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

Abstract

Abstract. 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 and the corresponding spherical harmonics was given by Maxwell. We show that the distribution of virtual geomagnetic poles (VGPs) is symmetrical about the Maxwell axes and converge to their poles. Utilizing this property of VGPs and a complimentary property of the distribution of equatorial virtual poles (EVPs), which are defined as points 90 ø from the VGP on the site meridian, leads to a means of obtaining the Gaussian spherical harmonic coefficients from paleomagnetic data. This VGP method involves the minimization of the horizontal components of the magnetic fields at VGPs and the radial components of the magnetic field at EVPs to yield the best fitting spherical harmonic coefficients. A hybrid variant of the VGP method involving this minimization and fitting the available mean vectors measured at sites has also been developed. Tests of the VGP and hybrid methods on model fields derived from the International Geomagnetic Reference Field (IGRF) 1995 demonstrate that they are effective means of determining the Gauss coefficients for any field requiring no a priori assumptions about the field. The hybrid method has been applied in a preliminary analysis of the time-averaged paleomagnetic data for the past 5 Myr and for the Bruhnes chron. The resulting mean fields were dominantly dipolar, but there were also persistent second 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: (1) a mean field model for reversed polarity, (2) a mean field model for normal polarity, (3) a mean field 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 initiated by decreases in strength of dipole, quadrupole, and octupole terms. The true dipole path of the transitional field tracks across eastern Asia, but a strong radially inward flux bundle moves over Africa. The paucity of demonstrably reliable data in these reversal records, however, requires that these results be interpreted cautiously.

Polarity Reversals from Paleomagnetic Observations and Numerical Dynamo Simulations

“…Thus the models' chronology depends on the accuracy of this age determination of the paleomagnetic data sets. As shown below, different modeling approaches (Shao et al 1999;Leonhardt and Fabian 2007; Brown colors indicate volcanic records. Sedimentary data is distinguished into sea sediments (yellow), lake sediments (light yellow) and löss (turquise).…”

“…Therefore, regularization procedures and additional assumptions about the reversal process are needed. Mazaud (1995) and Shao et al (1999) were the first to present reconstructions of transitional fields which are predominantly based on paleomagnetic data and less on assumptions about the reversal process itself. Both studies are based solely on paleomagnetic directional data from geomagnetic field reversals, namely the Olduvai/Matuyama and the last geomagnetic reversal, the Matuyama/Brunhes.…”

Evidence of a partitioned dynamo reversal process from paleomagnetic recordings in Tahitian lavas

“…Yet, by far the largest number of available records is associated with the last reversal, the Matuyama-Brunhes (M-B), and for this reason several attempts have been made to model global field behavior during this transition [e.g., Hoffman, 1981Hoffman, , 2000Love and Mazaud, 1997;Shao et al, 1999;Singer et al, 2005;Leonhardt and Fabian, 2007]. Notwithstanding the significant advances that have been provided through these analyses, the near impossibility of determining temporally synchronous behavior among globally scattered recording sites is one of many obstacles to a complete understanding of the dynamo process during this reversal.…”

“…Such a correlation offers evidence that significant features of the flux pattern emanating from the outer core remained stationary from the Plio-Pleistocene through to the present day. Apparent similarities in the location of two primary flux concentrations in the Southern Hemisphere observed in models at Earth's surface given removal of the axial dipole term (i.e., the complex, so-called non-axial dipole (NAD) field)--models deduced from both direct measurements of the present-day field and the time-averaged historic field [see Constable, 2007], as well as from paleomagnetic field measurements over the entire Brunhes Chron [Shao et al, 1999]--attest to the longevity of such a stasis.…”

The Fluid Mechanics of Astrophysics and Geophysics

“…Although dating techniques are steadily improving, it seems unlikely that it will be possible to know ages to an accuracy much better than a few thousand years. Thus the possibility of directly modeling the structure of the geomagnetic field during a reversal remains remote (although this has not stopped people from trying, Mazaud, 1995;Shao et al, 1999). There are no such dating limitations in the records of geomagnetic reversals provided by numerical geodynamo simulations.…”