Limitations on the parameters of the solar wind in modelling lunar electromagnetic induction

Abstract

A striking feature of the day-side response of the Moon to periodic fluctuations in the solar wind is the rapid rise, and subsequent fall, in the amplitude of the transfer function as the inducing field frequency increases. This behaviour can be characterized by the amplitude values at the two frequencies 24 and 40mHz. Before the response of a conductivity model representing the Moon can be calculated at a given frequency, the parameters (u, 0) (where u is the solar wind speed and 0 is the angle between the solar wind velocity and the magnetic field propagation direction) have to be specified. By applying some results due to Parker (1972) to the above two data points, we have determined constraints on the parameter space (u, 0). In particular, we determine the region of the (u, 8) space in which conductivity models may be found that satisfy our data pair. Outside this region, there are no conductivity models satisfying the data pair, and hence many (u, 0) values are inconsistent with the original data and the model assumptions.

Electromagnetic induction in the Moon

“…Though this includes Kallman filtering in attempting to also isolate noise sources, the technique demands a priori model assumptions. The application of Backus-Gilbert resolution tests to the inferred conductivity profile [Hobbs, 1973[Hobbs, , 1977Hobbs and Parker, 1978;Phillips, 1972] seems premature at the present time; forward calculations over a spread of parameterized values of k and vp appear to suffice for determining the limits on spatial resolution and conductivity . As details of the conductivity profile and the issue of core existence (and radius) of geophysical importance rest upon accuracy in response to (O)10 -2 and better, this requires the ability to compute spectra to a corresponding level of accuracy as well as the ability to identify and remove noise sources and to understand subtleties in the induction process, some of which have probably still not been identified with confidence.…”

“…The theory of TE induction, extended upward beyond wavelengths satisfying 2•rrM/X < 1 (the upper limit of the quasi-static approximation), requires additional details of geometry and makes contact for the first time with classical scattering theory [Schubert and Schwartz, 1972;Sonett and Colburn, 1974;Leavy, 1975;Hobbs and Parker, 1978].…”