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Annihilators at Mars: Are there alternative but reasonable magnetization distributions in the Martian crust that explain the MGS magnetic field observations? Spring AGU 2004 P33A-01 Michael Purucker, Raytheon Geodynamics Branch Goddard Space Flight Center, Greenbelt, MD USA A better spherical tesselation Summary: There are an infinity of magnetization distributions that produce no external magnetic field, a result demonstrated by Runcorn (1975) to bring attention to the non-uniqueness inherent in the interpretation of lunar magnetic field observations. These distributions have been given the name annihilators. Runcorn’s example, that of a spherical shell magnetized in the direction of and proportional to a magnetic field of origin internal to the shell, is not a reasonable explanation for the Mars that we think we know. Physically- based annihilators exist for the terrestrial case (Maus et al., 2003) but these are not appropriate for the Martian case because of the absence of a dominant present day core field. On the earth, comprehensive crustal thickness models predict many of the first order features of the crustal magnetic field seen from space (Purucker et al, 2002). A new crustal thickness model of Mars (Neumann et al., 2004), seen through an improved spherical tesselation (Katanforoush and Shahshahani, 2003), is used as a starting point to examine potentially reasonable magnetization distributions that might give insight into the distribution of Martian magnetization. The new crustal thickness model of Mars predicts few, if any, features of the Martian magnetic field, suggesting that magnetization variations dominate over thickness variations as a cause for the Martian magnetization. References: Arkani-Hamed et al., 2002 Katanforoush, A., and Shahshahani, M., 2003, Distributing points on a sphere I, Experimental Mathematics, 12(2), Maus, S. and Haak, V., 2003, Geophys. J. Int. Neumann, G. et al., 2004, The crustal structure of Mars from gravity and topography, J. Geophys. Res.-Planets, in press. Purucker et al., 2002, Geophys. Res. Let. Runcorn, S.K., 1975, On the interpretation of lunar magnetism, Phys. Earth Plan. Int., 10, Vestine, Spherical tesselations are used to create even distributions of equivalent point dipoles on a sphere. The magnetization of the individual dipoles can be easily modified, and associated with features in the solid body, with this approach. The quality of the tesselation can be tested using Runcorn’s theorem with a spherical shell and an internal dipole field. This should result in zero field. The initial results, via an icosahedral approach (Vestine, 1963) showed bands of non-zero values at the joins of the spherical triangles at 30 North and South latitude, and near the poles (see figures at right) The S/N ratio for this tesselation is about 10 (11562 nodes), assessed by placing an additional single dipole of the same strength at the equator, and comparing its field with the RMS background field. A superior tesselation, termed the polar coordinate subdivision (Katanforoush and Shahshahani, 2003), shows much lower magnetic field values over the sphere (see figures at right). The S/N ratio for this tesselation is about 100 (11519 nodes). The generating technique is as follows: Icosahedral tesselation Polar coordinate subdivision tesselation A new crustal thickness model Neumann et al. (in press), have produced a new crustal thickness model (right) for Mars based on gravity and topographic constraints. Features with wavelengths in excess of 340 km are well-resolved. We use this model, and an axisymmetric dipole field oriented along the present spin axis, to calculate the radial magnetic field expected at 200 km from a Mars in which the crust is uniformly magnetized. We assume a spherical Mars for this first-order exercise. Representative Martian magnetic field map (Arkani-Hamed et al.) for comparison with models Representative Martian magnetization map (Whaler and Purucker, 2003) Other examples of global crustal thickness distributions, and predicted radial magnetic fields at 200 km

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