Secular Acceleration Research Articles

Dynamic evolution of amplitude and position of geomagnetic secular acceleration pulses since 2000

Recent studies on the behavior of geomagnetic secular acceleration (SA) pulses have provided a basis for understanding the dynamic processes in the Earth’s core. This analysis statistically evaluates the evolution of the SA pulse amplitude and position since 2000 by computing the three-year difference in SA with the CHAOS-7 geomagnetic field model (CHAOS-7.17 release). Furthermore, the study explores the correlation between the acceleration pulse amplitude and geomagnetic jerks and the dynamic processes of alternating variation and polarity reversal of pulse patches over time. Research findings indicate that the variation in pulse amplitude at the Core Mantle Boundary (CMB) closely resembles that observed at the Earth’s surface, with an average period of 3.2 years. The timing of peak pulse amplitude aligns with that of the geomagnetic jerk, suggesting its potential utility as a novel indicator for detecting geomagnetic jerk events. The acceleration pulses are the strongest near the equator (2°N) and more robust in the high-latitude region (68°S) of the Southern Hemisphere, indicating that the variation is more dramatic in the Southern Hemisphere. The acceleration pulses fluctuate unevenly in the west-east direction, with characteristics of local variation. In the Western Hemisphere, the pulse patches are distributed near the equator, exhibiting an evident westward drifting mode. The positive and negative patches alternate in time, displaying a polarity reversal in the west-east direction, with an average interval of approximately 32°. These characteristics can be attributed to the rapid magnetic field fluctuations disclosed by the model of stratification at the top of the Earth’s core. In the Eastern Hemisphere, the pulses are weaker between 10°E and 60°E, with the most active pulses occurring around 80°E to 105°E and near 150°E. The pulse patches exhibit a broader distribution in the north-south direction, with relatively strong patches still occurring near 40°N and 40°S. These local variation characteristics match the actual cases of zonal flows and geostrophic Alfvén waves in the Earth’s core.

Geomagnetic jerks observed in geomagnetic observatory data over southern Africa between 2017 and 2023

Abstract Geomagnetic jerks are jumps observed in the second derivative of the main magnetic field that occur on annual to decadal timescales. Understanding these jerks is crucial as they provide valuable insights into the complex dynamics of the Earth’s outer liquid core. In this study, we investigate the occurrence of geomagnetic jerks in geomagnetic observatory data collected at southern African magnetic observatories, Hermanus (HER), Tsumeb (TSU), Hartebeesthoek (HBK) and Keetmanshoop (KMH) between 2017 and 2023. The observatory data was processed and analysed by retaining quiet night-time data recorded during quiet geomagnetic activities with the help of planetary K (Kp), Disturbance storm time (Dst) and ring current (RC) indices. Results confirm the occurrence of 2019 to 2020 geomagnetic jerk in the region, and identify the recent 2021 jerk detected with V-shaped secular variation changes in X and Z components at all four observatories. The highest estimated 2021 jerk secular acceleration amplitudes in X and Z components were found at HBK, 12.7 nT/year2 and 19.1 nT/year2, respectively. Notably, the global CHAOS-7 model aptly identifies this 2021 jerk in the Z component at all magnetic observatories in the region.

Dynamic Mode Decomposition of the Core Surface Flow Inverted From Geomagnetic Field Models

AbstractContinuous satellite measurements of the Earth's magnetic field have advanced the characterization of spatial‐temporal variations of the main field over the past two decades. To comprehend the underlying mechanism responsible for the geomagnetic field variations, we develop a novel core surface flow inversion scheme based on physics‐informed neural networks. The inversion method can account for the secular variation contributed by the interaction between the core flow and undetectable small‐scale magnetic fields. Based on the novel inversion framework, we derive a time‐dependent core surface flow model between 2000 and 2022 from the CHAOS‐7 core field model. The inverted core flow is then analyzed using the dynamic mode decomposition to extract wave‐like fluid motions. By calculating the magnetic secular acceleration contributed by each dynamic mode, we identify that the dynamic modes with period of about 10 and 7 years are responsible for geomagnetic jerks in the Atlantic and Pacific equatorial regions.

