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A basaltic lava flow erupted from the Tajogaite volcano on 4 December 2021, in La Palma (Canary Islands, Spain) was sampled to find out to what extent reliable and correct information on both intensity and direction of the Earth's magnetic field can be obtained from the palaeomagnetic signal recorded in a lava flow which erupted under known conditions. Samples were taken every few centimetres across a flow up to a total of 27 oriented cores. Palaeomagnetic experiments showed a strong viscous overprint in many samples. Nevertheless, the mean palaeomagnetic direction obtained agrees well with the actual value from IGRF-13. Rock magnetic experiments were performed to obtain additional information about the quality and reliability of the results and the reasons for unsuccessful determinations. Analysis of mostly irreversible thermomagnetic curves showed that the carriers of remanence were magnetite and titanomagnetite of low and/or intermediate Curie-temperature. Hysteresis parameter ratios showed a pronounced variability across the flow. Analyses of frequency dependent susceptibility, IRM acquisition coercivity spectra and FORCs showed a noticeably presence of very low coercivity grains (multidomain and superparamagnetic-single domain boundary). Multimethod palaeointensity experiments were performed with the Thellier-Coe, multispecimen and Tsunakawa-Shaw methods. Only three of 25 cores from the flow yielded successful Thellier-Coe determinations, in agreement with the expected field value of 38.7 μT (IGRF-13). However, palaeointensities of 60 per cent of the specimens agree with the expected value performing an informal analysis without considering criteria thresholds. Four of six Tsunakawa-Shaw determinations performed on samples from the flow yielded correct results, but three multispecimen determinations providing apparently successful determinations largely underestimate the expected field intensity. Combination of three Thellier-Coe and four Tsunakawa-Shaw successful determinations yields a multimethod palaeointensity result B = (36.9 ± 2.0) μT in good agreement with the expected field intensity. [ABSTRACT FROM AUTHOR]

Accurate absolute palaeointensity is essential for understanding dynamo processes on the Earth and other planetary bodies. Although great efforts have been made to propose techniques to obtain magnetic field strength from rock samples, such as Thellier-series methods, the amount of high-fidelity palaeointensities remains limited. One primary reason for this is the thermal alteration of samples that pervasively occurred during palaeointensity experiments. In this study, we developed a comprehensive rock magnetic experiment, termed thermal rock magnetic cycling (TRMC), that can utilize measurements of critical rock magnetic properties at elevated temperatures during multiple heating-cooling cycles to track thermal changes in bulk samples and individual magnetic components with different Curie temperatures in samples for palaeointensity interpretations. We demonstrate this method on a Galapagos lava sample, GA 84.6. The results for this specimen revealed that GA 84.6v underwent thermophysical alteration throughout the TRMC experiment, resulting in changes in its remanence carrying capacity. These findings were then used to interpret the palaeointensity results of specimen GA 84.6c, which revealed that the two-slope Arai plot yielded two linear segments with distinct palaeointensity values that were both biased by thermophysical alteration. To further test the TRMC method, we selected another historical lava sample (HS 2) from Mt Lassen, detecting slight thermal-physical changes after heating the specimen HS 2–8C to a target temperature of 400 °C. We also isolated a stable magnetic component with a Curie temperature below 400 °C using the TRMC method, which may provide a more reliable palaeointensity estimate of 51 μT. By providing a method for tracking thermal alteration independent of palaeointensity experiments, the TRMC method can explore subtle, unrecognizable thermal alteration processes in less detailed palaeointensity measurements, which can help to assess the thermal stability of the measured samples and interpret the changes in the TRM unblocking spectrum and palaeointensity estimates, facilitating the acquisition of more reliable records for constrain the formation of the inner core and the evolution of Earth's magnetic field. [ABSTRACT FROM AUTHOR]

Geomagnetic field data from six magnetic observatories in and adjacent to the South Atlantic Anomaly were individually analysed to detect abrupt secular variation changes occurring on timescales of less than a year and to explore any correlation with the evolution of the South Atlantic Anomaly. After applying external field corrections by means of the CHAOS-7 model, 12-month differences of the respective observatory monthly mean of the eastward component Y revealed evidence of several geomagnetic jerks with varying amplitudes during the period 2000–2020. These observations were compared to the CHAOS-7 spherical harmonic model and previous studies of the South Atlantic Anomaly's evolution. It emerged from this study that global field models like CHAOS are not very effective in identifying rapid localized changes in the geomagnetic field, highlighting the importance of using observatory data in conjunction with satellite data when studying geomagnetic jerks. [ABSTRACT FROM AUTHOR]

The Earth's magnetic field is generated by a dynamo in the outer core and is crucial for shielding our planet from harmful radiation. Despite the established importance of the core–mantle boundary (CMB) heat flux as driver for the dynamo, open questions remain about how heat flux heterogeneities affect the magnetic field. Here, we explore the distribution of the CMB heat flux on Earth and its changes over time using compressible global 3-D mantle convection models in the geodynamic modelling software ASPECT. We discuss the use of the consistent boundary flux method as a tool to more accurately compute boundary heat fluxes in finite element simulations and the workflow to provide the computed heat flux patterns as boundary conditions in geodynamo simulations. Our models use a plate reconstruction throughout the last 1 billion years—encompassing the complete supercontinent cycle—to determine the location and sinking speed of subducted plates. The results show how mantle upwellings and downwellings create localized heat flux anomalies at the CMB that can vary drastically over Earth's history and depend on the properties and evolution of the lowermost mantle as well as the surface subduction zone configuration. The distribution of hot and cold structures at the CMB changes throughout the supercontinent cycle in terms of location, shape and number, indicating that these structures fluctuate and might have looked very differently in Earth's past. We estimate the resulting amplitude of spatial heat flux variations, expressed by the ratio of peak-to-peak amplitude to average heat flux, q *, to be at least 2. However, depending on the material properties and the adiabatic heat flux out of the core, q * can easily reach values >30. For a given set of material properties, q * generally varies by 30–50 per cent over time. Our results have implications for understanding the Earth's thermal evolution and the stability of its magnetic field over geological timescales. They provide insights into the potential effects of the mantle on the magnetic field and pave the way for further exploring questions about the nucleation of the inner core and the past state of the lowermost mantle. [ABSTRACT FROM AUTHOR]

Temporal variations in the electromagnetic field generated by seismic waves are accounted for mainly by electrokinetic (EK) and motional induction (MI) effects. Currently, these effects are considered in terms of different sets of equations, even though both mechanisms are assumed in data interpretation. In principle, however, they should be described by a single set of equations, possibly including a new type of coupling effect. This inconsistency suggests that the deviation of conventional equations was somewhat incorrect, with some coupling mechanisms having been overlooked. Here, the derivation of the conventional equations was reconsidered, and necessary revisions were applied. The revised equations describe both EK and MI effects and include a previously unrecognized coupling effect (although its effect is negligible). The solution of the new equations is well approximated by a simple sum of EK and MI effects determined by conventional equations. In conclusion, it was confirmed that the conventional procedure for estimation of seismically induced EM variations in terms of the EK and MI effects is sufficiently accurate, in spite of the conventional governing equations missing some of coupling terms related to the EK and MI effects. [ABSTRACT FROM AUTHOR]

Absolute palaeointensities are notoriously hard to obtain, because conventional thermal Thellier palaeointensity experiments often have low success rates for volcanic samples. The thermal treatments necessary for these experiments potentially induce (magnetic) alteration in the samples, preventing a reliable palaeointensity estimate. These heating steps can be avoided by pseudo-Thellier measurements, where samples are demagnetized and remagnetized with alternating fields. However, pseudo-Thellier experiments intrinsically produce relative palaeointensities. Over the past years, attempts were made to calibrate pseudo-Thellier results into absolute palaeointensities for lavas by mapping laboratory induced anhysteretic remanent magnetizations (ARMs) to the thermally acquired natural remanent magnetizations (NRMs). Naturally occurring volcanic rocks, however, are assemblages of minerals differing in grain size, shape and chemistry. These different minerals all have their own characteristic mapping between ARMs and thermal NRMs. Here, we show that it is possible to find these characteristic mappings by unmixing the NRM demagnetization and the ARM acquisition curves into end-members, with an iterative method of non-negative matrix factorization. In turn, this end-member modelling approach (EMMA) allows for the calculation of absolute palaeointensities from pseudo-Thellier measurements. We tested our EMMA using a noise-free numerical data set, yielding a perfect reconstruction of the palaeointensities. When adding noise up to levels beyond what is expected in natural samples, the end-member model still produces the known palaeointensities well. In addition, we made a synthetic data set with natural volcanic samples from different volcanic edifices that were given a magnetization by heating and cooling them in a controlled magnetic field in the lab. The applied fields ranged between 10 and 70 µT. The average absolute difference between the calculated palaeointensity and the known lab field is around 10 µT for the models with 2–4 end-members, while the palaeointensity of almost all flows can be retrieved within a deviation of ±20 µT. The deviations between the palaeointensities and the known lab fields are almost Gaussian distributed around the expected values. Although the two data sets in our study show that there is potential for using this end-member modelling technique for finding absolute palaeointensities from pseudo-Thellier data, these synthetic data sets cannot be directly related to natural samples. Therefore, it is necessary to compile a data set of known palaeointensities from different volcanic sites that recently cooled in a known magnetic field to find the universal end-members in future studies. [ABSTRACT FROM AUTHOR]

