Spherical Harmonic Representation of Earth and Mars: a Comparison Based on Order of Harmonic

Physics

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1510 Dynamo: Theories And Simulations, 1532 Reference Fields: Regional, Global, 1545 Spatial Variations: All Harmonics And Anomalies, 1560 Time Variations: Secular And Longer, 1595 Planetary Magnetism: All Frequencies And Wavelengths

Scientific paper

The variation of the power of the spherical harmonics of Earth's magnetic field as a function of degree is well known. At Earth's surface the power decreases as a function of degree until the crustal component dominates at harmonic degree ~ 13. As a function of order the power tends to decrease as higher orders of harmonic are studied. If sources are randomly distributed within a sphere, then all orders within each degree will be statistically equal in power. High orders of harmonic represent sources at low geographic latitudes, and so a field in which there is a lack of high order power represents one in which low latitude sources are less intense than high latitude sources. Thus the explanation for the reduction in power for high order harmonics in Earth's core field is that in the core, low latitude sources of field are less intense than high latitude sources. This distribution of sources is also needed to explain why the scatter of virtual geomagnetic poles (VGPs) for high latitude paleomagnetic sites is considerably larger than the scatter of VGPs for low latitude sites. The crustal component of Earth's field also shows that on average the relative power falls off within each degree for higher orders of harmonic. This implies that there is an increase in the intensity of magnetic anomalies from the equator to the poles. This can be explained if it is assumed that the magnetizations have been produced by a dipole field aligned approximately along the spin axis (i.e. similar to the present day field). A dipole field is twice as strong at the poles as at the equator. This will be the case for continental sources because it is now generally believed that the long wavelength anomalies seen at satellite altitudes are caused by induced magnetization in the lower crust and will therefore vary in intensity like the dipole field, with sources at the equator that are only half as strong as sources at the poles. For oceanic sources, remanent magnetization is much stronger than induced magnetization. But because the oceanic crust is relatively young (average age of 60 Ma) and because many of the plate motions have been roughly east-west, the average motion of the oceanic crust NS has been small. Therefore the oceanic crust should have picked up the same variation in field intensity as the continental crust, i.e. dominated by a pattern in which the equatorial magnetization is only half that at the poles. Several spherical harmonic models of the Martian magnetic field have been produced. In this case, there is no central field, but there are extremely strong crustal sources that are assumed to have been created when Mars did have a planetary dynamo and presumably a dipolar field aligned close to the spin axis. So all degrees of spherical harmonic are caused by crustal sources. The Martian harmonics show the same pattern of variation as a function of harmonic order as those on Earth. High orders of harmonic are weaker than low orders of harmonic within each degree. One explanation is that the crustal sources were magnetized with a dipolar field which was aligned along the present spin axis. This implies that there has not been much Martian polar wander since the crustal rocks were magnetized.

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