Measurements of the Thermal Properties of the Lunar Regolith Using the LUNAR--A Penetrators and Data Interpretation

Details Measurements of the Thermal Properties of the Lunar Regolith Using the LUNAR--A Penetrators and Data Interpretation Measurements of the Thermal Properties of the Lunar Regolith Using the LUNAR--A Penetrators and Data Interpretation

Dec 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufm.p12d0519h&link_type=abstract

American Geophysical Union, Fall Meeting 2001, abstract #P12D-0519

Other

5418 Heat Flow, 5430 Interiors (8147), 5460 Physical Properties Of Materials, 5470 Surface Materials And Properties, 5494 Instruments And Techniques

Scientific paper

The two penetrators used in the LUNAR--A mission of ISAS, to be launched in 2003, will investigate the internal structure of the Moon by conducting seismic and heat--flow experiments. Heat--flow can be expressed as a product of two quantities: one is the thermal gradient ∂ T / ∂ z, the other is the thermal conductivity λ of the lunar regolith. For measuring the latter parameter, each penetrator will carry five thermal property sensors. These consist of small disc heaters in contact with the ambient regolith. The thermal response of the heater itself to the constant known power supply of approx. 50 mW serves as the data for the subsequent data interpretation. The problem of deriving the unknown thermal properties of a medium from known heat sources and temperatures is necessarily an Identification Heat Conduction Problem (IDHCP), an ill--posed inverse problem in the sense that uniqueness of the solution is not warranted. Assuming that thermal conductivity λ and heat capacity ρ c are linear functions of temperature, one can apply a Kirchhoff transformation to linearize the heat conduction equation, which minimizes computing time. Then the error functional, i.e. the difference between measured and predicted temperature response, can be minimized, thus solving for thermal dissusivity κ = λ / ρ c. In order to find the thermal diffusivity, several methods of optimization have been tested, and two algorithms are proposed: the first is a conjugate gradient method (CGM) with finite difference gradient, the second is a quasi--Newton method with bounds on the parameters. While the first method usually converges faster, the second method provides more reliable results. Model calculations revealed that the CGM is not robust if systematic errors are considered. Especially in cases where false prior assumptions with regard to the known thermal parameters of the penetrator are made, this method fails. Due to the ill--posedness of the problem, the number of parameters to be solved for should be limited. As the model calculations reveal, a homogeneous regolith allows for a fast and accurate inversion, whereas a reliable inversion of the thermal properties of a layered regolith is more difficult.

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