Estimating high resolution models of the Earth's core magnetic field and its time variation in the polar regions requires that one can adequately account for magnetic signals produced by polar ionospheric currents, which vary on a wide range of time and length scales. Limitations of existing ionospheric field models in the challenging polar regions can adversely affect core field models, which in turn has important implications for studies of the core flow dynamics in those regions. Here we implement a new approach to co-estimate a climatological model of the ionospheric field together with a model of the internal and magnetospheric fields within the CHAOS geomagnetic field modelling framework. The parametrization of the ionospheric field exploits non-orthogonal magnetic coordinates to efficiently account for the geometry of the Earth's magnetic field and scales linearly with external driving parameters related to the solar wind and the interplanetary magnetic field. Using this approach we derive a new geomagnetic field model from measurements of the magnetic field collected by low Earth orbit satellites, which in addition to the internal field provides estimates of the typical current system in the polar ionosphere and successfully accounts for previously unmodelled ionospheric signals in field model residuals. To resolve the ambiguity between the internal and ionospheric fields when using satellite data alone, we impose regularization. We find that the time derivative of the estimated internal field is less contaminated by the polar currents, which is mostly visible in the zonal and near-zonal terms at high spherical harmonic degrees. Distinctive patches of strong secular variation at the core–mantle boundary, which have important implications for core dynamics, persist. Relaxing the temporal regularization reveals annual oscillations, which could indicate remaining ionospheric field or related induced signals in the internal field model. Using principal component analysis we find that the annual oscillations mostly affect the zonal low-degree spherical harmonics of the internal field. [ABSTRACT FROM AUTHOR]

The Svecofennian gabbro intrusions coincide temporally with the global 2100–1800 Ma orogens related to the amalgamation of the Mesoproterozoic supercontinent Nuna. We provide a new reliable 1891–1875 Ma palaeomagnetic pole for Fennoscandia based on rock magnetic and palaeomagnetic studies on the Svecofennian intrusions in central Finland to fill gaps in the Palaeoproterozoic palaeomagnetic record. By using the new pole together with other global high-quality data, we propose a new palaeogeographic reconstruction at 1885 Ma. This, together with previous data, supports a long-lived relatively stable position of Fennoscandia at low to moderate latitudes at 1890–1790 Ma. Similar stable pole positions have also been obtained for Kalahari at 1880–1830 Ma, Siberia at 1880–1850 Ma, and possibly India at 1980–1775 Ma. A new reconstruction at the beginning of this period indicates the convergence of several cratons at 1885 Ma in the initial stages of the amalgamation of the Nuna supercontinent at low to moderate latitudes. The close proximity of cratons at low to moderate latitudes is further supported by global and regional palaeoclimatic indicators. Stable position of several cratons could indicate a global period of minimal apparent drift at ca. 1880–1830 Ma. Before this period, the global palaeomagnetic record indicates large back-and-forth swings, most prominently seen in the high-resolution 2020–1870 Ma Coronation loops of the Slave craton. These large back-and-forth movements have been explained as resulting from an unstable geomagnetic field or basin- or local-scale vertical-axis rotations. However, the most likely explanation is inertial interchange true polar wander (IITPW) events, which is in line with the suggestion of large amplitude true polar wander events during the formation of the supercontinent. [ABSTRACT FROM AUTHOR]

Our understanding of the geodynamo has recently progressed thanks to geomagnetic data of improved quality, and analyses resting on numerical simulations of increasing realism. Here, these two advances are combined in order to diagnose the state and present dynamics of Earth's core in physically realistic conditions. A sequential, ensemble-based framework assimilates the output of geomagnetic field models covering the past 180 yr into a numerical geodynamo simulation, the physical realism of which is also advanced as data is assimilated. The internal dynamical structure estimated for the geodynamo at present reproduces previously widely documented features such as a planetary-scale, eccentric westwards gyre and localization of buoyancy release beneath the Eastern (0°E−180°E) hemisphere. Relating the typical magnetic variation timescale of the assimilated states to the power at which they operate, the present convective power of the geodynamo is estimated at 2.95 ± 0.2 TW, corresponding to an adiabatic heat flow out of the core of 14.8 ± 1 TW if the top of the core is convectively neutrally stratified at present. For the first time, morphologically and dynamically relevant trajectories are obtained by integrating the estimated states forward for a few decades of physical time using a model reaching the physical conditions of Earth's core. Such simulations accurately account for the spatio-temporal content of high-resolution satellite geomagnetic field models and confirm earlier interpretations in terms of rapid core dynamics. The enforcement of a realistic force balance approaching a Taylor state allows for propagation of weak (velocity perturbation of about 0.6 |$\mathrm{km\,yr^{-1}}$|⁠) axisymmetric torsional waves with period about 5 yr, supported by a magnetic field of root-mean-squared amplitude of 5.6 mT inside the core. Quasi-geostrophic magneto-Coriolis waves of interannual periods and significantly stronger velocity perturbation (about |$7 \mathrm{km\,yr^{-1}}$|⁠) are also reproduced, with properties that converge towards those recently retrieved from the analysis of geomagnetic variations before fully achieving Earth's core conditions. The power spectral density of magnetic variations falls off rapidly at frequencies exceeding the inverse Alfvén time (about |$0.6\mathrm{yr^{-1}}$|⁠), which indicates that the excitation of hydromagnetic waves occurs preferentially at large spatial scales. The possibility to account for geomagnetic variations from years to centuries in physically realistic models opens the perspective of better constraining properties of the deep Earth through geomagnetic data assimilation. [ABSTRACT FROM AUTHOR]

Palaeosecular variation (PSV) determinations and studies of the geometry of the Earth's main magnetic field provide important information about the field evolution, and to constrain numerical geodynamo models. Palaeomagnetic directional data from lava flows over the last few million years is of particular interest because the regional and global tectonic effects are minimal. However, the distribution of this type of palaeomagnetic data is uneven where the Southern Hemisphere is the destitute side. Therefore, the better knowledge of the geomagnetic field behaviour depends on the increased availability of high-quality data, especially in the Southern Hemisphere. A PSV and the time-averaged field (TAF) study was then performed in 0–5 Ma lava flows from the Caviahue–Copahue Volcanic Complex located in Northern Patagonia, Argentina (37°0′S, 71°10′W). The magnetic mineralogy of lava flows was investigated through thermomagnetic susceptibility curves, isothermal remanent magnetization (IRM) acquisition curves, hysteresis loops and first-order reversal curves (FORCs). Samples are essentially comprised of titanomagnetite with different Ti contents and magnetic domain structures typical of vortex state particles. A total of 50 volcanic sites were sampled, which provided 42 reliable palaeomagnetic site-mean directions after alternating field and thermal demagnetization. From these 42 sites, 36 are of normal and 6 are of reversed polarity. The mean direction from normal (reversed) sites is D = 356.2°, I = −50.1°, α95 = 4.0° and N = 36 (D = 176.5°, I = 59.5°, α95 = 14.1° and N = 6). Using only site-level data with the precision parameter k ≥ 100, we obtain 26 palaeomagnetic sites for PSV and TAF investigations in the study region. The filtered data set has a mean direction (D = 354.4°, I = −53.2° and α95 = 5.1°) close to the expected direction for a geocentric axial dipole (GAD) field (I GAD = −57.3°). The palaeopole (Plat = 84.4°, Plon = 229.1° and A 95 = 5.7°) coincides with the Earth's spin axis within the 95 per cent confidence interval. Virtual geomagnetic pole scatter (⁠|$S_{B} = {15.8^{18.9}_{11.8}}^{\circ }$|⁠) and the inclination anomaly (⁠|$\Delta I = 4.1_{-1.0}^{{9.2}^{\circ }}$|⁠) are both consistent at the 95 per cent confidence level with recent PSV and TAF models, respectively. Our results support the presence of small non-dipole field contributions (<3 per cent) superimposed on the GAD term, as reported by South American studies at mid southern latitudes. [ABSTRACT FROM AUTHOR]

SUMMARY: A series of models of the Earth magnetic field and core surface flow have been simultaneously and sequentially co-estimated from year 1999 to 2022. The models were derived from magnetic satellite and ground observatory data using a linear Kalman filter approach and prior statistics based on numerical dynamo simulations. The core field and secular variation model components present the same characteristics as the most recent core field models with slightly higher resolution in time. A principal component analysis of the core surface flow series of models shows that the largest flow variations are observed at high latitudes and under the western part of the Pacific Ocean. Filtering out the flow variation periods longer than ∼11.5 yr leads to a filtered azimuthal flow that presents ∼7 yr periodicities with patterns propagating westward by ∼60° longitude per year. These patterns are present mainly at mid- and equatorial latitudes. They are compatible with a perturbation of the main flow made of small columnar flows with rotation axis intersecting the core–mantle boundary between 10° and 15° latitudes, and flow speed of less than 5 km yr–1. Present at all longitudes, these columnar flows are particularly strong under the Pacific Ocean after 2013. They can also be clearly identified under the Atlantic Ocean from 2005 to 2015. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A detailed palaeointensity study was performed using the modified Thellier method on 18 Quaternary and Neogene volcanic units, ages ranging from 0.08 to 5.98 Ma, in Central Anatolia, Turkey. Robust data, which were estimated from 12 lava units in the study area, significantly increase the database of palaeomagnetic data, directions and absolute palaeointensity for the Anatolian region covering the time window back to ∼6 Ma. Previous studies sensitively dated the samples, except for one site dated in this study. The palaeointensity (VDM) value from the upper Miocene site estimated as 48.6 ± 9.2 μT (10.1 × 1022 ± 1.9 Am2) fits well into the Neogene VDM range in the data archives. For Pliocene samples with an age of 4.7 Ma, the palaeointensity was calculated to be 21.0 ± 4.7 μT. For these samples, an inclination of +42.9° was determined, and together with the results of low palaeointensity and normal polarity, this corresponds to the Nunivak or Sidufjall subchrons. These are normal polarity chrons within the Gilbert Chron which predominantly has reversed polarity. Palaeodirectional data and field strength with age between 0.08 and 2.57 Ma clearly showed the Brunhes and Matuyama Chrons in the Pleistocene. Three new data with 25.0 ± 7.9 μT (age 1.84 Ma), 59.7 ± 8.2 μT (age 2.15 Ma) and 79.6 ± 19.3 μT (age 2.57 Ma) from the early Pleistocene period significantly contribute to global data archives, which lack palaeointensity data from similar latitude range. The average VDM values for nine Pleistocene sites were calculated to be 51.5 ± 16.4 μT (10.3 × 1022 ± 3.7 Am2). According to the comparison of our data with the palaeointensity database, field model record and previous studies of the Pleistocene, significantly high field strength obtained from Central Anatolia, located in the Northern Hemisphere, could have occurred due to asymmetry between the Northern and Southern Hemispheres during the Pleistocene. [ABSTRACT FROM AUTHOR]

