Equivalent Source Modeling of the Core Magnetic Field Using Magsat Data

抄録

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 21° apart was computed based on observatory annual means data from 1974 through 1977 and a selected Magsat data set and is compared with candidate IGRF 1975 models and their 1980 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.