Estimating planetary heat flow from a shallow subsurface heat flow measurement

Cornwall, Marc Andrew (2015). Estimating planetary heat flow from a shallow subsurface heat flow measurement. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f885

Abstract

This study investigates the feasibility of estimating planetary heat flow from a shallow subsurface heat flow measurement with a Function Specification Inversion (FSI) model. Heat flow is a product of the thermal conductivity and gradient at depth; these are measured and therefore contain errors. The model estimates other parameters, as well as the former, while not explicitly accounting for temperature dependent thermal properties.

The heat flow is decomposed into steady state basal (planetary) and unsteady state (related to the surface temperature variation) heat flow components. Surface heat flow is typically several orders of magnitude higher than the planetary heat flow; therefore unsteady components in a shallow subsurface heat flow measurement may mask the planetary heat flow. The extent of masking positively correlates with the skin depth and amplitude of the surface heat flow, and negatively correlates with the magnitude of the planetary heat flow.

The planetary heat flow is estimated by inverting the temperature measurement and optimising the basal heat flow. The basal heat flow is most effectively optimized from instantaneous measurements, taken when the surface temperature is relatively constant. Long-period measurements, while more accurately optimized, introduce more unsteady temperature gradients, thereby increasing the ill-determinacy and instability of the problem. The model tolerates errors up to 25% in simultaneous optimization of several unknown parameters, with related errors in the optimized basal heat flow.

On Mars, the heat flow is optimized to within 10% for measurements over at least twice the skin depth and 0.5 of a Martian year, or at least five times the skin depth and 0.25 of a Martian year. On Mercury, temperature amplitudes control optimized heat flow accuracy; sensor penetration depths well below three skin depths are required. On Vesta, very low heat flows render FSI ineffective with a noise amplitude of 1 mK.