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 ITSS @ Geodynamics Branch

Goddard Space Flight Center, Greenbelt, MD USA 20771

purucker@geomag.gsfc.nasa.gov +1 301 614 6473

http://geodynamics.gsfc.nasa.gov/personal_pages/purucker/purucker.html

A better spherical tesselationA better spherical tesselation

Summary: Summary: There are an infinity of magnetization distributions that produce no external magnetic field, 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 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. 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 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-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 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 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 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 (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 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 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 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 field, suggesting that magnetization variations dominate over thickness variations as a cause for the Martian magnetization.magnetization.

References:References:Arkani-Hamed et al., 2002Arkani-Hamed et al., 2002

Katanforoush, A., and Shahshahani, M., 2003, Distributing Katanforoush, A., and Shahshahani, M., 2003, Distributing points on a sphere I, Experimental Mathematics, 12(2), points on a sphere I, Experimental Mathematics, 12(2), www.expmath.orgwww.expmath.org

Maus, S. and Haak, V., 2003, Geophys. J. Int.Maus, S. and Haak, V., 2003, Geophys. J. Int.

Neumann, G. et al., 2004, The crustal structure of Mars from Neumann, G. et al., 2004, The crustal structure of Mars from gravity and topography, J. Geophys. Res.-Planets, in press.gravity and topography, J. Geophys. Res.-Planets, in press.

Purucker et al., 2002, Geophys. Res. Let.Purucker et al., 2002, Geophys. Res. Let.

Runcorn, S.K., 1975, On the interpretation of lunar Runcorn, S.K., 1975, On the interpretation of lunar magnetism, Phys. Earth Plan. Int., 10, 327-335.magnetism, Phys. Earth Plan. Int., 10, 327-335.

Vestine, 1963.Vestine, 1963.

Spherical tesselations are used to create even Spherical tesselations are used to create even distributions of equivalent point dipoles on a distributions of equivalent point dipoles on a sphere. The magnetization of the individual dipoles sphere. The magnetization of the individual dipoles can be easily modified, and associated with features can be easily modified, and associated with features in the solid body, with this approach. The quality of in the solid body, with this approach. The quality of the tesselation can be tested using Runcorn’s the tesselation can be tested using Runcorn’s theorem with a spherical shell and an internal theorem with a spherical shell and an internal dipole field. This should result in zero field. The dipole field. This should result in zero field. The initial results, via an icosahedral approach (Vestine, initial results, via an icosahedral approach (Vestine, 1963) showed bands of non-zero values at the joins 1963) showed bands of non-zero values at the joins of the spherical triangles at 30 North and South of the spherical triangles at 30 North and South latitude, and near the poles (see figures at right) latitude, and near the poles (see figures at right) The S/N ratio for this tesselation is about 10 (11562 The S/N ratio for this tesselation is about 10 (11562 nodes), assessed by placing an additional single nodes), assessed by placing an additional single dipole of the same strength at the equator, and dipole of the same strength at the equator, and comparing its field with the RMS background field.comparing its field with the RMS background field.

A superior tesselation, termed the polar A superior tesselation, termed the polar coordinate subdivision (Katanforoush and coordinate subdivision (Katanforoush and Shahshahani, 2003), shows much lower magnetic Shahshahani, 2003), shows much lower magnetic field values over the sphere (see figures at right). field values over the sphere (see figures at right). The S/N ratio for this tesselation is about 100 The S/N ratio for this tesselation is about 100 (11519 nodes). The generating technique is as (11519 nodes). The generating technique is as follows:follows:

Icosahedral Icosahedral tesselationtesselation

Polar Polar coordinate coordinate subdivision subdivision tesselationtesselation

A new crustal thickness modelA new crustal thickness modelNeumann et al. (in press), have produced a new crustal Neumann et al. (in press), have produced a new crustal thickness model (right) for Mars based on gravity and thickness model (right) for Mars based on gravity and topographic constraints. Features with wavelengths in topographic constraints. Features with wavelengths in excess of 340 km are well-resolved. We use this model, and excess of 340 km are well-resolved. We use this model, and an axisymmetric dipole field oriented along the present spin an axisymmetric dipole field oriented along the present spin axis, to calculate the radial magnetic field expected at 200 axis, to calculate the radial magnetic field expected at 200 km from a Mars in which the crust is uniformly km from a Mars in which the crust is uniformly magnetized. We assume a spherical Mars for this first-magnetized. We assume a spherical Mars for this first-order exercise. order exercise.

Representative Martian magnetic field map (Arkani-Hamed Representative Martian magnetic field map (Arkani-Hamed et al.) for comparison with modelset al.) for comparison with models

Representative Martian magnetization map Representative Martian magnetization map (Whaler and Purucker, 2003)(Whaler and Purucker, 2003)

Other examples of global crustal thickness distributions, and predicted radial Other examples of global crustal thickness distributions, and predicted radial magnetic fields at 200 kmmagnetic fields at 200 km