**DPS 2001 meeting, November 2001**

*Session 57. Future Missions and Instruments posters*

Displayed, 9:00am Tuesday - 3:00pm Saturday, Highlighted, Saturday, December 1, 2001, 2:00-2:30pm, French Market Exhibit Hall
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## [57.17] Regolith thermal property inversion in the LUNAR-A heat-flow experiment

*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
T_{s}(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.

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