CONSTRAINING THE COMPOSITION AND THERMAL STATE OF THE MOON FROM AN INVERSION OF ELEC

Introduction. Constraining the present-day lunar ther- mal state is important as it holds the potential of providing valuable information on lunar origin and evolution. Moreover, temperature is a fundamental parameter in understanding the dynamic behaviour of the mantle in that it governs properties such as viscosity, density, convection, melting and electrical conductivity. However, there are presently few data available that directly constrain lunar thermal state and most of these provide only indirect constraints and include surface heat flow measurements (1), seismic -values inferred from the Apollo lunar seismic data (2) and maintenance of mascon anisostasy over a period of 3-4 b.y. (3). Several theoretically predicted selenotherms have been disseminated over the years (e.g. 4-8) and show considerable scatter, due to the different prior as- sumptions that are usually a prerequisite in thermal modeling. A method that, in principle, can be used to put limits on the present-day lunar temperature profile involves the use of electromagnetic sounding data, which, when inverted provide knowledge on the conductivity profile of the lunar interior (9). As mineral conductivity measured in the laboratory has been found to depend inversely on temperature, limits on the selenotherm can be derived from the inferred bounds on the lunar electrical conductivity profile when combined with lab- oratory measurements of electrical conductivity as a function of temperature. Attempts along these lines have previously been undertaken (10,11), but were limited because of, among other things, uncertainty in bulk lunar composition and in- verted electrical conductivity structure. Purpose. Building upon earlier as well as recent labo- ratory measurements of mineral electrical conductivities (e.g. 12-14) our intent here is to invert measurements of the lunar inductive response to time-varying external magnetic fields during intervals when the Moon was in the solar wind or ter- restrial magnetosheath in order to constrain the lunar thermal state and bulk chemical composition. Details are specified in (15). Briefly, given the Moon's temperature profile and com- position, equilibrium mineral modes and physical properties can be calculated by thermodynamic methods. When com- bined with laboratory electrical conductivity measurements and appropriate mixing laws, the bulk electrical conductivity of the Moon can be estimated. From a knowledge of the bulk conductivity the geomagnetic response at the lunar surface or in space can be evaluated. Whereas previous studies assumed both mineralogy, and hence compositon, and temperature as known a priori, our unknowns are composition and tempera- ture, determining all other parameters. The inverse method presented here is general and pro- vides through the unified description of phase equilibria a way of constructing planetary models where the radial variation of mineralogy and density with pressure and temperature is natu- rally specified, permitting a direct inversion for chemical com- position and temperature. Given these parameters mineralogy, Mg# (MgO/(MgO+FeO) 100) and bulk physical properties are calculated. Method of Analysis. We assume a spherically symmetric model of the Moon, which is divided into three layers whose thicknesses are variable. The three layers correspond to crust, mantle and core. The two outermost shells are described by the model parameters: thickness , composition and temper- ature . The physical properties of the core are specified by the model parameters: size, density and electrical conductiv- ity. The temperature is defined at six fixed radial nodes. To determine the mineralogical structure and corresponding mass density it is also necessary to specify the pressure profile in addition to composition and temperature.