Thickness of the Magnetic Crust of Mars from Magneto-spectral Analysis

Previous analysis of the magnetic spectrum of Mars showed only a crustal source field [1]. The observational spectrum was fairly well fitted by the spectrum expected from random dipolar sources scattered on a spherical shell about 46 ± 10 km below Mars’ 3389.5 km mean radius. This de-correlation depth overestimates the typical depth of extended magnetized structures, and so was judged closer to mean source layer thickness than twice its value. To better estimate the thickness of the magnetic crust of Mars, six different magnetic spectra were fitted with the theoretical spectrum expected from a novel, bimodal distribution of magnetic sources. This theoretical spectrum represents both compact and extended, laterally correlated sources, so source shell depth is doubled to obtain layer thickness. The typical magnetic crustal thickness is put at 47.8 ± 8.2 km. The extended sources are enormous, typically 650 km across, and account for over half the magnetic energy at low degrees. How did such vast regions form? Observational Spectra: The magnetic spectrum of a planet is the mean square magnetic induction configured in spherical harmonics of degree n, averaged over a sphere of radius r containing the sources [2], n Rn(r) = (n + 1)(a/r) 2n+4 Σ [(gn) + (hn)]. (1) m=0 Here a denotes reference radius and (gn , hn ) the Gauss coefficients of degree n and order m in a Schmidt-normal spherical harmonic expansion of the scalar potential V: B = -∇V. Observational spectra are calculated from coefficients obtained via harmonic analysis of either measured data [3], binned data [4, 5], a map of such data [6], or fields from equivalent source models fitted to such data [7, 8]. These spectra differ, especially for n > 50, for each comes from a different analysis of variously selected MGS-MAG/ER measurements of the vector magnetic field around Mars. Theoretical Spectra: Consider a thin crust with compact, effectively dipolar, sources. If we expect dipole positions to be uncorrelated, random samples of a uniform distribution on a spherical shell of radius rx < a, and vector dipole moments to be vertical, uncorrelated, random samples of a zero mean distribution, then our expectation spectrum from an ensemble of such random radial dipoles on a shell is [1, 9]