Inferring basic parameters of the geodynamo from sequences of polarity reversals

Abstract

Abstract. The asymmetric time dependence and various statistical properties of polarity reversals of the Earth's magnetic field are utilized to infer some of the most essential parameters of the geodynamo, among them the effective (turbulent) magnetic diffusivity, the degree of supercriticality, and the relative strength of the periodic forcing which is believed to result from the Milankovic cycle of the Earth's orbit eccentricity. A time-stepped spherically symmetric α 2 -dynamo model is used as the kernel of an inverse problem solver in form of a downhill simplex method which converges to solutions that yield a stunning correspondence with paleomagnetic data.

Spectral properties of oscillatory and non-oscillatory α2-dynamos

“…changes in statistical properties of the convection caused by gradual growth of the solid inner core) are suspected to encroach/expand into the comparably simple mean field coefficients. Nevertheless, mean field modelling of reversing magnetic fields has been remarkably successful (Hoyng et al 2002, Stefani and Gerbeth 2005, Fischer et al 2009. The present work is based on the idea that a polarity change is part of an oscillation of the dominant dipole mode (Stefani et al 2007).…”

On a spectral problem in magnetohydrodynamics and its relevance for the geodynamo

“…In Fischer et al we have pursued this comparison up to the point that we identified (by means of a simplex method) a number of essential parameters of the geodynamo by matching a synthetic reversal process to various paleomagnetic reversal data. In doing so, we have carefully avoided any over‐interpretation of our simple model by focusing only on those parameters to be determined, and those functionals to be minimized, that refer to the temporal properties of reversal sequences, and not to any spatial features.…”

“…[13,14] This is in contrast to "diabolical points" [15] which are points of an accidental crossing of two or more spectral branches with an unchanged diagonal block structure of the operator and without coalescing eigenvectors. [12,14] In a series of papers, [16][17][18][19][20][21] the magnetic field dynamics in the vicinity of an exceptional point was analyzed in greater detail numerically. For this purpose a so-called mean-field dynamo model of 2 type was utilized, with a supposed spherically symmetric helical turbulence function , which is, admittedly, far away from the reality of the Earth's dynamo.…”

Forward and inverse problems in fundamental and applied magnetohydrodynamics

“…This model was later used to develop simple models of geomagnetic reversals that are just based on noise triggered jumps and relaxation oscillations in the vicinity of spectral exceptional points [59,60,61]. On this basis, a first attempt was further made to infer some of the most essential parameters of the geodynamo, such as its overcriticality and the turbulent resistivity from the temporal behavior and the statistical properties of field reversals [62].…”