Excitation of high-latitude MAC waves in Earth’s core

SUMMARY Recent geomagnetic observations reveal localized oscillations in the field’s secular acceleration at high latitudes, with periods of about 20 yr. Several types of waves in rotating magnetized fluids have been proposed to explain equatorial oscillations with similar high frequencies. Among these are non-axisymmetric Alfvén waves, magneto-Coriolis waves and, in the presence of fluid stratification, magnetic-Archimedes–Coriolis (MAC) waves. We explore the hypothesis that the observed high latitude patterns are the signature of MAC waves by modelling their generation in Earth’s core. We quantitatively assess several generation mechanisms using output from dynamo simulations in a theoretical framework due to Lighthill. While the spatio-temporal structure of the sources from the dynamo simulations are expected to be realistic, their amplitudes are extrapolated to reflect differences between the simulation’s parameter space and Earth-like conditions. We estimate full wave spectra spanning monthly to centennial frequencies for three plausible excitation sources: thermal fluctuations, Lorentz force and magnetic induction. When focusing on decadal frequencies, the Lorentz force appears to be most effective in generating high-latitude MAC waves with amplitude estimates falling within an order of magnitude of observed oscillations. Overall, this study puts forward MAC waves as a viable explanation, in the presence of fluid stratification at the top of Earth’s core, for observed field variations at high latitudes.

Dynamic mode decomposition of the geomagnetic field over the last two decades

Earth's magnetic field, which is generated in the liquid outer core through the dynamo action, undergoes changes on timescales of a few years to several million years, yet the underlying mechanisms responsible for the field variations remain to be elucidated. In this study, we apply a novel data analysis technique developed in fluid dynamics, namely the dynamic mode decomposition, to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available. The dominant dynamic modes are extracted by solving an eigen-value problem, so one can identify modes with periods longer than the time span of data. Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration, justifying the validity of applying the dynamic mode decomposition method to geomagnetic field. We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years, a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years. These modes are possibly related to magnetohydrodynamic waves in the Earth's outer core.

Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of E and B

For an axisymmetric tokamak plasma, Hamiltonian theory predicts that the orbits of charged particles must stay on invariant tori of conserved energy in the moving frame of reference of a wave that propagates along the torus with fixed angular phase velocity, amplitude, and shape. The mode structure in the poloidal plane is arbitrary if the fluctuations are expressed in terms of potentials Φ and A, which satisfy Faraday's law and the solenoidal condition by definition. Consequently, smoothing operations (such as gyroaveraging and noise suppression) do not violate the conservative laws. However, this is not guaranteed for models expressed in terms of the physical fields E and B. Here, we demonstrate that manipulations of E and B in the poloidal (R, z) plane can cause spurious heating that is independent of time steps or numerical methods, but can be sensitive to geometry. In particular, we show that secular acceleration is enhanced when one imposes nonnormal modes that possess strong up–down asymmetry instead of the usual in–out asymmetry of normal toroidal (eigen)modes. We compare full gyro-orbit and guiding center models and find similar behavior. We also examine the effect of ad hoc N-point gyroaveraging in a guiding center model, as is done in some simulation codes. If one uses Faraday's law to (re)compute B(t) after gyroaveraging E, the guiding center motion remains conservative. Otherwise, spurious heating should be expected and monitored, but it may be tolerable when normal modes dominate.

