Statistical palaeomagnetic field modelling and dynamo numerical simulation

Abstract

International audienceBy 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 core–mantle boundary (CMB) conditions. One simulation has been run with homogeneous CMB conditions, the other with more realistic non-homogeneous symmetry breaking CMB conditions. In both simulations, it is found that, as required by the GGP approach, the field behaves as a short-term memory process. Some severe non-stationarity is however found in the non-homogeneous 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 non-stationarity is found in the case of the homogeneous simulation, which happens to display a more Earth-like temporal behaviour than the non-homogeneous 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 second-order 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 non-homogenous 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 well-known axial quadrupole term in the time-averaged 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

Observations and Models of the Long-Term Evolution of Earth’s Magnetic Field

“…Both numerical models fail to predict an axial quadrupole as strong as that inferred from inclination anomalies. On the time-average, the equatorial symmetry of numerical dynamos is not broken in models with homogeneous boundary conditions (Olson and Christensen 2002), though Bouligand et al (2005) report a statistically significant quadrupole component present in a time average of the Glatzmaier and Roberts (1995) dynamo model. Olson and Christensen (2002) further showed that the axial quadrupole component is crucially sensitive to the amount of equatorial asymmetry present in the imposed heterogeneous heat flow condition.…”

Domino model for geomagnetic field reversals

“…In our simplified spin model the dynamic equations only concern the relative angles of the spins to the rotation axis while a typical numerical dynamo deals with magnetic field, velocity, pressure and temperature. Based on the close analysis of numerical simulations [4,5,13,17,20,[34][35][36][37][38][39][40], see Fig. 9 as an example, we may nevertheless build some analogies, in particular concerning the reversal behavior.…”

A new model for the (geo)magnetic power spectrum, with application to planetary dynamo radii

“…Any extrapolation to high degree is limited by the magnetic dissipation scale, from which the spectrum is expected to rapidly decay. The spherical harmonic degree corresponding to the magnetic dissipation scale is estimated to be about 150 (Christensen and Tilgner, 2004;Buffett and Christensen, 2007;Finlay and Amit, 2011). This is much larger than the typical truncation degree of core field models and will be ignored in the following.…”

“…Time-average paleomagnetic field and paleo secular variation modeling strategies rely on a GGP description (for a review see Hulot et al, 2010). In addition, it was shown that GGP describes well the field produced by numerical dynamo models (e.g., Bouligand et al, 2005). Following this rationale, it is therefore expected that some part of the spectrum will be flat immediately above the magnetic field sources (Backus et al, 1996).…”