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The secular variation of the geomagnetic field is the temporal variation that takes place in the field on time scales between few years to hundreds or thousands of years. On the other hand, impulses or ”geomagnetic jerks” indicate a rapid change in the slope of the secular variation. The origin of these phenomena is linked to the behavior of the geodynamo and the contribution of the outer mantle-core interaction.ROMP (acronym from spanish “ Red de Observatorios Magnéticos Permanentes”) is composed by the following observatories: ”Las Acacias ”(LAS) at Buenos Aires,” Trelew ”(TRW) at Chubut,” Pilar ”(PIL) at Córdoba and ”Orcadas”(ORC) at the Argentine sector in Antartic; the first two depend on the National University of La Plata and the latter on the National Meteorological Service. In the present work one analyzes the secular variation and the determination of jerks in the geomagnetic elements recorded at the ROMP stations, in historical times up to the present.

Simple magnetometers are the gateway instruments for exploring the geomagnetic field that can be used by hobbyists and teachers alike to monitor and study a variety of space weather phenomena. This article provides designs for four different instruments that can be built for under ${\$}50$ , yet have the sensitivity to detect the diurnal ionospheric Sq variation, and geomagnetic disturbances due to the arrival of solar coronal mass ejections. A comparison of the data from these instruments against contemporaneous data from the Fredericksburg Magnetic Observatory reveal the accuracy of these instruments. Also provided is an example of how these instruments have been used in high school Earth Science and Astronomy classes to improve student learning and scientific curiosity.

The paper presents the results of archaeological excavations within the residential area of the fortified posad of Tyumen. The earliest period of habitation in this area dates back to the XVII century. Two household structures, a cellar and an underground storage, dated to the XVIII – the first half of the XIX century, have been identified. These structures were deepened into the earth to a depth of 1.7–1.9 meters and constructed using log-building techniques. In the middle of the XIX century, some of the household structures were demolished, and the newly cleared area was repurposed to expand the trading area near the Merchant Court (Gostiny Dvor). For the first time in dating archaeological wood, a method based on reflecting the Earth’s geomagnetism during the growth of arboreal plants was used. The obtained results demonstrate the prospects of its application for regions where there are no developed dendro-scales. An additional advantage of this method in dating archaeological objects is the ability to use fragmented material.

Abstract The Levantine Iron Age anomaly (LIAA) is a regional short-decadal geomagnetic strength field variation located at the Levantine region characterized by high intensities with maximum virtual axial dipole moments around 190 ZAm2. It has been constrained by archeomagnetic data coming from Eastern Europe and Western Asia between 1050 and 700 BC. The LIAA can be related to a fast and spatially localized geomagnetic positive anomaly (spike) at the Earth’s surface. In this study, we model the LIAA by using a Fisher–von Mises function that fits the most recent archeomagnetic intensity database in the region. A spherical harmonic analysis is implemented for this spike function to perturb a base model in order to build a global reconstruction (perturbed-model) that reproduces the spatial and temporal characteristics of the LIAA. Our results show the importance of harmonic degrees from n = 3–4 to n = 20 to reconstruct the anomaly extension suggested by the database. Two maxima linked with the LIAA are reproduced by our global perturbed-model at the Levantine region at 950 BC and 750 BC. A third maxima in intensity around 500 BC is also observed, affecting the whole Europe. Graphical Abstract

Abstract GOES‐16 and GOES‐17 are the first of NOAA's Geostationary Operational Environmental Satellite (GOES)‐R series of satellites. Each GOES‐R satellite has a magnetometer mounted on the end (outboard) and one part‐way down a long boom (inboard). This paper demonstrates the relative accuracy and stability of the measurements on a daily and long‐term basis. The GOES‐16 and GOES‐17 magnetic field observations from 2017 to 2020 have been compared to simultaneous magnetic field observations from each other and from the previous GOES‐NOP series satellites (GOES‐13, GOES‐14 and GOES‐15). These comparisons provide assessments of relative accuracy and stability. We use a field model to facilitate the inter‐satellite comparisons at different longitudes. GOES‐16 inboard and outboard magnetometers data suffer daily variations which cannot be explained by natural phenomena. Long‐term‐averaged GOES‐16 outboard (OB) data has daily variations of ±3 nT from average values with one‐sigma uncertainty of ±1.5 nT. Long‐term averaged GOES‐17OB magnetometer data have minimal daily variations. Daily average of the difference between the GOES‐16 outboard or GOES‐17 outboard measurements and the measurements made by another GOES satellite are computed. The long‐term averaged results show the GOES‐16OB and GOES‐17OB measurements have long‐term stability (±2 nT or less) and match measurements from magnetometers on other GOES within limits stated herein. The GOES‐17OB operational offset (zero field value) was refined using the GOES‐17 satellite rotated 180° about the Earth pointing axis (known as a yaw flip).