Tidal Constraints on the Martian Interior

AbstractWe compare several recent Martian interior models and evaluate how these are impacted by the tidal constraints provided by the Love number k2 and the secular acceleration in longitude s of its main moon, Phobos. The expression of the latter is developed up to harmonic degree 5 to match the accuracy of the current observations. We match a number of current interior structure models to the recent measurements of the tidal parameters and derive estimations of the possible core radius, temperature profile, and attenuation in the Martian interior. Our estimation of the core radius is 1,820 ± 80 km, consistent with recent seismic measurements. The attenuation profiles in the Martian interior at the main tidal period of Phobos are similar between the considered models, giving a range for the degree‐2 bulk tidal attenuation Q2 = 93.0 ± 8.40 but diverge at seismic frequencies. At seismic frequencies, model shear attenuation Qμ ranges between 100 and 4,000 in the lower mantle, so that a measurement of seismic shear attenuation could be used as an effective means for distinguishing between the models considered. Other constraints such as elastic lithosphere thickness and Chandler Wobble period favor a thicker elastic lithosphere and models with a frequency dependence α of the shear attenuation between 0.15 and 0.4. Improved constraints on the Martian interior should be possible with additional seismic and radio observations from the InSight mission.

Classical and relativistic n-body problem: from Levi-Civita to the most advanced interplanetary missions

The n-body problem is one of the most important issue in Celestial Mechanics. This article aims to retrace the historical and scientific events that led the Paduan mathematician, Tullio Levi-Civita, to deal with the problem first from a classic and then a relativistic point of view. We describe Levi-Civita's contributions to the theory of relativity focusing on his epistolary exchanges with Einstein, on the problem of secular acceleration and on the proof of Brillouin's cancellation principle. We also point out that the themes treated by Levi-Civita are very topical. Specifically, we analyse how the mathematical formalism used nowadays to test General Relativity can be found in Levi-Civita's texts and evolves over the years up to the current Parametrized version of the Post-Newtonian approximation (PPN) which is used in high precision contexts such as important space missions designed also to test General Relativity and which aim to estimate with very high accuracy the PPN parameters.

Signs of a new geomagnetic jerk between 2019 and 2020 from Swarm and observatory data

Following the observed pattern of a new geomagnetic jerk every 3–4 years, certain predictions suggested that a new event should occur around 2020 after the one observed around 2017.5. In this work, we explore this scenario by analysing the secular variation of the East geomagnetic field component in both ground and satellite geomagnetic data. At ground, we use the available data from 2015 to 2021 in 10 observatories worldwide distributed. This analysis shows the occurrence of the mentioned jerk in mid-2017 at observatories located in the Pacific region, but also reveals a new jerk between mid-2019 and early 2020 with a clear global character. Swarm satellite data also corroborate these findings by means of the secular variation estimated using virtual observatories at 440 km altitude. In addition, a general view using the most recent CHAOS geomagnetic model confirms the global character of the 2020-jerk with V-shaped secular variation changes in meridional sectors covering the Eastern Pacific, America, Asia and the Indian Ocean; and Λ-shapes in Europe, Africa and Western Pacific. The radial geomagnetic field at the core–mantle boundary is investigated as the origin of the new jerk. Results show that the global-average secular acceleration of the radial field exhibits a new pulse at mid-2018, establishing the starting epoch of the 2020-jerk.

Applications for CryoSat-2 satellite magnetic data in studies of Earth\u2019s core field variations