Lacustrine and marine sediments are one of the main sources of information in constructing Holocene global geomagnetic field models. The use of sediment records, however, leads to the question whether the compaction of sediments leads to a systematic biasing of inclination. We evaluate 78 sedimentary records worldwide for inclination flattening using the Elongation–Inclination (E/I) method; 20 records indicate flattening. The uncorrected and corrected values for inclination are compared to global geomagnetic field models. The results suggest that the uncorrected values agree better with the predictions from global geomagnetic field models based on sediment and archaeomagnetic data, but also with a model independent of sediment data. The 20 sites are located in mid-latitudes where inclination anomalies are predicted both in the Holocene and throughout the Brunhes epoch. Our results demonstrate that shallow inclination may not only result from compaction but may reflect the structure of the geomagnetic field on short timescales. This suggests that secular variation is not averaged out over a time period that covers the Holocene. [ABSTRACT FROM AUTHOR]

We present new absolute archaeointensity data from six archaeological sites situated in the Okayama Prefecture, Japan. The materials studied are well-dated fragments from pottery, ceramic coffins and haniwa artefacts. Their ages range from 160 AD to 675 AD, covering the Late Yayoi and Kofun periods. Rock magnetic experiments suggest the presence of magnetite and/or Ti-magnetite as the main carrier of the remanence, with a possible minor contribution of higher coercivity minerals. After thermal demagnetization experiments, the most magnetically stable samples were selected for archaeointensity analysis performed following the double-heating method proposed by Thellier and modified by Coe. Partial thermoremanent magnetization (pTRM) checks and pTRM tail-checks were performed for monitoring possible chemical alterations during heating. All measurements were corrected for both anisotropy and cooling-rate effects. Successful archaeointensity determinations, following rigorous selection criteria, were obtained for samples from all the investigated archaeological sites. Compared with literature data from Japan, the new high-quality data show significantly lower intensity values. They also reveal possible fast secular variation changes during the Late Yayoi period and very weak geomagnetic intensity field around 630 AD. Such values offer evidence of a possible recurrence of weak intensity field in East Asia, suggesting an ancient recurrence of the West Pacific Anomaly. The new data might change the archaeomagnetic field models interpretations in the area, even though more data are still necessary to better understand the secular variation in Japan and the temporal evolution of the geomagnetic field's behaviour in East Asia. [ABSTRACT FROM AUTHOR]

Unravelling the long-term behaviour of the geomagnetic field is crucial for understanding the dynamics of the deep Earth. Yet, obtaining an accurate measure of geomagnetic palaeosecular variations (PSV) is difficult, partly because of tectonically induced rotations that overprint the original palaeomagnetic signal. We present a detailed palaeomagnetic investigation based on 99 sampling sites collected from the 119 to 112.6 Ma Ramon Volcanics exposed near the dormant Ramon Fault, southern Israel. These basaltic rocks were emplaced at equatorial palaeolatitudes during the beginning of the Cretaceous Normal Superchron (CNS; 123.4–83.6 Ma), during which there were no polarity reversals. Structurally corrected remanence directions consistently vary across the investigated area, whereby the sites found near a sharp bend of the Ramon Fault are clockwise rotated, whereas the other sites show no obvious rotational pattern. Elasto-plastic modelling suggests that the rotations were induced by up to 1.5 km of dextral horizontal slip accommodated by the fault, consistent with previous geological and geophysical estimations. Considering the remanence directions obtained from sites that were not influenced by the fault, we calculated an S B value of |$13.3_{ - 1.3}^{ + 1.9 \circ }$| (95 percent confidence, 46 sites), which corresponds to previous S B estimations from pre- and early-CNS volcanic bodies emplaced at low palaeolatitudes (λ < 20°). This observation suggests that the emergence of the superchron was not accompanied by a change in the behaviour of the geomagnetic PSV. Finally, our results, together with previous palaeo-equatorial observations, show that the middle part of the superchron had lower angular dispersion (i.e. lower S B) compared to the scatter that prevailed during the beginning of the superchron. This observation suggests that the geomagnetic field transitioned into a more axial dipole dominance state towards the middle part of the superchron. Altogether, our analysis indicates that the superchron cannot be treated as a period characterized by a steady-state field behaviour. [ABSTRACT FROM AUTHOR]

Geomagnetic jerks—abrupt changes in the acceleration of Earth's magnetic field that punctuate geomagnetic records— have been richly documented over the past decades by taking advantage of the complementary strengths of ground observatory and satellite measurements. It has recently been proposed that these events originate from the interplay and timescale separation between slow convection and rapid hydromagnetic wave propagation in Earth's outer core, with these latter waves playing a key role in the generation of jerk signals. To assess the generality of this explanation, here we analyse a catalogue of 14 events obtained during a 14 000-yr-long temporal sequence from a numerical geodynamo simulation that is the closest to date to Earth's core conditions regarding timescale separation. Events are classified according to their dynamic origin and the depth at which they are triggered in the outer core. The majority of jerk events are found to arise from intermittent local disruptions of the leading-order force balance between the pressure, Coriolis, buoyancy and Lorentz forces (the QG-MAC balance), that leads to an inertial compensation through the emission of rapid, non-axisymmetric, quasi-geostrophic Alfvén waves from the region where this force balance is disrupted. Jerk events of moderate strength arise from the arrival at low latitudes at the core surface of hydromagnetic wave packets emitted from convective plumes rooted at the inner core boundary. As in an earlier simulation, these account well for jerk features that have recently been documented by satellite and ground observations. The more realistic timescales in the simulation reported here allow further details to be distinguished, such as multiple temporal alternations of geomagnetic acceleration pulses at low latitudes, long-range synchronization of pulse foci in space and rapid longitudinal drift of these foci at the core surface. The strongest events in the catalogue arise from disruption of the leading-order force balance near or at the core surface, from the combined influence of the arrival of buoyancy plumes and magnetic field rearrangement. The hydromagnetic waves that are sent laterally and downwards generate signals that clearly illustrate the presence of nearly synchronous 'V-shaped' magnetic variation patterns over a wide portion of Earth's surface and also at mid to high latitudes, despite the source being confined to low latitudes at the core surface. Other well-known characteristics of strong geomagnetic jerks such as surges in the intensity of the secular variation and inflexions in the length-of-day variations are also reproduced in these events. Irrespectively of the event strength, our results support the hypothesis of a single physical root cause—the emission of magneto-inertial waves following a disruption of the QG-MAC balance—for jerks observed throughout the geomagnetic record. [ABSTRACT FROM AUTHOR]

Earth's internal magnetic field is dominated by the contribution of the axial dipole whose temporal variations are wide ranging and reflect characteristic timescales associated with geomagnetic reversals and large scale palaeosecular variation, ranging down to decadal and subannual field changes inferred from direct observations. We present a new empirical power spectrum for the axial dipole moment based on composite magnetic records of temporal variations in the axial dipole field that span the frequency range 0.1 to 5 × 105  Myr–1 (periods from 10 million to 2 yr). The new spectrum is used to build a stochastic representation for these time variations, based on an order 3 autoregressive (AR) process and placed in the context of earlier stochastic modelling studies. The AR parameter estimates depend on the frequency of transitions in the spectral regime and may be influenced by Ohmic diffusion, advection and torsional oscillations in Earth's core. In several frequency ranges across the interval 200–5000 Myr–1(5000 to 200 yr periods) the empirical power spectrum lies above the AR3 model and may be influenced by Magneto–Coriolis (MC) waves in Earth's core. The spectral shape and parameter estimates provide a potentially useful guide for developing assessments of whether numerical dynamo simulations meet criteria for being considered Earth like. [ABSTRACT FROM AUTHOR]

It is well known that the axial dipole part of Earth's magnetic field reverses polarity, so that the magnetic North Pole becomes the South Pole and vice versa. The timing of reversals is well documented for the past 160 Myr, but the conditions that lead to a reversal are still not well understood. It is not known if there are reliable 'precursors' of reversals (events that indicate that a reversal is upcoming) or what they might be. We investigate if machine learning (ML) techniques can reliably identify precursors of reversals based on time-series of the axial magnetic dipole field. The basic idea is to train a classifier using segments of time-series of the axial magnetic dipole. This training step requires modification of standard ML techniques to account for the fact that we are interested in rare events—a reversal is unusual, while a non-reversing field is the norm. Without our tweak, the ML classifiers lead to useless predictions. Perhaps even more importantly, the usable observational record is limited to 0–2 Ma and contains only five reversals, necessitating that we determine if the data are even sufficient to reliably train and validate an ML algorithm. To answer these questions we use several ML classifiers (linear/non-linear support vector machines and long short-term memory networks), invoke a hierarchy of numerical models (from simplified models to 3-D geodynamo simulations), and two palaeomagnetic reconstructions (PADM2M and Sint-2000). The performance of the ML classifiers varies across the models and the observational record and we provide evidence that this is not an artefact of the numerics, but rather reflects how 'predictable' a model or observational record is. Studying models of Earth's magnetic field via ML classifiers thus can help with identifying shortcomings or advantages of the various models. For Earth's magnetic field, we conclude that the ability of ML to identify precursors of reversals is limited, largely due to the small amount and low frequency resolution of data, which makes training and subsequent validation nearly impossible. Put simply: the ML techniques we tried are not currently capable of reliably identifying an axial dipole moment (ADM) precursor for geomagnetic reversals. This does not necessarily imply that such a precursor does not exist, and improvements in temporal resolution and length of ADM records may well offer better prospects in the future. [ABSTRACT FROM AUTHOR]

