Statistical palaeomagnetic field modelling and dynamo numerical simulation
Abstract
By relying on two numerical dynamo simulations for which such investigations are possible, we test the validity and sensitivity of a statistical palaeomagnetic field modelling approach known as the giant gaussian process (GGP) modelling approach. This approach is currently used to analyse palaeomagnetic data at times of stable polarity and infer some information about the way the main magnetic field (MF) of the Earth has been behaving in the past and has possibly been influenced by coremantle boundary (CMB) conditions. One simulation has been run with homogeneous CMB conditions, the other with more realistic nonhomogeneous symmetry breaking CMB conditions. In both simulations, it is found that, as required by the GGP approach, the field behaves as a shortterm memory process. Some severe nonstationarity is however found in the nonhomogeneous case, leading to very significant departures of the Gauss coefficients from a Gaussian distribution, in contradiction with the assumptions underlying the GGP approach. A similar but less severe nonstationarity is found in the case of the homogeneous simulation, which happens to display a more Earthlike temporal behaviour than the nonhomogeneous case. This suggests that a GGP modelling approach could nevertheless be applied to try and estimate the mean μ and covariance matrix γ(τ) (first and secondorder statistical moments) of the field produced by the geodynamo. A detailed study of both simulations is carried out to assess the possibility of detecting statistical symmetry breaking properties of the underlying dynamo process by inspection of estimates of μ and γ(τ). As expected (because of the role of the rotation of the Earth in the dynamo process), those estimates reveal spherical symmetry breaking properties. Equatorial symmetry breaking properties are also detected in both simulations, showing that such symmetry breaking properties can occur spontaneously under homogeneous CMB conditions. By contrast axial symmetry breaking is detected only in the nonhomogenous simulation, testifying for the constraints imposed by the CMB conditions. The signature of this axial symmetry breaking is however found to be much weaker than the signature of equatorial symmetry breaking. We note that this could be the reason why only equatorial symmetry breaking properties (in the form of the wellknown axial quadrupole term in the timeaveraged field) have unambiguously been found so far by analysing the real data. However, this could also be because those analyses have all assumed to simple a form for γ(τ) when attempting to estimate μ. Suggestions are provided to make sure future attempts of GGP modelling with real data are being carried out in a more consistent and perhaps more efficient way.
 Publication:

Geophysical Journal International
 Pub Date:
 June 2005
 DOI:
 10.1111/j.1365246X.2005.02613.x
 Bibcode:
 2005GeoJI.161..603B
 Keywords:

 dynamo theory;
 geomagnetism;
 geostatistics;
 palaeomagnetism;
 spherical harmonics;
 statistical methods