Current loop models of the Earth's magnetic field

Abstract

Eleven models of the earth's magnetic field, of a new kind, were derived. They are based on sets of circular loops of filamentary electric current (current loops). Seven of the models consist of one to seven current loops that were constrained to lie on the surface of the earth's core. The other four models consist of one to four unconstrained current loops. The magnetic field of current loops was evaluated by numerical approximation of the Biot‐Savart formula. The parameters of the models were estimated by least squares using 412 uniformly distributed field vectors representing the observed field at 1975. The Marquardt nonlinear least squares method was used. Twenty preliminary computer runs, using randomly determined initial parameter values, were made for each model. Of the eleven models derived, only the one consisting of two unconstrained current loops is significantly more efficient than spherical harmonic analysis of comparable order at representing the static field. In the models consisting of four or fewer core‐surface current loops, the radii of the loops are greater than 2655 km. The currents flow generally westward and range in magnitude from 0.5 to 1.9 GA. The other core‐surface current loop models have, in addition, a small‐radius current loop in the western hemisphere and an eastward flowing current. In the models consisting of unconstrained current loops all the currents are located below the surface of the core. Their radii range from 812 to 2984 km.