Changes in the geomagnetic field over geologic timescales can be used to study the evolution and processes of its sources in Earth's deep interior. As a stark contrast to the geomagnetic field behaviour of the recent past, the field in the late Neoproterozoic is defined by ambiguous polar wander paths, ultralow field strengths and a period of extreme reversal hyperactivity. Palaeointensity data from this time are still scarce and conclusions made from these data suffer from large uncertainties brought by a low sampling density. In this study, we present new palaeomagnetic and palaeointensity data from quarry outcrops and five deep drill cores, covering the longest and most complete profiles through the Ediacaran units in the Volyn Basalt Province (NW Ukraine) to date. Palaeodirectional analysis of thermal and alternating field demagnetization experiments reveals at least six reversals in the profile as well as four palaeopoles that agree with previously published poles. Whole-rock palaeointensity estimates are derived from a multimethod approach that utilizes thermal and microwave Thellier experiments performed using Coe and IZZI protocols as well as Wilson and double-heating Shaw experiments. These produce instantaneous site-mean palaeointensity estimates in the range of 2.1 ± 0.4 to 11.1 ± 3.5 µT and virtual dipole moments in the range of 0.31 ± 0.06 × 1022 to 1.67 ± 0.53 × 1022 A m2. Small-scale variations of palaeointensities throughout the profile not only show extremely weak field strengths around polarity changes but could also suggest that the field strength never fully recovered between reversals. These new results increase the density of intensity data coverage for Baltica in the Late Ediacaran and, in combination with previously published Ediacaran dipole moments, support an extremely weak field that seems to increase in strength towards the Ediacaran–Cambrian transition. [ABSTRACT FROM AUTHOR]

We present new radiometric ages and full-vector palaeomagnetic data from São Vicente Island, Cape Verde. Samples were obtained from a sequence of 11 flows. A K-Ar age determination was performed on the lowermost flow of the sequence, yielding an upper Miocene age of 6.07 ± 0.16 (2 σ) Ma. Considering the normal polarity observed in all flows, the age of the sequence could be narrowed down to an interval between 6.03 and 6.23 Ma. The mean palaeomagnetic direction of the studied sequence was compared with the expected direction, calculated from the African Apparent Polar Wander Path (5 Ma). While inclinations approximately agree, the palaeodeclination appears westwardly deviated by 26.5° ± 2.9°. Moreover, nearly no scatter of virtual geomagnetic poles around their mean value is observed and its comparison with the scatter observed in palaeomagnetic directions obtained from geomagnetic field model SHA.DIF.14k suggests that the sequence was very rapidly emplaced in only a few centuries. Thus, the obtained anomalous palaeomagnetic direction seems to reflect the effect of non-averaged secular variation, although a local vertical-axis counter-clockwise rotation of the sequence, cannot be entirely ruled out. Thellier–Coe palaeointensity experiments on 66 specimens yielded 22 successful determinations and multispecimen (MS) palaeointensity experiments on 11 samples yielded 8 successful determinations. In the upper part of the sequence, Thellier–Coe determinations fail due to the presence of multidomain (MD) grains, but the MS method yields successful results in several of these flows, demonstrating that this method can provide reliable palaeointensity determinations on samples with a higher MD grain fraction. A mean palaeointensity BSV = (18.5 ± 1.9) µT is obtained from the joint analysis of the results from both methods. This value lies clearly below the present-day value BP  = 33.1 μT. The virtual axial dipole moment (VADM = 4.3 × 1022 Am2), however, cannot be considered anomalous if compared to available upper Miocene–Pliocene data and represents a new high-reliability contribution to the very limited African palaeointensity database. [ABSTRACT FROM AUTHOR]

Changes in palaeosecular variation, dipole moment and polarity reversal frequency are salient features of the Earth's magnetic field over the geological past, yet how these changes are linked by the geodynamo remains controversial. To further understand this issue, we provide new absolute (API) and relative (RPI) palaeointensities from the ∼1-km-thick basaltic sequence of Waja (North Ethiopia) emplaced around 31 Ma, yielding an instantaneous virtual dipole moment of 57 ± 9 ZAm2 (1 σ, N = 18) and a relative variability in intensity ε F = 0.39 ± 0.07 (1 σ, N = 19). Our analysis of the API database with strict selection criteria (inclusion of Thellier-style determinations with pTRM checks only, at least five determinations per cooling unit, and within-unit relative standard error lower than 10 per cent) fails to identify any robust correlation between changes in dipole moment and reversal frequency over the past 155 Myr. More convincingly, the available RPI results are consistent with an increase of the palaeosecular-variation proxy εF with reversal rate, as predicted by numerical dynamo simulations. We also find that the API-based estimate ε F = 0.40 ± 0.03 (1 σ, N = 104), computed from the filtered version of the World Palaeointensity Database for the 0.77–31 Ma interval, is consistent with the scaling rule, suggesting that the API record has been sufficiently sampled over the past 31 Ma. We thus speculate that the absence of negative correlation between changes in dipole moment and reversal frequency in the API database over the past 155 Myr may be the result of insufficient sampling prior to 31 Ma rather than the signature of an intrinsic geomagnetic feature. [ABSTRACT FROM AUTHOR]

Space weather alerting systems for power systems require real-time calculations of the electric fields that drive geomagnetically induced currents. In this paper, we present a new method for calculating the Earth impulse response that can be convolved with real-time magnetic field data to give the required electric fields. We start with the Earth transfer function which can be expressed in two ways: as a relationship between the electric field, E , and the geomagnetic field, B , which has characteristics equivalent to that of a high-pass filter, and between E and the time derivative of the magnetic field, d B /d t , which has characteristics of a low-pass filter. An inverse Fourier transform of these transfer functions should then give the corresponding Earth impulse responses in the time domain. This works well for a uniform conductivity model for which the inverse Fourier transform of the transfer function has an analytic solution. However, the inverse Fourier transform of the transfer function for a non-uniform conductivity model requires numerical calculations and produces an acausal impulse response with oscillations because of the Gibbs phenomenon. To investigate the origin of the Gibbs oscillations, the real and imaginary parts of the transfer functions are transformed separately. This shows that the Gibbs oscillations arise from the inverse transform of the real and imaginary parts of the high-pass transfer function and the imaginary part of the low-pass transfer function. A new method is introduced that just transforms the real part of the low-pass transfer function and uses the requirement of causality to construct the full low-pass impulse response. From this, the derivative theorem of convolution is used to obtain the high-pass impulse response. Electric fields can then be calculated by convolution of the low-pass impulse response with the rate of change of the magnetic field, d B /d t , or by convolution of the high-pass impulse response with the magnetic field, B. Tests of the new method by comparison with analytic solutions for specified earth models and synthetic magnetic field data gave very high correlation coefficients, slopes near 1.0 and intercepts near zero, showing the accuracy of the new method. The method can be used with any Earth transfer function whether obtained from magnetotelluric measurements or from 1-D, 2-D or 3-D conductivity models. Thus, it provides a versatile technique that avoids the Gibbs phenomenon and produces a causal impulse response suitable for time domain calculations of electric fields. [ABSTRACT FROM AUTHOR]

We present local time-series of the magnetic field gradient tensor elements at satellite altitude derived using a Geomagnetic Virtual Observatory (GVO) approach. Gradient element time-series are computed in 4-monthly bins on an approximately equal-area distributed worldwide network. This enables global investigations of spatio-temporal variations in the gradient tensor elements. Series are derived from data collected by the Swarm and CHAMP satellite missions, using vector field measurements and their along-track and east–west differences, when available. We find evidence for a regional secular variation impulse (jerk) event in 2017 in the first time derivative of the gradient tensor elements. This event is located at low latitudes in the Pacific region. It has a similar profile and amplitude regardless of the adopted data selection criteria and is well fit by an internal potential field. Spherical harmonic models of the internal magnetic field built from the GVO gradient series show lower scatter in near-zonal harmonics compared with models built using standard GVO vector field series. The GVO gradient element series are an effective means of compressing the spatio-temporal information gathered by low-Earth orbit satellites on geomagnetic field variations, which may prove useful for core flow inversions and in geodynamo data assimilation studies. [ABSTRACT FROM AUTHOR]