We use 20 years of continuous magnetic field measurements from the Ørsted, CHAMP and Swarm satellite missions, supplemented by calibrated platform magnetometer data from the CryoSat-2 satellite, to study time variations of the Earth’s core field at satellite altitude and at the core–mantle boundary (CMB). From the satellite data we derive composite time series of the core field secular variation (SV) with 4-month cadence, at 300 globally distributed Geomagnetic Virtual Observatories (GVO). A previous gap in the GVO series between 2010 and 2014 is successfully filled using CryoSat-2, and sub-decadal variations are identified during this period. Tests showed that similar sub-decadal SV patterns were obtained from the CryoSat-2 data regardless of whether IGRF-13 or CHAOS-6x9 was used in their calibration. Cryosat-2 radial field SV series at non-polar latitudes have a mean standard deviation level compared to smoothing spline fits of 3.5 nT/yr compared to 1.8 nT/yr for CHAMP and 0.9 nT/yr for Swarm. GVO radial SV series display regional fluctuations with 5–10 years duration and amplitudes reaching 20 nT/yr, most notably at low latitudes over Indonesia (2014), over South America and the South Atlantic (2007, 2011 and 2014), and over the central Pacific (2017). Applying the Subtractive Optimally Localized Averages (SOLA) method, we also map the radial SV at the CMB as a collection of locally averaged SV estimates. We demonstrate that using 2-year windows of CryoSat-2 data, it is possible to reliably estimate the SV and its time derivative, the secular acceleration (SA), at the CMB, with a spatial resolution, corresponding to spherical harmonic degree 10. Along the CMB geographic equator, we find strong SA features with amplitude pm 2.5mu mathrm{T}/mathrm{yr}^2 under Indonesia from 2011–2014, under central America from 2015 to 2019, and sequences of SA with alternating sign under the Atlantic during 2004–2019. We find that platform magnetometer data from CryoSat-2 make a valuable contribution to the emerging picture of sub-decadal core field variations. Using 1-year windows of data from the Swarm satellites, we show that it is possible to study SA changes at low latitudes on timescales down to 1 year, with spatial resolution corresponding to spherical harmonic degree 10. We find strong positive and negative SA features appearing side-by-side in the Pacific in 2017, and thereafter drift westward.

The BGS candidate models for IGRF-13 with a retrospective analysis of IGRF-12 secular variation forecasts

The three candidate models submitted by the British Geological Survey for the 13th generation International Geomagnetic Reference Field are described. These DGRF and IGRF models are derived from vector and scalar magnetic field data from the European Space Agency Swarm satellites and ground observatories, covering the period 2013.9 to 2019.7. The internal field model has time dependence for degrees 1 to 15, represented by order 6 B-splines with knots at six monthly intervals. We also solve for a degree 1 external field time dependence describing annual and semi-annual signals with additional dependence on a bespoke Vector Magnetic Disturbance index. Satellite data are weighted by spatial density, along-track standard deviations, and a larger-scale noise estimator defined in terms of a measure of Local Area Vector Activity at the geographically closest magnetic observatories to the sampled datum. Forecasting of the magnetic field secular variation for 2020–2025 is by advection of the main field using steady core surface flows with steady acceleration applied. We also investigate the performance of the previous generation of candidate secular variation models, for IGRF-12, analysing the agreement of the candidates between 2015 and 2020 with the retrospective IGRF-13. We find that there is no clear distinction between the performance of mathematically and physically extrapolated forecasts in the period 2015–2020. We confirm that the methodology for the BGS IGRF-12 predictions performed well, despite observed secular accelerations that are highlighted by our analysis, and thus justify the methodology used for our IGRF-13 SV candidate.

Co-estimating geomagnetic field and calibration parameters: modeling Earth\u2019s magnetic field with platform magnetometer data

