Current loops fitted to geomagnetic model spherical harmonic coefficients.

Abstract

One hundred-sixty circular current loops with radial axes were fitted by least squares to the 899 spherical harmonic coefficients of a 29 th degree model. In the first case, the parameters that were fitted for each loop were the normalized magnetic moment, the distance from the center of the Earth to the current element, the colatitude and E. longitude of the loop axis, and one-half of the central apex angle of the loop. For this case, two of the loops converged near the inner-core outer-core boundary. They accounted for most of the dipolar field. Twenty of the loops, all with much smaller magnetic moments than the two deep loops, converged in the distance range of 0.42 to 0.67 Earth's radius from the center of the Earth. The other 138 loops, after many iterations, were located at distances between 0.81 and 1.0 Earth's radius from the center of the Earth. The loops with radial distances between 0.21 and 0.67 Earth's radius from the center of the Earth are referred to as “core” loops and those at distances greater than 0.81 Earth's radius as “crustal” loops. The spherical harmonic coefficients from these 160 loops, when subtraced from the 899 coefficients of the original model, left a root-mean-square residual of only 0.2nT. A second case was tried which constrained the 138 “crustal” loops to be at 0.996 Earth's radius (25.5km depth). In this case, the root-mean-square residual of the spherical harmonic coefficients from the original model was 0.9nT.