Equivalent source modeling of the core magnetic field using magsat data.

Abstract

An iterative least squares estimation algorithm with the capability for including a priori statistical information has been implemented to recover multiple magnetic dipole models of the Earth's main magnetic field. The dipoles are fixed to a specified radius at or below the core-mantle boundary and centered on equal area blocks. The algorithm can solve for dipole magnitudes only (fixed orientations), or allow full freedom of orientation and solve for vector components. First-order external field parameters can be estimated simultaneously, as well as magnetic observatory biases when observatory annual means data is used. Secular variation is modeled by making the dipole components linear functions of time. Single-epoch and time dependent dipole models are derived using Magsat and observatory annual means data. Equivalent spherical harmonic representations are computed in closed form from the dipole models for comparison with truncated spherical harmonic models estimated in the standard way from the same data sets. A model consisting of 93 dipoles arranged 1977 and a selected Magsat data set and is compared with candidate IGRF 1975 models and their 1984 secular variation. The equivalent dipole source representation is shown to be comparable to the standard spherical harmonic approach in accuracy and, for high resolution models, to be superior in computational efficiency for field model evaluation when three degree-of-freedom dipoles (i.e., unconstrained by direction) are utilized. Fixing of the dipole positions results in rapid convergence of the dipole solutions for single-epoch models. For time-dependent models, a sufficiently long time interval of data or a priori values and statistics must be available for the derivatives to achieve convergence. In contrast to spherical harmonic models incorporating secular variation parameters based on the same data, the correlation structure of dipole magnetic moment derivatives with the constant magnetic moment parameters is small, indicating the ability to strongly separate the constant field and the secular variation.

Planetary Magnetism

“…In addition to the field generated deep within Earth, induced and remanent magnetization in the crust can be modeled with another set of dipoles, scattered about a sphere of radius 1.0 R e to approximate sources in the crust (Mayhew and Estes, 1983). Earth's field has been approximated by adding one or more smaller dipoles to a 'main dipole' and treating the field as a summation over distinct sources; this provides a simple means of introducing an anomaly, or departure from dipole geometry.…”

Planetary Magnetism

“…The Earth's field has been approximated by an ensemble of many dipoles located on the surface of a sphere of radius 0.5R e , the fluid core radius. In addition to the field generated deep within Earth, induced and remanent magnetizations in the crust can be modeled with another set of dipoles, scattered about a sphere of radius 1.0R e to approximate sources in the crust (Mayhew and Estes, 1983). A similar approach has been taken to model the crustal magnetic field of Mars (Purucker et al, 2000).…”

Current loops fitted to geomagnetic model spherical harmonic coefficients.

“…They used fewer dipoles than MAYHEW and ESTES (1983), but they adjusted the magnetic moment, colatitude, longitude, and distance from the center of the Earth for each dipole using a non-linear least-squares method. To simplify the procedure, a common radius was used for all of the dipoles.…”

“…MAYHEW and ESTES (1983) used dipoles fixed to a specified radius at or below the core-mantle boundary centered on equal area blocks. They found that a model consisting of 93 dipoles arranged 21 degrees apart was comparable inaccuracy to the standard spherical harmonic approach.…”