Jc. Shao et al., Spherical harmonic analyses of paleomagnetic data: The time-averaged geomagnetic field for the past 5 Myr and the Brunhes-Matuyama reversal, J GEO R-SOL, 104(B3), 1999, pp. 5015-5030
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.