Models of the geomagnetic field rely on magnetic data of high spatial and temporal resolution to give an accurate picture of the Earth’s internal magnetic field and its time-dependence. The magnetic data from low-Earth orbit satellites of dedicated magnetic survey missions such as CHAMP and Swarm play a key role in the construction of such models. Unfortunately, there are no magnetic data available from such satellites after the end of the CHAMP mission in 2010 and before the launch of the Swarm mission in late 2013. This limits our ability to recover signals on timescales of 3 years and less during this gap period. The magnetic data from platform magnetometers carried by satellites for navigational purposes may help address this data gap provided that they are carefully calibrated. Earlier studies have demonstrated that platform magnetometer data can be calibrated using a fixed geomagnetic field model as reference. However, this approach can lead to biased calibration parameters. An alternative approach has been developed in the form of a co-estimation scheme which consists of simultaneously estimating both the calibration parameters and a model of the internal part of the geomagnetic field. Here, we go further and develop a scheme, based on the CHAOS field modeling framework, that involves co-estimation of both internal and external geomagnetic field models along with calibration parameters of platform magnetometer data. Using our implementation, we are able to derive a geomagnetic field model spanning 2008 to 2018 with satellite magnetic data from CHAMP, Swarm, secular variation data from ground observatories, and platform magnetometer data from CryoSat-2 and the GRACE satellite pair. Through a number of experiments, we explore correlations between the estimates of the geomagnetic field and the calibration parameters, and suggest how these may be avoided. We find evidence that platform magnetometer data provide additional information on the secular acceleration, especially in the Pacific during the gap between CHAMP and Swarm. This study adds to the evidence that it is beneficial to use platform magnetometer data in geomagnetic field modeling.

South Atlantic Anomaly Areal Extent as a Possible Indicator of Geomagnetic Jerks in the Satellite Era

Geomagnetic jerks are sudden changes in the geomagnetic field secular variation related to changes in outer core flow patterns. Finding geophysical phenomena related to geomagnetic jerks provides a vital contribution to better understand the geomagnetic field behavior. Here, we link the geomagnetic jerks occurrence with one of the most relevant features of the geomagnetic field nowadays, the South Atlantic Anomaly (SAA), which is due to the presence of reversed flux patches (RFPs) at the Core-Mantle Boundary (CMB). Our results show that minima of acceleration of the areal extent of SAA calculated using the CHAOS-7 model (CHAOS-7.2 release) coincide with the occurrence of geomagnetic jerks for the last 2 decades. In addition, a new pulse in the secular acceleration of the radial component of the geomagnetic field has been observed at the CMB, with a maximum in 2016.2 and a minimum in 2017.5. This fact, along with the minimum observed in 2017.8 in the acceleration of the areal extent of SAA, could point to a new geomagnetic jerk. We have also analyzed the acceleration of the areal extent of South American and African RFPs at the CMB related to the presence of the SAA at surface and have registered minima in the same periods when they are observed in the SAA at surface. This reinforces the link found and would indicate that physical processes that produce the RFPs, and in turn the SAA evolution, contribute to the core dynamics at the origin of jerks.

Average nonlinear dynamics of particles in gravitational pulses: Effective Hamiltonian, secular acceleration, and gravitational susceptibility

Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton's equations. We derive the Hamiltonian of this "ponderomotive" dynamics to the second order in the GW amplitude for a general background metric. For the special case of vacuum GWs, we show that our Hamiltonian is equivalent to that of a free particle in an effective metric, which we calculate explicitly. We also show that already a linear plane GW pulse displaces a particle from its unperturbed trajectory by a finite distance that is independent of the GW phase and proportional to the integral of the pulse intensity. We calculate the particle displacement analytically and show that our result is in agreement with numerical simulations. We also show how the Hamiltonian of the nonlinear averaged dynamics naturally leads to the concept of the linear gravitational susceptibility of a particle gas with an arbitrary phase-space distribution. We calculate this susceptibility explicitly to apply it, in a follow-up paper, toward studying self-consistent GWs in inhomogeneous media within the geometrical-optics approximation.

Decomposition of Geomagnetic Secular Acceleration Into Traveling Waves Using Complex Empirical Orthogonal Functions

AbstractSatellite observations reveal short pulses in the second time derivative of the geomagnetic field. We seek to interpret these signals using complex empirical orthogonal functions (CEOFs). This methodology decomposes the signal into traveling waves, permitting estimates for the period, angular wave number, and phase velocity. We recover CEOFs from the CHAOS‐6 model, focusing on three geographic regions with strong secular acceleration. Two regions are confined to the equator, while the third is located under Alaska. We find evidence for both eastward and westward traveling waves with periods between 7 and 20 years. There is also evidence for weaker standing waves with complex spatial patterns. Two of the three regions have waves that are compatible with predictions for waves in a stratified fluid. Our results yield estimates for the structure of fluid stratification at the top of the core.

