Periodic heating of a layer over a semi-infinite solid

Abstract

Extraction of geologic information from thermal infrared images requires a suitable mathematical model with which to relate diurnal surface temperatures to incident flux and surface and near-surface physical properties. Some success has been achieved in discriminating several rock types and mapping thermal inertia differences by assuming a semi-infinite solid. However, the widespread presence of surface effects caused by soils, lichen cover, and coatings suggests the need to extend current models. Jaeger's technique for treating the periodic heating of a solid has been applied to a layer over a semi-infinite solid. Numerical examples for limiting cases demonstrate both the influence of surface coating and the ‘effective’ penetration of the ground that can be sensed by observing surface temperatures. A 0.01-cm ‘lichen’ layer and a 0.1-cm ‘soil’ layer have a negligible effect, whereas a 1-cm lichen layer produces a surface temperature similar to that of an infinitely thick soil cover. A 10-cm thickness of soil or lichen completely masks the underlying rock.