Abstract Previous studies of rapid geomagnetic changes have highlighted the most extreme changes in direction and field strength found in paleomagnetic field models over the past 100 ky. Here we study distributions of rates of change in both time and space. Field models based on direct observations provide the most accurate values for rates of change, but their short duration precludes a complete description of field behavior. Broader representation is provided by time‐varying paleofield models, here including GGF100k, GGFSS70, LSMOD.2, CALS10k.2, HFM.OL1.A1, pfm9k.2, and SHAWQ‐iron age although variability across models and lack of temporal and spatial resolution of fine scale variations make direct comparisons difficult. For the paleofield we define rapid changes as exceeding the peak overall value of 0.4° yr−1 for directional changes and 150 nT yr−1 for intensities as established by the gufm1 model spanning 1590–1990 CE. We find that rapid directional changes are associated with low field strength and can spread across all latitudes during such episodes. Distributions of directional rates of change exhibit high skewness for models that include excursions. Rates of change in field intensity exceeding 150 nT yr−1 arise in brief intervals during the Holocene particularly associated with the strong field Levantine Iron Age Anomaly. Around the Laschamp excursion there are also rare localized occurrences of rapid intensity change. Limitations in current models make it difficult to define absolute rates for past changes, but we see that rapid changes are essential field characteristics not observed in the modern field that should nevertheless be regarded as an essential for Earth‐like dynamo simulations.

Abstract The Earth’s magnetic field originated in the fluid core, the so-called core field, is the dominant contribution to the geomagnetic field. Since ancient times, the core geomagnetic field has been used primarily for geographical orientation and navigation by means of compasses. Nowadays, thanks to the large amount of geomagnetic data available, core field models can be developed on a global or regional scale. Global models resolve large-scale geomagnetic field features, while regional models can resolve greater detail over a particular region. The spherical harmonic cap analysis is a widely used technique for regional-scale modelling of the geomagnetic field. In this work we have developed a regional model of the core field and its secular variation between 2014.5 and 2020.5 over the Iberian Peninsula, based on data from Swarm satellites, geomagnetic observatories and repeat stations. Its performance has been validated by comparing the fit to the available geomagnetic data using the regional model and the global models IGRF and CHAOS over the whole spatio-temporal range studied. In order to optimise the model, a detailed study of its input parameters has been carried out, showing that not all parameters have an equal influence on the modelling. This new model reproduces the input data with a root mean square error of 2.9 nT, improving the outcome of global models on this region. The results of this work will allow the Spanish Instituto Geográfico Nacional to produce the magnetic cartography of Iberia and the Balearic Islands in 2020.0, which for the first time will be based on a regional core field model, replacing the polynomial variation method used in the past. Graphical abstract

The geomagnetic observation data of FHD-2B at Datong seismic station in Shanxi is mainly affected by the interference of the instrument’s own observation system and the surrounding environment. Since the performance of the instrument is nearly stable after delivery, we can improve the quality of observation data by improving the environment. In this paper, the quality of observation data from 2017 to 2021 was evaluated from three aspects: continuity rate, integrity rate and background noise, and it is found that the background noise level of the instrument has been significantly reduced since the instrument was updated in June 2019. By analyzing the data curves of different interferences such as construction interference, vehicle interference, high-voltage direct current transmission interference and power failure, it is found that the construction interference is generally manifested in the same period of time when each component is interfered, and the interference amplitude is different; the interference of high-voltage direct current transmission is usually serious in Z component, which can be processed through the interference period given by the National Geomagnetic Network Center and combined with the data of surrounding geomagnetic stations; vehicle interference interferes with each component of data, corresponding to vehicle activity period; the power failure interference shows that the observed data curves of D, H and Z components become thicker, burrs increase, and even wrong data appear, which can be solved by modifying the parameters of the instrument home page. The characteristics of different interference curves are summarized, which is convenient for workers to use FHD-2B geomagnetic data correctly for seismic research.

