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

Abstract

Paleomagnetic observations offer insights into the origin of the geomagnetic field. Limited spatial resolution often restricts attention to the axial dipole component of the field, but quantitative information can be extracted from its time dependence. The most dramatic changes in the dipole are connected with geomagnetic reversals (e.g., Valet & Fournier, 2016). A record of geomagnetic reversals over the past 180 Ma is constructed from measurements of marine magnetic anomalies (Cande & Kent, 1995;Kent & Gradstein, 1986). Finer details are recovered from high-resolution observations of "tiny wiggles" in seafloor magnetization. Globally coherent variations are commonly attributed to changes in paleointensity (Cande & Kent, 1992;Gee et al., 2000). Complementary information is recorded as paleomagnetic directions and relative intensities in marine sediments (Roberts et al., 2013). Stacks of relative paleointensity, calibrated using absolute paleointensity from igneous rocks, establish quantitative models for the virtual axial dipole moment (VADM) over the past 2 Ma (Valet et al., 2005;.Several forms of asymmetry are evident in the time dependence of the dipole field. Relative paleointensities before and after reversals often reveal a slow decline into the reversal, followed by a more rapid rise back to a background level (e.g., Meynadier et al., 1994). This asymmetry is evident in estimates of VADM during the Brunhes-Matuyama reversal (Figure 1) from the PADM2M model of . A decline of the VADM from the long-term time average occurs prior to the reversal at t = 0.78 Ma. A more rapid rise after the

Asymmetric Dipole Trends in Geodynamo Models and the Paleomagnetic Field

“…We now turn to the question of what the stochastic model tells us about the paleomagnetic field. Skewness of dipole trends from PADM2M is nominally s ≈ 0.5 for time windows around w = 20 kyr (Buffett et al, 2022). Similar conclusions were drawn by Avery et al (2017), based on the statistics of the time derivative of PADM2M after filtering the record to remove periods shorter than 20-30 kyr.…”

“…These are the relevant time windows for observations of skewness in the paleomagnetic record (Avery et al., 2017). Low levels of skewness in the paleomagnetic record for short windows ( w < 10 kyr) have been attributed to the influence of measurement error (Buffett et al., 2022). Such low values at short w are not observed (or expected) in the geodynamo models.…”

“…We now turn to the question of what the stochastic model tells us about the paleomagnetic field. Skewness of dipole trends from PADM2M is nominally s ≈ 0.5 for time windows around w = 20 kyr (Buffett et al., 2022). Similar conclusions were drawn by Avery et al.…”

“…Once the parameters of the stochastic model are defined we are able to directly calculate the coefficients of the Kramers-Moyal expansion for the probability distribution p(x, t). Explicit expressions for the coefficients have previously been derived for the stochastic model with δ-function convection events (Buffett et al, 2022). The relevant coefficients for present purposes include the diffusion coefficient, D 2 ,…”

Evidence for Turbulent Magnetic Diffusion in Earth's Core

“… Autocorrelation function for the PADM2M paleomagnetic model (Ziegler et al., 2011) compared with the predictions of a stochastic model (Buffett et al., 2022) using two different values for the dipole decay time τ d . …”