Variation of spherical harmonic power as a function of harmonic order for Earth's core and crustal magnetic field and for Mars' crustal field

[1] The variation of 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 the core surface, the spectrum is flat apart from the dipole term, and each degree contributes about equally to the power. However, as a function of order the power tends to decrease for high harmonic orders. These represent sources at low geographic latitudes, and so a field in which high-order power is low represents one in which low-latitude sources are weaker 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 the nondipole field are less intense than high-latitude sources. Earth's crustal field is represented by harmonic degrees greater than 15 and also shows the power falling off as a function of order, implying that there is an increase in the intensity of magnetic anomalies from equator to poles. This can be explained if the magnetizations have been produced by a dipole field aligned along the spin axis because such a field is twice as strong at the poles as at the equator. For the Martian field there is no central dipole source, but there are strong crustal sources that were created when Mars had a planetary dynamo and presumably an axial dipolar field. Martian harmonics show the same pattern of variation as a function of order as those on Earth. One explanation for this is that these crustal sources were magnetized with a dipolar field aligned along the present spin axis, implying that there has not been much Martian polar wander since the crust was magnetized.