A Geomagnetic Estimate of Mean Paleointensity

To test a statistical hypothesis about Earth's magnetic field against paleomagnetism, the present field is used to estimate time averaged paleointensity. The estimate uses the modern magnetic multipole spectrum R(n), which gives the mean square induction represented by spherical harmonics of degree n averaged over the sphere of radius a = 6371.2 km. The hypothesis asserts that low degree multi-pole powers of the core-source field are distributed as chi-squared with 2n+1 degrees of freedom and expectation values \{R(n)\} = K[(n+1/2)/n(n+1)](c/a)⁽²ⁿ⁺⁴⁾, where c is the 3480 km radius of Earth's core. (This is compatible with a usually mainly geocentric axial dipolar field). Amplitude K is estimated by fitting theoretical to observational spectra through degree 12. The resulting calibrated expectation spectrum is summed through degree 12 to estimate expected square intensity \{F²\}. The sum also estimates \{F²\} averaged over geologic time, in so far as the present magnetic spectrum is a fair sample of that generated in the past by core geodynamic processes. Voorhies & Conrad (1996) excluded the dominant dipole and quadrupole from the fit, but not the sum, to predict mean paleointensity from the 1980 non-dipole field. Those predictions have a 30% standard deviation and a 9% standard error, yet are within 5% of the new estimates: \{F²\} = (37,300 nT)², an expected paleointensity \{F\} of about 34,400 nT, and an expected Virtual Axial Dipole Moment \{VADM\} of about 6.13x10²² Am². The values reflect the refined theoretical spectrum [Voorhies, 2004], self-consistent weights for all degrees 1-12, and the 41% increase in R(12) from 1980 Magsat to 2000 Oersted epochs. Both past predictions and new estimates are well within the range of published paleomagnetic determinations of mean paleointensity; therefore, the statistical hypothesis passes this test.