Palaeomagnetic records from geological archives provide significant information about the nature of geomagnetic polarity reversals; however, there are few detailed palaeomagnetic records of pre-Pleistocene reversals. The lower Mammoth Subchron boundary (late Pliocene) is recorded in a 10-m interval of a marine succession deposited at high accumulation rates (9–66 cm kyr–1) in the Boso Peninsula, central Japan. Here, we report a continuous palaeomagnetic record of the lower, normal to reverse boundary interval of the Mammoth Subchron, including the geomagnetic field direction and relative palaeointensity, with an average temporal resolution of ca. 800 yr. A hybrid method of thermal demagnetization at 200 °C and progressive alternating field demagnetization were used to effectively extract the primary palaeomagnetic component, which is carried by magnetite. The lower Mammoth transition is characterized by palaeomagnetic direction of instability and decay of the relative palaeointensity, and occurred from late Marine Isotope Stage MG3 (3351 ka) to MG2 (3336 ka) or MG1 (3331 ka), spanning 15–20 kyr. Virtual geomagnetic poles (VGPs), calculated from primary palaeomagnetic directions, rapidly rebounded twice from southern latitudes to northern latitudes within the transition. In contrast to the complex lower Mammoth reversal behaviour recorded in the Boso Peninsula succession, records from a lava sequence in O'ahu (Hawai'i) reveal a rebound following a 180° directional change, and those from a marl succession in Sicily (Italy) indicate a single rapid directional change. Diverse geomagnetic field evolution among these three sections is reflected resolution difference among the records likely in combination with an influence of non-axial dipole field. [ABSTRACT FROM AUTHOR]

Seismic and magnetic observations have suggested the presence of a stably stratified layer atop Earth's core. Such a layer could affect the morphology of the geomagnetic field and the evolution of the core, but the precise impact of this layer depends largely on its internal dynamics. Among other physical phenomena, stratified layers host internal gravity waves (IGW), which can be excited by adjacent convective motions. Internal waves are known to play an important role on the large-scale dynamics of the Earth's climate and on the long-term evolution of stars. Yet, they have received relatively little attention in the Earth's outer core so far and deserve detailed investigations in this context. Here, we make a first step in that direction by running numerical simulations of IGW in a non-rotating spherical shell in which a stratified layer lies on top of a convective region. We use a nonlinear equation of state to produce self-consistently such a two-layer system. Both propagating waves and global modes coexist in the stratified layer. We characterize the spectral properties of these waves and find that energy is distributed across a wide range of frequencies and length scales, that depends on the Prandtl number. For the control parameters considered and in the absence of rotational and magnetic effects, the mean kinetic energy in the layer is about 0.1 per cent that of the convective region. IGW produce perturbations in the gravity field that may fall within the sensitivity limit of present-day instruments and could potentially be detected in available data. We finally provide a road map for future, more geophysically realistic, studies towards a more thorough understanding of the dynamics and impact of internal waves in a stratified layer atop Earth's core. [ABSTRACT FROM AUTHOR]

Elucidating the processes in the liquid core that have produced observed palaeointensity changes over the last 3.5 Gyr is crucial for understanding the dynamics and long-term evolution of Earth's deep interior. We combine numerical geodynamo simulations with theoretical scaling laws to investigate the variation of Earth's magnetic field strength over geological time. Our approach follows the study of Aubert et al. adapted to include recent advances in numerical simulations, mineral physics and palaeomagnetism. We first compare the field strength within the dynamo region and on the core–mantle boundary (CMB) between a suite of 314 dynamo simulations and two power-based theoretical scaling laws. The scaling laws are both based on a Quasi-Geostropic (QG) force balance at leading order and a Magnetic, Archimedian, and Coriolis (MAC) balance at first order and differ in treating the characteristic length scale of the convection as fixed (QG-MAC-fixed) or determined as part of the solution (QG-MAC-free). When the data set is filtered to retain only simulations with magnetic to kinetic energy ratios greater than at least two we find that the internal field together with the root-mean-square and dipole CMB fields exhibit power-law behaviour that is compatible with both scalings within uncertainties arising from different heating modes and boundary conditions. However, while the extrapolated intensity based on the QG-MAC-free scaling matches Earth's modern CMB field, the QG-MAC-fixed prediction shoots too high and also significantly overestimates palaeointensities over the last 3.5 Gyr. We combine the QG-MAC-free scaling with outputs from 275 realizations of core–mantle thermal evolution to construct synthetic true dipole moment (TDM) curves spanning the last 3.5 Gyr. Best-fitting TDMs reproduce binned PINT data during the Bruhnes and before inner core nucleation (ICN) within observational uncertainties, but PINT does not contain the predicted strong increase and subsequent high TDMs during the early stages of inner core growth. The best-fitting models are obtained for a present-day CMB heat flow of 11–16 TW, increasing to 17–22 TW at 4 Ga, and predict a minimum TDM at ICN. [ABSTRACT FROM AUTHOR]

Geomagnetic data assimilation merges past and present-day observations of the Earth's magnetic field with numerical geodynamo models and the results are used to initialize forecasts. We present a new 'proxy model' that can be used to test, or rapidly prototype, numerical techniques for geomagnetic data assimilation. The basic idea for constructing a proxy is to capture the conceptual difficulties one encounters when assimilating observations into high-resolution, 3-D geodynamo simulations, but at a much lower computational cost. The framework of using proxy models as 'gate-keepers' for numerical methods that could/should be considered for more extensive testing on operational models has proven useful in numerical weather prediction, where advances in data assimilation and, hence, improved forecast skill, are at least in part enabled by the common use of a wide range of proxy models. We also present a large set of systematic data assimilation experiments with the proxy to reveal the importance of localization and inflation in geomagnetic data assimilation. [ABSTRACT FROM AUTHOR]

We present palaeo- and rock magnetic results from a well-dated, 21 m-thick, Late Pleistocene continental sedimentary section located in southern Germany. Rock magnetic measurements reveal a complex magnetic mineralogy dominated by low coercivity minerals likely related to single domain biogenic magnetite and biogenic or early diagenetic greigite. In the lower part of the section also detrital haematite is present. The stable remanence shows predominantly normal polarity with two marked deviations at ∼1280-1200 cm and at 886 cm profile depth. Whereas the lower excursion is well established by several samples and documented also by detrital haematite, the upper one is only represented by a single sample and revealed by magnetite and greigite. Using the radiocarbon-based age model for the section, the lower excursion yields an age of 42.8–41.3 ka cal BP and is interpreted to represent the Laschamps geomagnetic excursion. The increased abundance of greigite in the upper part of the section, especially in the sample responsible for the upper anomalous direction, renders the interpretation of an actual excursion problematic due to the reducing environment necessary for the greigite formation. [ABSTRACT FROM AUTHOR]

Rotation of coil-type magnetometers caused by seismic waves can change the magnetic flux of the earth's magnetic field through the coils and thereby give rise to rotation-induced magnetic fields (RIMFs), which have contribution to so-called coseismic magnetic disturbances during earthquake events. In this study, we present a method to numerically calculate the rotational motion and RIMFs excited by a seismic source in a horizontally layered model. Like computing synthetic seismograms, this method allows calculating the full response of magnetic disturbances during an earthquake event. Numerical examples are conducted to investigate characters of the magnetic fields under excitation of different kinds of sources. The results show that the P -SV-mode waves mainly contribute to radial and vertical magnetic disturbances, while the SH-mode waves dominate tangential magnetic disturbances. We also apply this method to the 2017 Jiuzhaigou earthquake. The synthetic magnetic signals explain well the observed data, suggesting that the coseismic magnetic fields observed during this earthquake are mainly caused by the rotation of the magnetometers. [ABSTRACT FROM AUTHOR]

Convection in the liquid outer core of the Earth is driven by thermal and chemical perturbations. The main purpose of this study is to examine the impact of double-diffusive convection on magnetic field generation by means of 3-D global geodynamo models, in the so-called 'top-heavy' regime of double-diffusive convection, when both thermal and compositional background gradients are destabilizing. Using a linear eigensolver, we begin by confirming that, compared to the standard single-diffusive configuration, the onset of convection is facilitated by the addition of a second buoyancy source. We next carry out a systematic parameter survey by performing 79 numerical dynamo simulations. We show that a good agreement between simulated magnetic fields and the geomagnetic field can be attained for any partitioning of the convective input power between its thermal and chemical components. On the contrary, the transition between dipole-dominated and multipolar dynamos is found to strongly depend on the nature of the buoyancy forcing. Classical parameters expected to govern this transition, such as the local Rossby number—a proxy of the ratio of inertial to Coriolis forces—or the degree of equatorial symmetry of the flow, fail to capture the dipole breakdown. A scale-dependent analysis of the force balance instead reveals that the transition occurs when the ratio of inertial to Lorentz forces at the dominant length scale reaches 0.5, regardless of the partitioning of the buoyancy power. The ratio of integrated kinetic to magnetic energy Ek / Em provides a reasonable proxy of this force ratio. Given that Ek / Em ≈ 10−4 − 10−3 in the Earth's core, the geodynamo is expected to operate far from the dipole–multipole transition. It hence appears that the occurrence of geomagnetic reversals is unlikely related to dramatic and punctual changes of the amplitude of inertial forces in the Earth's core, and that another mechanism must be sought. [ABSTRACT FROM AUTHOR]

The piezomagnetic effect is defined as a change in magnetization with applied stress. Changes in the geomagnetic field caused by the piezomagnetic effect, referred to as the piezomagnetic field, have been theoretically estimated and compared by previous studies to interpret observed variations in the geomagnetic field. However, the piezomagnetic field estimated in previous studies may not provide an accurate estimation because they ignored spatial variations in elasticity, leading to only a rough approximation of the properties of Earth's crust. In this paper, a semi-analytical procedure for calculating the piezomagnetic field arising from a point dislocation source embedded in a layered elastic medium is derived. Following a well-established method of the vector surface harmonic expansion, all of the governing equations written in partial differential equations in a real domain, together with the linear constitutive law of the piezomagnetic effect, are converted to a set of ordinary differential equations in a wavenumber domain. Equations in the wavenumber domain are solved analytically, and each component of the piezomagnetic field in the real domain is obtained after applying the Hankel transform. By using the derived procedure, the piezomagnetic and displacement fields due to a finite fault with strike-slip, dip-slip, and tensile-opening mechanisms are estimated for media with layered elasticity structures. Results for a finite fault are obtained by integrating the point source solution over the fault plane. The results of the numerical analysis allow the effect of heterogeneities in rigidity on the piezomagnetic effect to be examined and implications for the findings of previous investigations to be drawn. In cases where the moment-release at the dislocation source is fixed, the effect of the rigidity differences between upper and lower layers on the piezomagnetic field is minor even in the case where the Curie point depth is near the source of dislocation. This result is in contrast to a previous study that assumed the Mogi model and suggested that heterogeneities in the horizontal direction may be of importance when combined with layered rigidity structures. A contrast is seen between the piezomagnetic and displacement fields corresponding to models with layered rigidity structures: the piezomagnetic field is roughly proportional to the moment-release on a source fault, whereas the displacement field is proportional to slip or opening of the fault. Provided that the rigidity of the crust increases with increasing depth, the calculated piezomagnetic field is likely to have been underestimated in many earlier studies, which assumed uniform rigidity and a geodetically inverted size of slip. [ABSTRACT FROM AUTHOR]

