Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Details Spatial power spectra of the crustal geomagnetic field and core geomagnetic field Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Aug 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980pepi...23p...5m&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 23, Issue 2, p. P5-P19.

Physics

1

Scientific paper

Lowes (1966, 1974) has introduced the function Rn defined by Rn =(n + 1) Σm=0∞ [(gmn)2 + (hmn)2] where gnm and hnm are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = -∇V on a sphere of radius r > α is given by =Σn=1∞ Rn(a//r)2n=4 where a is the Earth's radius. We refer to Rn as the spherical harmonic spatial power spectrum of the geomagnetic field.
In this paper it is shown that Rn = RMn = RCn where the components RnM due to the main (or core) field and RnC due to the crustal field are given approximately by RMn = [(n =1)//(n + 2)](1.142 × 109)(0.288n Λ2 RCn = [(n =1){[1 - exp(-n/290)]//(n/290)} 0.52 Λ2 where Iγ = 1 nT. The two components are approximately equal for n = 15.
Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).
The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.
Equations relating average great circle power spectra of the geomagnetic field components to Rn are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the Rn for celestial bodies from average great circle power spectra of the magnetic field components.