An elastic model of Phobos’ libration

Context. Study the rotation of a celestial body is an efficient way to infer its interior structure, and then may give information of its origin and evolution. In this study, based on the latest shape model of Phobos from Mars Express (MEX) mission, the polyhedron approximation approach was used to simulate the gravity field of Phobos. Then, the gravity information was combined with the newest geophysical parameters such as GM and k2 to construct the numerical model of Phobos’ rotation. And with an appropriate angles transformation, we got the librational series respect to Martian mean equator of date. Aims. The purpose of this paper is to develop a numerical model of Phobos’ rotational motion that includes the elastic properties of Phobos. The frequencies analysis of the librational angles calculated from the numerical integration results emphasize the relationship between geophysical properties and dynamics of Phobos. This work will also be useful for a future space mission dedicated to Phobos. Methods. Based on the latest shape model of Phobos from MEX mission, we firstly modeled the gravity field of Phobos, then the gravity coefficients were combined with some of the newest geophysical parameters to simulate the rotational motion of Phobos. To investigate how the elastic properties of Phobos affect its librational motion, we adopted various k2 into our numerical integration. Then the analysis was performed by iterating a frequency analysis and linear least-squares fit of Phobos’ physical librations. From this analysis, we identified the influence of k2 on the largest librational amplitude and its phase. Results. We showed the first ten periods of the librational angles and found that they agree well with the previous numerical results which Phobos was treated as a perfectly rigid body. We also found that the maximum amplitudes of the three parameters of libration are also close to the results from a rigid model, which is mainly due to the inclination of Phobos and moments of inertia. The other amplitudes are slightly different, since the physics contained in our model is different to that of a previous study, specifically, the different low-degree gravity coefficients and ephemeris. The libration in longitude τ has the same quadratic term with previous numerical study, which is consistent with the secular acceleration of Phobos falling onto Mars. We investigated the influence of the tidal Love number k2 on Phobos’ rotation and found a detectable amplitude changes (0.0005°) expected in the future space mission on τ, which provided a potential possibility to constrain the k2 of Phobos by observing its rotation. We also studied the influence of Phobos’ orbit accuracy on its libration and suggested a simultaneous integration of orbit and rotation in future work.

Geomagnetic secular variation changes in Southern Africa during the SWARM period 2013 - 2018

Geomagnetic field observations from 4 magnetic observatories located in Southern Africa located at Hermanus (HER), Hartebeesthoek (HBK), Keetmanshoop (KMH) and Tsumeb (TSU) have been analysed with the main purpose to identify abrupt secular variation changes on time scales of less than 1 year. Removal of an annual variation resulting from large-scale magnetospheric and ionospheric currents by means of 12-month differences of the respective observatory monthly mean of northward component X, eastward component Y and vertical component Z, revealed clear evidence of several geomagnetic secular variation changes that took place in this region during the period between 2013 and 2018. The geomagnetic field model CHAOS6-x7, based exclusively on SWARM satellite and magnetic observatory data during this period, has been used to determine secular acceleration patterns across Southern Africa. The results obtained revealed that the observed secular variation changes took place over a range of strengths in the respective X, Y and Z components at every magnetic observatory. In addition, the respective observatories in the region also exhibited strong individual characteristics. The findings in this investigation show once again that the southern African region is characterised by unpredictable abrupt geomagnetic secular variation changes that have the potential to render linear prediction models less accurate.

Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth’s core surface

Geomagnetic jerks are abrupt changes in the second time derivative—the secular acceleration—of Earth’s magnetic field that punctuate ground observatory records. As their dynamical origin has not yet been established, they represent a major obstacle to the prediction of geomagnetic field behaviour for years to decades ahead. Recent jerks have been linked to short-lived, temporally alternating and equatorially localized pulses of secular acceleration observed in satellite data, associated with rapidly alternating flows at Earth’s core surface. Here we show that these signatures can be reproduced in numerical simulations of the geodynamo that realistically account for the interaction between slow core convection and rapid hydromagnetic waves. In these simulations, jerks are caused by the arrival of localized Alfven wave packets radiated from sudden buoyancy releases inside the core. As they reach the core surface, the waves focus their energy towards the equatorial plane and along lines of strong magnetic flux, creating sharp interannual changes in core flow and producing geomagnetic jerks through the induced variations in magnetic field acceleration. The ability to numerically reproduce jerks offers a new way to probe the physical properties of Earth’s deep interior. Geomagnetic jerks in the Earth’s magnetic field are caused by the arrival of hydromagnetic waves and could be generated by sudden releases of buoyancy in the Earth’s core, suggest geodynamic numerical model simulations.

Geomagnetic jerk features produced using synthetic core flow models

Geomagnetic jerks are the shortest temporal variations of the magnetic field generated in the Earth's core. The physical mechanism producing such abrupt changes as well as their spatio-temporal characteristics are not well understood. In order to explore geomagnetic jerks generation and their characteristics, we use a set of synthetic core flow models to solve the radial magnetic induction equation. We analyze changes of trend in the secular variation time series using a cubic polynomial fit, by invoking a new formalism of jerk amplitude per unit duration time. A new visualization scheme allows interpreting jerk amplitudes and occurrences in space and time. We find that a mild time-dependence of flow amplitude, while keeping a fixed pattern, reproduces geomagnetic jerk amplitudes. The polynomial fits were compared with two line-segments fits at ten sampled magnetic observatories about historical jerk occurrences. The differences between the misfits in the two approaches are small, which may question the definition of geomagnetic jerks as sharp “V-shape”. The local time series in our models exhibit secular acceleration changes of sign that reproduce some main observed characteristics of geomagnetic jerks: (i) a range of amplitudes that encompass those observed in geomagnetic jerks, (ii) non-simultaneous occurrence, (iii) non-global occurrence, (iv) spatial variability of amplitudes and (v) strongest amplitudes in the radial component.

Geomagnetic acceleration and rapid hydromagnetic wave dynamics in advanced numerical simulations of the geodynamo

Geomagnetic secular acceleration is a unique window on the dynamics taking place in Earth's core. In this study, the behaviours of the secular acceleration and underlying core dynamics are examined in new numerical simulations of the geodynamo that reside on a theoretical path in parameter space connecting the region where most classical models are found to the natural conditions. The typical time scale for geomagnetic acceleration is found to be invariant along this path, at a value close to 10 years that matches Earth's core estimates. Despite this invariance, the spatio-temporal properties of secular acceleration show significant variability along the path, with an asymptotic regime of rapid rotation reached after 30% of this path (corresponding to a model Ekman number $E=3~10^{-7}$). In this regime, the energy of secular acceleration is entirely found at periods longer than that of planetary rotation, and the underlying flow acceleration patterns acquire a two-dimensional columnar structure representative of the rapid rotation limit. The spatial pattern of the secular acceleration at the core-mantle boundary shows significant localisation of energy within an equatorial belt. Rapid hydromagnetic wave dynamics is absent at the start of the path but can be clearly exhibited in the asymptotic regime. This study reports on ubiquitous axisymmetric geostrophic torsional waves of weak amplitude relatively to convective transport, and also stronger, laterally limited, quasi-geostrophic Alfv\'en waves propagating in the cylindrical radial direction from the tip of convective plumes towards the core-mantle boundary. Quasi-geostrophic Alfv\'en waves are shown to be an important carrier of flow acceleration to the core surface that links with the generation of strong, short-lived and intermittent equatorial pulses in the secular acceleration energy.