We report 24 palaeomagnetic directions and 10 high-quality Thellier-derived palaeointensity (PI) values, obtained from 27 sites located in Baja California Peninsula, northwestern Mexico. Sampling was done in four rock units (magnesian andesites, calc-alkaline lavas, ignimbrites, adakites) belonging to San Borja and Jaraguay monogenetic volcanic fields. These units have erupted between ∼15 and 2.6 Ma (previous K-Ar and 40Ar/39Ar data); hence results are presented in two consecutive periods: middle-late Miocene and Pliocene. The identified main magnetic minerals in the sampled sites are titanomagnetite, magnetite and minor hematite, of variable grain size, present as intergrowths or surrounding grains, which reflect varying oxidation/reduction conditions during emplacement of high-temperature magmas. Based on previous geological and geophysical records, the kinematic evolution was carefully considered in the region, allowing for the independent restoration of the palaeoposition of each sampled site. Previous palaeodirections were also evaluated and corrected for tectonic motion in order to combine them with present data. Accordingly, a number of 15 and 36 directional data are used to calculate palaeopole position for Pliocene and middle-late Miocene periods, respectively, selected from a total of 74 data points. Pliocene (Plat = 87.8°, Plong = 147.5°, K = 41.06, A95 = 6.0°) and middle-late Miocene (Plat = 86.0°, Plong = 172.7°, K = 41.08, A95 = 3.8°) palaeopole positions, calculated after tectonic corrections, are not statistically different from expected North American reference pole. Tectonic correction for Middle-late Miocene virtual geomagnetic poles plays an important role in reducing the resultant tilting from 2.7° to –0.8°. PI mean were calculated for Pliocene and middle-late Miocene periods at 29.2 ± 9.1 and 23.2 ± 6.3 μT, respectively. Compiling global filtered PI data, together with our results, indicates that the strength of the geomagnetic field during middle-late Miocene was weak (virtual dipole moment = 5.0 ± 2.2 × 1022 Am2) compared to Pliocene (6.4 ± 2.8 × 1022 Am2), and also relative to the present-day value (7.6 × 1022 Am2). This indicates the global nature of the low dipole moment during the middle-late Miocene period. However, issues related to the spatio-temporal distribution of PI data still present an obstacle to validating these suggestions; therefore, more reliable data are still needed. [ABSTRACT FROM AUTHOR]

Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual timescale range where Earth's core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth's core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the relevance of the approach to describe Earth's core dynamics. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfvén torsional waves, and non-axisymmetric, quasi-geostrophic Alfvén and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal timescales, thereby providing a constraint on the extent of the |$f^{-4}$| range observed in the geomagnetic frequency power spectrum. As the model approaches Earth's core conditions, this spectral broadening arises because the decreasing inertia allows for waves at increasing frequencies. Through non-linear energy transfers with convection underlain by Lorentz stresses, these waves also extract an increasing amount of energy from the underlying convection as their key timescale decreases towards a realistic value. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion timescale to the Alfvén timescale, highlighting the dominance of Alfvén waves in the signal and the stabilizing control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth's core conditions supports the detectability of Alfvén waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution. [ABSTRACT FROM AUTHOR]

Palaeomagnetic poles form the building blocks of apparent polar wander paths and are used as primary input for quantitative palaeogeographic reconstructions. The calculation of such poles requires that the short-term, palaeosecular variation (PSV) of the geomagnetic field is adequately sampled and averaged by a palaeomagnetic data set. Assessing to what extent PSV is recorded is relatively straightforward for rocks that are known to provide spot readings of the geomagnetic field, such as lavas. But it is unknown whether and when palaeomagnetic directions derived from sedimentary rocks represent spot readings of the geomagnetic field and sediments are moreover suffering from inclination shallowing, making it challenging to assess the reliability of poles derived from these rocks. Here, we explore whether a widely used technique to correct for inclination shallowing, known as the elongation–inclination (E/I) method, allows us to formulate a set of quality criteria for (inclination shallowing-corrected) palaeomagnetic poles from sedimentary rocks. The E/I method explicitly assumes that a sediment-derived data set provides, besides flattening, an accurate representation of PSV. We evaluate the effect of perceived pitfalls for this assumption using a recently published data set of 1275 individual palaeomagnetic directions of a >3-km-thick succession of ∼69–41.5 Ma red beds from the Gonjo Basin (eastern Tibet), as well as synthetic data generated with the TK03.GAD field model. The inclinations derived from the uncorrected data set are significantly lower than previous estimates for the basin, obtained using coeval lavas, by correcting inclination shallowing using anisotropy-based techniques, and by predictions from tectonic reconstructions. We find that the E/I correction successfully restores the inclination to values predicted by these independent data sets if the following conditions are met: the number of directions N is at least 100, the A95 cone of confidence falls within a previously defined A95min-max reliability envelope, no negative reversal test is obtained and vertical-axis rotation differences within the data set do not exceed 15°. We propose a classification of three levels (A, B and C) that should be applied after commonly applied quality criteria for palaeomagnetic poles are met. For poles with classification 'A', we find no reasons to assume insufficient quality for tectonic interpretation. Poles with classification 'B' could be useful, but have to be carefully assessed, and poles with classification 'C' provide unreliable palaeolatitudes. We show that application of these criteria for data sets of other sedimentary rock types classifies data sets whose reliability is independently confirmed as 'A' or 'B', and that demonstrably unreliable data sets are classified as 'C', confirming that our criteria are useful, and conservative. The implication of our analysis is that sediment-based data sets of quality 'A' may be considered statistically equivalent to data sets of site-mean directions from rapidly cooled igneous rocks like lavas and provide high-quality palaeomagnetic poles. [ABSTRACT FROM AUTHOR]

Palaeomagnetic secular variation (PSV) and excursion data obtained across MIS 8 (243–300 ka) from the western North Atlantic Ocean ODP (Ocean Drilling Program) sites 1060–1063 show composite high-resolution PSV records (both directions and relative palaeointensity) developed for each site and intercompared. Two methods of chronostratigraphy allow us to date these records. First, we used published results that compared the calcium carbonate records of ODP Leg 172 sediments and tuned them with Milankovich cyclicity. We also compared our palaeointensity records with the PISO-1500 global palaeointensity record that was dated with oxygen isotope stratigraphy. We prefer the PISO-1500 record to date our cores. Two excursions are preserved in our PSV records—Excursions 8α and 9α. Our revised age estimates for both excursions are 8α (236.7–239.8 ka) and 9α (283.7–286.9 ka). We have compared shipboard measurements of the two excursions with u-channel measurements of selected excursion intervals. Excursion 8α is interpreted as a 'Class II' excursion (local reversal) with in-phase inclination and declination changes; Excursion 9α is a 'Class I' excursion with 90° out-of-phase inclination and declination changes. Averaged directions (after removal of true excursional directions) and relative palaeointensity in 3 and 9 ka overlapping intervals show significant PSV directional variability over 104 yr timescales that is regionally correlatable among the four sites. A notable pattern of angular dispersion variability involves most time spent with low (∼10°) dispersion, with three shorter intervals of high (∼25°) dispersion. The relative palaeointensity variability also shows significant variability over 104 yr timescales with three notable intervals of low palaeointensity in all four records and a direct correspondence between the three low-palaeointensity intervals and the three intervals of high angular dispersion. The two magnetic field excursions occur in two of the three low-palaeointensity/high-dispersion intervals. This suggests that the geomagnetic field operates in two states between reversals, one with regular to high palaeointensity and low directional variability and one with low palaeointensity and significantly higher directional variability and excursions. [ABSTRACT FROM AUTHOR]

Accurate models of the spatial structure of ionospheric magnetic fields in the diurnal variation (DV) band (periods of a few hours to a day) would enable use of magneto-variational methods for 3-D imaging of upper mantle and transition zone electrical conductivity. Constraints on conductivity at these depths, below what is typically possible with magnetotellurics, would in turn provide valuable constraints on mantle hydration and Earths deep water cycle. As a step towards this objective, we present here a novel approach to empirical modelling of global DV magnetic fields. First, we apply frequency domain (FD) principal components analysis (PCA) to ground-based geomagnetic data, to define the dominant spatial and temporal modes of source variability. Spatial modes are restricted to the available data sites, but corresponding temporal modes are effectively continuous in time. Secondly, we apply FD PCA to gridded surface magnetic fields derived from outputs of the physics-based Thermosphere–Ionosphere–Electrodynamics General Circulation Model (TIEGCM), to determine the dominant modes of spatial variability. The TIEGCM spatial modes are then used as basis functions, to fit (or interpolate) the sparsely sampled data spatial modes. Combining the two steps, we have a FD model of DV band global magnetic fields that is continuous in both space and time. We show that the FD model can easily be transformed back to the time domain (TD) to directly fit time-series data, allowing the use of satellite, as well as ground-based, data in the empirical modelling scheme. As an illustration of the methodology we construct global FD and TD models of DV band source fields for 1997–2018. So far, the model uses only ground-based data, from 127 geomagnetic observatories. We show that the model accurately reproduces surface magnetic fields in both active and quiet times, including those at sites not used for model construction. This empirical model, especially with future enhancements, will have many applications: improved imaging of electrical conductivity, ionospheric studies and improved external field corrections for core and crustal studies. [ABSTRACT FROM AUTHOR]

