Spherical harmonic analyses of paleomagnetic data: The time-averaged geomagnetic field for the past 5 Myr and the Brunhes-Matuyama reversal

Maxwell's multiple pole theory provides the basis for a convenient means of determining the spherical harmonics of geomagnetic fields from directional paleomagnetic data. The relationship between the Maxwell poles and axes an d the corresponding spherical harmonics was given by Maxwell. We show that the distribution of virtual geomagnetic poles (VGPs) is symmetrical about t he Maxwell axes and converge to their poles. Utilizing this property of VGP s and a complimentary property of the distribution of equatorial virtual po les (EVPs), which are defined as points 90 degrees from the VGP on the site meridian, leads to a means of obtaining the Gaussian spherical harmonic co efficients from paleomagnetic data. This VGP method involves the minimizati on of the horizontal components of the magnetic fields at VGPs and the radi al components of the magnetic field at EVPs to yield the best fitting spher ical harmonic coefficients. A hybrid variant of the VGP method involving th is minimization and fitting the available mean vectors measured at sites ha s also been developed. Tests of the VGP and hybrid methods on model fields derived from the International Geomagnetic Reference Field (IGRF) 19195 dem onstrate that they are effective means of determining the Gauss coefficient s for any field requiring no a priori assumptions about the field. The hybr id method has been applied in a preliminary analysis of the time-averaged p aleomagnetic data for the past 5 Myr and for the Bruhnes chron. The resulti ng mean fields were dominantly dipolar, but there were also persistent seco nd order features, suggesting some longterm smaller-scale control over the dynamo process. The hybrid method was also applied to data from the Brunhes -Matuyama reversal. Four models were obtained: (I)a mean field model for re versed polarity, (2) a mean field model for normal polarity, (3) a mean fie ld model for the entire reversal, and (4) a time sequence field model. The results were consistent with the Americas being a persistent site of inward field lines in the nondipole field and suggested that the reversal is init iated by decreases in strength of dipole, quadrupole, and octupole terms. T he true dipole path of the transitional field tracks across eastern Asia, b ut a strong radially inward flux bundle moves over Africa. The paucity of d emonstrably reliable data in these reversal records, however, requires that these results be interpreted cautiously.