accuracy of planetary heat flow directly estimated from depth-dependent thermal conductivity with 10–20% precision errors, temperatures with 50–100 mK precision errors and modelling uncertainties up to 500 mK, can, on average, be improved by a factor of 27 with optimization to 13%. Accuracies increase with sensor penetration depth and regolith monitoring period. Heat flow optimized from instantaneous measurements or those with the shortest regolith monitoring periods have increased accuracy where the frequency and amplitude of the temperature variation are lowest. The inverse model is based on the Function Specification Inversion method. This study demonstrates that a solution subspace can be identified within a space of uncertainties modelled for the temperature measurements and planetary heat flow: the subspace is defined by a constant log-ratio of their respective standard deviations. Optimized heat flow estimates display reduced correlation with increasing temperature precision and systematic conductivity errors, with the constraint of other known model parameters. Consequently, the model permits upper bounds to be placed on the conductivity estimate without conductivity optimization, as heat flows are optimized to a limiting value with increasing systematic conductivity errors for any given parameter set. Overall, the results demonstrate a 52% chance of achieving a direct heat flow estimate accurate to within 40%, with the same being 82% after optimization. © 2016 Elsevier Ltd