We study predictions of reversals of Earth's axial magnetic dipole field that are based solely on the dipole's intensity. The prediction strategy is, roughly, that once the dipole intensity drops below a threshold, then the field will continue to decrease and a reversal (or a major excursion) will occur. We first present a rigorous definition of an intensity threshold-based prediction strategy and then describe a mathematical and numerical framework to investigate its validity and robustness in view of the data being limited. We apply threshold-based predictions to a hierarchy of numerical models, ranging from simple scalar models to 3-D geodynamos. We find that the skill of threshold-based predictions varies across the model hierarchy. The differences in skill can be explained by differences in how reversals occur: if the field decreases towards a reversal slowly (in a sense made precise in this paper), the skill is high, and if the field decreases quickly, the skill is low. Such a property could be used as an additional criterion to identify which models qualify as Earth-like. Applying threshold-based predictions to Virtual Axial Dipole Moment palaeomagnetic reconstructions (PADM2M and Sint-2000) covering the last two million years, reveals a moderate skill of threshold-based predictions for Earth's dynamo. Besides all of their limitations, threshold-based predictions suggests that no reversal is to be expected within the next 10 kyr. Most importantly, however, we show that considering an intensity threshold for identifying upcoming reversals is intrinsically limited by the dynamic behaviour of Earth's magnetic field. [ABSTRACT FROM AUTHOR]

We present high-resolution palaeomagnetic and rock magnetic results from 92 successive volcanic units on a 2 km tall Lima Limo (LL) section of the Oligocene Ethiopian flood basalts (OEFB). A total of 85 well-defined flow-mean characteristic remanent magnetization directions representing seven stable magnetic polarity zones with six transitional/excursional directions were determined. These results indicate the identification of four more polarity reversals than previous palaeomagnetic studies; the resulting magnetostratigraphy has, therefore, more polarity zonation. Comparison of this result with the most recently revised geomagnetic polarity time scale (GPTS, hereafter GPTS2016), by using available radiometric age data, could not find a unique correlation. Instead, it strongly suggests the recording of at least one very brief polarity chron or putative geomagnetic excursion. Our magnetostratigraphic interpretation infers that the relative timing between the OEFB eruptions and the Oi-2 global cooling estimated two possible scenarios: one where the lowermost reverse-polarity (R1) interval for the LL section is correlated to Chron C11r of GPTS2016, same as the interpretations of earlier studies, would make a causal linkage between the OEFB eruptions and the Oi-2 cooling less possible; and, the eruption timing estimated in another scenario correlating the R1 to Chron C12r might preserve the probability of its causal influence in the Oi-2 cooling. The resulting overall mean pole for the LL section of this study, 78.2° N in latitude and 213.0° E in longitude (A 95 = 3.4°, N  = 79), is closer to other co-eval palaeomagnetic poles from different regions and the reference pole of Africa. Our analysis of geomagnetic palaeosecular variation (PSV) shows that, compared to the Plio-Pleistocene, the Early Oligocene has higher degrees of PSV but its slightly weaker latitude dependence. [ABSTRACT FROM AUTHOR]

Magnetostratigraphic investigation of sediment cores from two different water depths in the SE Black Sea based on discrete samples, and parallel U-channels in one of the cores, yielded high-resolution records of geomagnetic field variations from the past about 68 ka. Age constrains are provided by three tephra layers of known age, accelerator mass spectrometry 14C dating, and by tuning element ratios obtained from X-ray fluorescence scanning to the oxygen isotope record from Greenland ice cores. Sedimentation rates vary from a minimum of ∼5 cm ka−1 in the Holocene to a maximum of ∼50 cm ka−1 in glacial marine isotope stage 4. Completely reversed inclinations and declinations as well as pronounced lows in relative palaeointensity around 41 ka provide evidence for the Laschamps geomagnetic polarity excursion. In one of the investigated cores also a fragmentary record of the Mono Lake excursion at 34.5 ka could be revealed. However, the palaeomagnetic records are more or less affected by greigite, a diagenetically formed magnetic iron sulphide. By definition of an exclusion criterion based on the ratio of saturation magnetization over volume susceptibility, greigite-bearing samples were removed from the palaeomagnetic data. Thus, only 25–55 per cent of the samples were left in the palaeomagnetic records obtained from sediments from the shallower coring site. The palaeomagnetic record from the deeper site, based on both discrete samples and U-channels, is much less affected by greigite. The comparison of palaeomagnetic data shows that the major features of the Laschamps polarity excursion were similarly recovered by both sampling techniques. However, several intervals had to be removed from the U-channel record due to the presence of greigite, carrying anomalous directions. By comparison to discrete sample data, also some directional artefacts in the U-channel record, caused by low-pass filtering of the broad magnetometer response functions, averaging across fast directional and large amplitude changes, can be observed. Therefore, high-resolution sampling with discrete samples should be the preferred technique when fast geomagnetic field variations, such as reversals and excursions, shall be studied from sedimentary records in the very detail. [ABSTRACT FROM AUTHOR]

An archaeomagnetic, rock magnetic and magnetic fabric study has been carried out on seven anthropogenic ash horizons in the Middle Palaeolithic sedimentary level XXIV at the rock shelter of Crvena Stijena ('Red Rock'), Montenegro. The study has multiple goals, including the identification of iron bearing minerals formed during combustion, assessment of the suitability of these combustion features for recording the Earth´s magnetic field direction, revelation of the magnetic fabric and its significance in the characterization of cave (rock shelter) burnt facies, and identification of post-burning alteration processes. Magnetite has been identified as the main ferromagnetic component of the ash. The ash layers exhibit a high thermomagnetic reversibility in contrast to the irreversible behaviour of their subjacent burnt black layers which is related to the different temperatures attained. Seven mean archaeomagnetic directions were obtained with acceptable statistical values indicating that these features recorded the field direction at the time of burning. However, some of them are out of the expected range of secular variation for mid-latitude regions suggesting post-burning alterations. The magnetic fabric of the ash was characterized by anisotropy of low field magnetic susceptibility measurements. Statistical analysis (box and whisker plot) of the basic anisotropy parameters, such as foliation, lineation, degree of anisotropy and the shape parameter, along with the alignment of the principal susceptibilities on stereoplots, revealed variation among the ash units. The diverse, oblate to prolate, lineated or strongly foliated, quasi-horizontally and vertically oriented fabrics of the units may indicate different slope processes, such as orientation by gravity, solifluction, run-off water, quasi-vertical migration of groundwater and post-burning/post-depositional alteration of the fabric by rockfall impact. In sum, the magnetic characterization of the ash layers has shown the occurrence of different post-burning alteration processes previously not identified at the site. Alteration processes in prehistoric combustion features are often identified from macroscopic observations but our study demonstrates that multiple processes can affect them and are usually unnoted because they take place on a microscopic scale. Their identification is critical for a correct chronological and cultural interpretation of a site (e.g. collection of samples for dating, stratigraphic displacement of remains), especially if significant alterations are involved. Magnetic methods are therefore a powerful but underutilized tool in palaeolithic research for the identification and evaluation of taphonomic processes affecting prehistoric fires. [ABSTRACT FROM AUTHOR]

Planetary scale interannual deformations of the Earth's surface, of millimetric amplitude, have recently been related to both geomagnetic field changes and motion within the fluid outer core. We calculate the temporal variations of the dynamical pressure at the surface of the core associated with core flow models inverted from geomagnetic observations. From these we compute predictions of the changes in Earth's topography in response to elastic deformations in the mantle. We show that at decadal periods, the predicted changes in Earth's topography are at most of the order of 0.3 mm. Focused at interannual periods between 4 and 9.5 yr, the predicted topography variations are smaller than 0.05 mm, at least an order of magnitude smaller than the reported observations. These amplitudes are only weakly sensitive to the choice of hypothesis used to reconstruct fluid motions at the core surface. We conclude that surface deformations induced by dynamical pressure changes in the core are below the detection level at present-day. Alternative geophysical sources must be sought to explain the observed millimetric interannual variations of the planetary scale topography, and its associated gravity variations. We currently see no justification for a physical relationship between interannual fluctuations of the geomagnetic field and of Earth's observed deformations. We conjecture that the largest gravity signal of core origin is potentially associated with decadal longitudinal oscillations of the inner core. It might be detectable as longer series will become available. [ABSTRACT FROM AUTHOR]

An algorithm and software are developed for fast and accurate evaluation of the elements of the geomagnetic field represented in high-degree (>720) solid spherical harmonics at many scattered points in the space above the surface of the Earth. The algorithm is based on representation of the geomagnetic field elements in solid ellipsoidal harmonics and application of tensor product needlets. Open source FORTRAN and MATLAB realizations of this algorithm that rely on data from the Enhanced Magnetic Models 2015, 2017 (EMM2015, EMM2017) have been developed and extensively tested. The capabilities of the software are demonstrated on the example of the north, east and down components of the geomagnetic field as well as the derived horizontal intensity, total intensity, inclination and declination. For the range from −417 m under the Earth reference ellipsoid up to 1000 km above it the FORTRAN and MATLAB versions of the software run 465 and 189 times faster than the respective FORTRAN and MATLAB versions of the software using the standard spherical harmonic series method, while the accuracy is less than 1 nT and the memory (RAM) usage is 9 GB. [ABSTRACT FROM AUTHOR]

