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A. Hagermann, S. Tanaka, S. Yoshida, A. Fujimura, H. Mizutani (ISAS, Sagamihara, Japan)
In 2003, two penetrators of the LUNAR--A mission of ISAS will investigate the internal structure of the Moon by conducting seismic and heat--flow experiments. Heat-flow is the product of thermal gradient tial T / tial z, and thermal conductivity \lambda of the lunar regolith. For measuring the thermal conductivity (or dissusivity), each penetrator will carry five thermal property sensors, consisting of small disc heaters. The thermal response Ts(t) of the heater itself to the constant known power supply of approx. 50 mW serves as the data for the subsequent data interpretation. Horai et al. (1991) found a forward analytical solution to the problem of determining the thermal inertia \lambda \rho c of the regolith for constant thermal properties and a simplyfied geometry. In the inversion, the problem of deriving the unknown thermal properties of a medium from known heat sources and temperatures is an Identification Heat Conduction Problem (IDHCP), an ill--posed inverse problem. Assuming that thermal conductivity \lambda and heat capacity \rho c are linear functions of temperature (which is reasonable in most cases), 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 the measured temperature response of the heater and the predicted temperature response, can be minimized, thus solving for thermal dissusivity \kappa= \lambda / (\rho c), wich will complete the set of parameters needed for a detailed description of thermal properties of the lunar regolith. Results of model calculations will be presented, in which synthetic data and calibration data are used to invert the unknown thermal diffusivity of the unknown medium by means of a modified Newton Method. 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.