Dipole model of the sources of the Earth's magnetic field and secular change

Abstract

The magnitude, colatitude, longitude, and distance from the center for radial dipoles were adjusted by a least‐squares procedure so as to reproduce the surface magnetic field synthesized from the Fineh‐Leaton (F.L.) 1955 Spherical Harmonic Coefficients and for the 1965 International Geomagnetic Reference Field (IGRF). The rms residual was reduced to 28 γ using 21 dipoles for the 1955 field (6th degree and order) and to 25 γ using 35 dipoles for the IGRF (8th degree and order). These residuals include all components of the surface field. The dipole parameters were then varied using a least‐squares method to approximate the secular change field. These solutions match the Z component of secular change field synthesized from Leaton's 1955 coefficients to a rms residual of 2.15 γ per year and the IGRF secular change field to a rms residual of 1.26 γ per year. In both cases the dipole sources were found to be approximately 0.2 earth radius from the center of the earth.

Interpreting regional geomagnetic anomalies and their secular variation with the aid of radial dipoles and current loops.

“…A typical value of this distance is 80 to 90, corresponding to a radial dipole at 0.25 Re from the geocentre. This is roughly the same value as found by ALLDREDGE and STEARNS (1969) and others for global radial dipole models.…”

“…This version of the TWOD is comparable to the dipole models of HURWITZ (1964) andSTEARNS (1969): it contains a model (parameters P;) for the observed anomaly field and a model for the secular variation field (parameters Ps). The P/s obtained (see Table 6) are roughly the same as in Table 4, thus confirming conclusions made in Chapter 3.1.…”

“…MCNISH (1940), LOWES and RUNCORN (1951), LOWES (1955), ALLDREDGE and HURWITZ (1964), ALLDREDGE and STEARNS (1969). Model in which the dipoles are not necessarily radial have also been studied by ZIDAROV (1969) and ZIDAROV and BOCHEV (1969).…”

“…Equation (18), which defines the square function, differs from that used by ALLDREDGE and STEARNS (1969). They first calculated parameters Pj, j=1,... , 35, from B values, then used the linear Eq.…”

Circular Current Loops, Magnetic Dipoles and Spherical Harmonic Analyses

“…Some moderately successful efforts have been made to represent the field in terms of dipoles placed in the core (MCNISH, 1940;ALLDREDGE and HURWITZ, 1964;ALLDREDGE and STEARNS, 1969;ZIDAROV and BOCHEV, 1969) in an effort to have the model come closer to representing real sources. Dipole sources are only a first approximation to the real sources which are thought to be a very complicated network of electrical currents in the core of the Earth.…”