For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective a priori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. A priori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided. [ABSTRACT FROM AUTHOR]

Magnetostratigraphic and geochemical analyses were performed on two sediment cores recovered from the Sea of Marmara to investigate geomagnetic field variations over the last 70 ka. A chronology for each of the two cores was developed from eight AMS 14C datings, tephrochronology, and tuning of Ca concentrations with stadials and interstadials observed in Greenland ice core oxygen isotope data. Based on the age models, cores MD01–2430 and MRS-CS19 reach back to 70 and 32 ka, respectively. High average sedimentation rates of 43 cm kyr–1 for core MD01–2430 and 68 cm kyr–1 for core MRS-CS19 allow high-resolution reconstruction of geomagnetic field variations for the Sea of Marmara. Mineral magnetic properties are sensitive to glacioeustatic sea level changes and palaeoclimate variations in this region, reflecting the variable palaeoenvironmental conditions of the Sea of Marmara during last 70 ka. Despite the impairment of the palaeomagnetic record in some stratigraphic intervals due to early diagenesis, relative palaeointensity variations in the Sea of Marmara sediments correlate well with similar records derived from other regions, such as the nearby Black Sea and the GLOPIS-75 stack. The directional record derived from the Sea of Marmara cores exhibits typical palaeosecular variation patterns, with directional anomalies at 41 and 18 ka, representing the Laschamps and postulated Hilina Pali excursions, respectively. Both directional anomalies are also associated with palaeointensity minima. A further palaeointensity minimum at 34.5 ka is likely related to the Mono Lake excursion, with no directional deviation documented in the Sea of Marmara palaeomagnetic record so far. [ABSTRACT FROM AUTHOR]

Mounting evidence from both seismology and numerical experiments on core composition suggests the existence of a layer of stably stratified fluid at the top of Earth's outer core. In such a layer, a magnetostrophic force balance and suppressed radial motion lead to stringent constraints on the magnetic field, named Malkus constraints , which are a much more restrictive extension of the well known Taylor constraints. Here, we explore the consequences of such constraints for the structure of the core's internal magnetic field. We provide a new simple derivation of these Malkus constraints, and show solutions exist which can be matched to any external potential field with arbitrary depth of stratified layer. From considerations of these magnetostatic Malkus constraints alone, it is therefore not possible to uniquely infer the depth of the stratified layer from external geomagnetic observations. We examine two models of the geomagnetic field defined within a spherical core, which obey the Taylor constraints in an inner convective region and the Malkus constraints in an outer stratified layer. When matched to a single-epoch geomagnetic potential field model, both models show that the toroidal magnetic field within the outer layer is about 100 times stronger compared to that in the inner region, taking a maximum value of 8 mT at a depth of 70 km. The dynamic regime of such a layer, modulated by suppressed radial motion but also a locally enhanced magnetic field, may therefore be quite distinct from that of any interior dynamo. [ABSTRACT FROM AUTHOR]

Assessment of long-term palaeosecular variation (PSV) of the geomagnetic field is frequently based on simplified versions of a class of statistical models known as giant Gaussian processes (GGP) used to represent temporal variations in spherical harmonic descriptions of the field. Here we propose a new type of analysis to assess the shape and dispersion of the directional distributions caused by PSV. The quantities analysed in this study are equal-area coordinates of rotated distributions of palaeomagnetic directions, |${x_E}$| (east−west) and |${x_N}\ $| (north−south) and their standard deviations (⁠|${\sigma _E}$| and |${\sigma _N}$|⁠). These are easy to determine, and can readily be numerically predicted for any GGP model, avoiding the need for the numerous simulations generally used to determine the scatter and/or elongation of directional distributions. Mean predictions of |$\overline {{x_N}} $| for a simplified GGP model are different from the expected geocentric axial dipole (GAD) directions, in agreement with inclination differences noted in previous studies. The best estimates for palaeomagnetic inclination are the expected directions from the mean of virtual geomagnetic poles (VGPs) calculated using an iterative angular cut-off process. Predictions of |${\sigma _{\rm E}}$| and |${\sigma _{\rm N}}$| vary with latitude and are symmetric about the Equator. The N–S direction (⁠|${\sigma _{\rm N}}$|⁠) is always larger than E–W (⁠|${\sigma _{\rm E}}$|⁠), but the difference decreases from a maximum at the Equator to the poles, where |${\sigma _{\rm N}} = \ {\sigma _{\rm E}}$|⁠. A simplified GGP model is used to show that the parameter α (affecting variances in all Gauss coefficients) is positively correlated with |${\sigma _{\rm E}}$| and |${\sigma _{\rm N}}\ $| while the β parameter, the ratio of dipole to quadrupole family standard deviations, modifies the latitudinal dependence of |${\sigma _{\rm E}}$| and |${\sigma _{\rm N}}$|⁠. Experimental error in |${\sigma _{\rm E}}$| and |${\sigma _{\rm N}}$| can be accommodated using the common statistical parameters found in palaeomagnetic data sets, as |${\alpha _{95}}$| from site-mean directions. Predictions of simplified GGP models are compared with both numerical simulations and real data spanning the last 10 Ma. The latitudinal dependence of the proposed measures of PSV (⁠|${\sigma _{\rm E}}$| and |${\sigma _N}$|⁠) provide useful diagnostics for testing the validity of a GGP model. For the past 10 Ma the best-fitting GGP model with a mean GAD field set to |$g_1^0 = \ - 18\ \mu T$| has α = 6.7 µT and β = 4.2. These new directional diagnostics will be used to investigate changes in overall geomagnetic field behaviour over other geological time intervals. [ABSTRACT FROM AUTHOR]

By utilizing the addition theorems of the arctangent function and the logarithm, we developed a new expression of Bessel's exact formula to compute the prismatic gravitational field using the triple difference of certain analytic functions. The use of the new expression is fast since the number of transcendental functions required is significantly reduced. The numerical experiments show that, in computing the gravitational potential, the gravity vector, and the gravity gradient tensor of a uniform rectangular parallelepiped, the new method runs 2.3, 2.3 and 3.7 times faster than Bessel's method, respectively. Also, the new method achieves a slight increase in the computing precision. Therefore, the new method can be used in place of Bessel's method in any situation. The same approach is applicable to the geomagnetic field computation. [ABSTRACT FROM AUTHOR]

The existence of a stably stratified layer underneath the core–mantle boundary (CMB) has been recently revived by corroborating evidences coming from seismic studies, mineral physics and thermal evolution models. Such a layer could find its physical origination either in compositional stratification due to the accumulation of light elements at the top or the core or in thermal stratification due to the heat flux becoming locally subadiabatic. The exact properties of this stably stratified layer, namely its size |$\mathcal {H}_s$| and the degree of its stratification characterized by the Brunt–Väisälä frequency N , are however uncertain and highly debated. A stable layer underneath the CMB can have crucial dynamical impacts on the geodynamo. Because of the inhibition of the convective motions, a stable layer is expected to primarily act as a low-pass filter on the magnetic field, smoothing out the rapidly varying and small-scale features by skin effect. To investigate this effect more systematically, we compute 70 global geodynamo models varying the size of the stably stratified layer from 0 to 300 km and its amplitude from N /Ω = 0 to N /Ω ≃ 50, Ω being the rotation rate. We show that the penetration of the convective flow in the stably stratified layer is controlled by the typical size of the convective eddies and by the local variations of the ratio N /Ω. Using quantitative measures of the degree of morphological semblance between the magnetic field obtained in numerical models and the geomagnetic field at the CMB, we establish an upper bound for the stable layer thickness |$\mathcal {H}_s\lt (N/\Omega)^{-1} \mathcal {L}_s$|⁠ , |$\mathcal {L}_s$| being the horizontal size of the convective flow at the base of the stable layer. This defines a strong geomagnetic constraint on the properties of a stably stratified layer beneath the CMB. Unless unaccounted double-diffusive effects could drastically modify the dynamics of the stable layer, our numerical geodynamo models hence favour no stable stratification atop the core. [ABSTRACT FROM AUTHOR]

Observations of changes in the geomagnetic field provide unique information about processes in the outer core where the field is generated. Recent geomagnetic field reconstructions based on palaeomagnetic data show persistent westward drift at high northern latitudes at the core–mantle boundary (CMB) over the past 4000 yr, as well as intermittent occurrence of high-latitude weak or reverse flux patches. To further investigate these features, we analysed time-longitude plots of a processed version of the geomagnetic field model pfm9k.1a, filtered to remove quasi-stationary features of the field. Our results suggest that westward drift at both high northern and southern latitudes of the CMB have been a persistent feature of the field over the past 9000 yr. In the Northern Hemisphere we detect two distinct signals with drift rates of 0.09° and 0.25° yr−1 and dominant zonal wavenumbers of m  = 2 and 1, respectively. Comparisons with other geomagnetic field models support these observations but also highlight the importance of sedimentary data that provide crucial information on high-latitude geomagnetic field variations. The two distinct drift signals detected in the Northern Hemisphere can largely be decomposed into two westward propagating waveforms. We show that constructive interference between these two waveforms accurately predicts both the location and timing of previously observed high-latitude weak/reverse flux patches over the past 3–4 millennia. In addition, we also show that the 1125-yr periodicity signal inferred from the waveform interference correlates positively with variations in the dipole tilt over the same time period. The two identified drift signals may partially be explained by the westward motion of high-latitude convection rolls. However, the dispersion relation might also imply that part of the drift signal could be caused by magnetic Rossby waves riding on the mean background flow. [ABSTRACT FROM AUTHOR]