Joint Bayesian inference of Earth's magnetic field and core surface flow on millennial timescales

TL;DR

This work addresses millennial-scale core dynamics by jointly constraining Earth's core field and core-surface flow from archaeo-/palaeomagnetic records within a Bayesian framework. It combines a reduced, geodynamo-informed, discrete-time stochastic model with forward calculations in the spatial domain and discrete marginalisation of observation ages, avoiding convergence issues in high-dimensional HMC inversions. Synthetic tests using Earth-like geodynamo data show the method reliably recovers large-scale geomagnetic variations, westward drift, and planetary-scale eccentric gyres, illustrating the capacity of archaeomagnetic records to inform millennial-scale core dynamics when physically informed priors are used. The approach offers a pathway to real-data reconstructions, while also underscoring the importance of using multiple geodynamo priors to gauge data-driven versus prior-driven features and encouraging expansion to more sedimentary records and refined age-depth modelling.

Abstract

Understanding Earth's core dynamics over millennial timescales requires models that jointly describe the evolution of the geomagnetic field and core surface flow, while accommodating the sparse, irregular, and uncertain nature of archaeomagnetic and palaeomagnetic data. We present a new Bayesian core field and core flow modelling framework that utilises archaeo/palaeomagnetic data directly, combining a reduced stochastic representation of core surface dynamics derived from numerical geodynamo statistics with a probabilistic treatment of observational and chronological uncertainties. A key innovation is an efficient discrete marginalisation of age uncertainties, which avoids the convergence difficulties associated with co-estimating ages in high-dimensional Hamiltonian Monte Carlo inversions. The framework aims to reconstruct the coupled evolution of the geomagnetic field and core surface flow over the past 9000 years while preserving dynamical correlations implied by the prior geodynamo time series. Tests using synthetic data generated from an Earth-like geodynamo demonstrate that the method reliably recovers large-scale geomagnetic field variations and key aspects of core dynamics, including long-term westward drift and the evolution of planetary-scale eccentric gyres. These results show that, when combined with physically informed priors, archaeo/palaeomagnetic data can constrain millennial-scale core flow, paving the way for reconstructions based on real data.

Figures (13)

• Figure 1: A schematic chart of the model with data highlighted in blue, model parameters (variables) in red and transformed parameters/quantities in black (for more details see main text). The left-hand part of the chart depicts the iterative construction of the core field and core flow discrete time series, at times $t_1,...,t_{N_t}$. The right-hand part of the chart depicts the likelihood function which is split into two blocks of data: Archeomagnetic data ($k = 1, \dots, N_{ARC}$) and Sedimentary data ($k = 1, \dots, N_{SED}$, from $s = 1, \dots, N_{S}$ records).
• Figure 2: Time series and temporal power spectra of (a-f) three core flow coefficients and (g-l) three MF gauss coefficients. The Midpath prior geodynamo series (black) is compared to a 100k long random time series generated with the multivariate core flow and field process (blue), with the shaded blue areas representing the 95% range of 300 random samples. Dashed black lines show the 95% interval ($\pm 2\sigma$) of the prior dynamo series and the dashed red line shows the equivalent range from the 'white noise' term in equation \ref{['b_i+1']}. Black dot-dashed lines corresponds to a spectral index of $p = 2$ and $p = 4$, for core flow and core field coefficients respectively. Note that the differences in the power spectra towards long periods are due to the limited duration for the Midpath dynamo series.
• Figure 3: Comparison of cross-correlation matrices for various MF and SV vectors (see eq. \ref{['cov_matrices']}) empirically derived from the Midpath prior geodynamo series (left hand plot) and a 100k long random time series generated with the multivariate core field and flow process (right hand plot). For each plot the Gauss coefficients are ordered according to the following sequence: $[g_1^0,g_1^1,h_1^1,g_2^0,g_2^1,h_2^1,g_2^2,h_2^2,...,g_5^5,h_5^5]$
• Figure 4: The "prior" age-depth model for the Gyltigesjön (GYL) sediment record Snowball2013Nilsson2022. Mean model (solid black line), 95% credible interval (dashed black lines) and 50 samples drawn from the posterior (gray lines).
• Figure 5: Model-data comparison of intensity variations in (a), Central Europe (b). Western USA and (c) New Zealand. The posterior mean (solid lines) and 95% range (shaded areas) of models CFF.MP based on Midpath prior (blue) and CFF.NT based on Neutral_top1 (red) are compared to the reference (black lines). The archaeomagnetic data (black dots) were selected from radii of $10^{\circ}$ and relocated assuming an axial dipole field. Error bars denote 1-sigma uncertainties.