Simple stochastic model for geomagnetic excursions and reversals reproduces the temporal asymmetry of the axial dipole moment

Abstract

We present a simple model for the axial dipole moment (ADM) of the geomagnetic field based on a stochastic differential equation for two coupled particles in a biquadratic potential, subjected to Gaussian random perturbations. This model generates aperiodic reversals and excursions separated by stable polarity periods. The model reproduces the temporal asymmetry of geomagnetic reversals, with slower decaying rates before the reversal and faster growing rates after it. This temporal asymmetry is possible because our model is out of equilibrium. The existence of a thermal imbalance between the two particles sets a preferential sense for the energy flux and renders the process irreversible.

Unveiling Geomagnetic Reversals: Insights From Tipping Points Theory

“…This suggest that our results can be reconciled with those reported by Molina‐Cardín et al. (2021) if we define the occurrence of reversals when λ < λ c and excursions when λ c < λ < λ e , with λ e ∼ 1. Thus, our simple model can be used to characterize both reversals and excursions in a simple 1‐D framework.…”

“…By further inspecting Figure 4 we clearly observe that reversals occur when λ → 0 and specifically when λ < λ c , although we report the evidence of decreasing λ with no reversals when λ > λ c . This suggest that our results can be reconciled with those reported by Molina-Cardín et al (2021) if we define the occurrence of reversals when λ < λ c and excursions when λ c < λ < λ e , with λ e ∼ 1. Thus, our simple model can be used to characterize both reversals and excursions in a simple 1-D framework.…”

“…We detect a critical threshold λ c below which a polarity reversal starts as well as an average reversal time of about 5 Kyr, in agreement with previous studies (Clement, 2004). Through the proper use of this early warning indicator λ we are able to detect the main features of polarity reversals using a non-autonomous stochastic model and reconcile our results in a similar recently-proposed framework (Molina-Cardín et al, 2021). This analysis can be the starting point to provide insight on future polarity reversals and we are confident that the proposed formalism can be helpful for building up a novel framework for paleomagnetic studies.…”

“…The results are intriguing since it is clear that when approaching a geomagnetic polarity reversal the parameter λ tends to 0. This clearly suggests that the behavior of geomagnetic polarity reversals can be described in a simple framework based on Equation , strengthening the importance of using simple stochastic models in geomagnetism and paleomagnetism (Molina‐Cardín et al., 2021; Raphaldini et al., 2021). Indeed, we are able to detect all geomagnetic polarity reversals occurring during the time interval covered by sedimentary Section 689D (i.e., approximately from 25 to 36 million years ago) by selecting a critical threshold $${\lambda }_{c}=0.3{0}_{0.20}^{0.41}$$, where 0.20 and 0.41 are the 5th and the 95th percentile of the distribution of the λ values over the set of chosen windows.…”

A Physical Interpretation of Asymmetric Growth and Decay of the Geomagnetic Dipole Moment

“…Estimates for reversal rates or dipole variance are found to converge as we bring the relevant parameters of the two models into closer agreement. We can even account for a modest asymmetry during reversals, although other models have also been proposed to reproduce this type of asymmetry (Molina‐Cardin et al., 2021). However, we cannot account for the third and higher‐order moments in the time dependence of the dipole moment using a Langevin model.…”