Earth’s magnetic field is a dynamic, changing phenomenon. The geomagnetic field consists of contributions from several sources, of which the main field originating in Earth’s core makes up the bulk. On regional and local scales at Earth’s surface, the lithospheric field can make a substantial contribution to the overall field and therefore needs to be considered in field models. A locally derived regional core field model, named HMOREG, has been shown to give accurate predictions of the southern African region. In this study, a new regional field model called the South African Regional Core and Crust model (SARCC) is introduced. This is the first time that a local lithospheric model, estimated by employing the revised spherical cap harmonic analysis modelling method, has been combined with the core component of CHAOS-6, a global field model. It is compared here with the existing regional field model as well as with global core field models. The SARCC model shows small-scale variations that are not present in the other three models. Including a lithospheric magnetic field component likely contributed to the better performance of the SARCC model when compared to other global and local field models. The SARCC model showed a 33% reduction in error compared to surface observations obtained from field surveys and INTERMAGNET stations in the Y component, and HMOREG showed a 7% reduction in error compared to the global field models. The new model can easily be updated with global geomagnetic models that incorporate the most recent, state-of-the-art core and magnetospheric field models. Significance: Earth’s magnetic field is an integral part of many current navigational methods in use. Updates of geomagnetic field models are required to ensure the accuracy of maps, navigation, and positioning information. The SARCC regional geomagnetic field model introduced here was compared with global geomagnetic field models, and the inclusion of a lithospheric magnetic field component likely contributed to the better performance of the SARCC model. This regional model of southern Africa could easily be updated on a regular basis, and used for high-resolution information on the Earth’s magnetic field for the wider scientific community.

Abstract Time-varying electromagnetic field observed on the ground or at a spacecraft consists of contributions from (i) electric source currents, such as those in the ionosphere and magnetosphere, and (ii) corresponding fields induced by source currents within the conductive Earth’s interior by virtue of electromagnetic induction. Knowledge about the spatio-temporal structure of inducing currents is a key component in ionospheric and magnetospheric studies, and is also needed in space weather hazard evaluation, whereas the induced currents depend on the Earth’s subsurface electrical conductivity distribution and allow us to probe this physical property. In this study, we present an approach that reconstructs the inducing source and subsurface conductivity structures simultaneously, preserving consistency between the two models by exploiting the inherent physical link. To achieve this, we formulate the underlying inverse problem as a separable nonlinear least-squares (SNLS) problem, where inducing current and subsurface conductivity parameters enter as linear and nonlinear model unknowns, respectively. We solve the SNLS problem using the variable projection method and compare it with other conventional approaches. We study the properties of the method and demonstrate its feasibility by simultaneously reconstructing the ionospheric and magnetospheric currents along with a 1-D average mantle conductivity distribution from the ground magnetic observatory data. Graphical Abstract

Abstract Continuous geomagnetic records of the strength and direction of the Earth's field at the surface extend back to the 1840s. Over the past two centuries, eight observatories have existed in the United Kingdom, which measured the daily field variations using light‐sensitive photographic paper to produce analogue magnetograms. Around 350,000 magnetograms have been digitally photographed at high resolution. However, converting the traces to digital values is difficult and time consuming as the magnetograms can have over‐lapping lines, low quality recordings and obscure metadata for conversion to SI units. We discuss our approach to digitizing the traces from large geomagnetic storms and highlight some of the issues to be aware of when capturing magnetic information from analogue measurements. These include cross‐checking the final digitized values with the recorded hourly mean values from observatory year books and comparing several observatory records for the same storm to catch errors such as sign inversions or incorrect ‘wrap‐around’ of data on the paper records.

Abstract In 2019, the World Data Center for Solar-Terrestrial Physics in Moscow digitized the archive of observations of the Earth’s magnetic field carried out by the Soviet satellites Kosmos-49 (1964) and Kosmos-321 (1970). As a result, the scientific community for the first time obtained access to a unique digital data set, which was registered at the very beginning of the scientific space era. This article sets out three objectives. First, the quality of the obtained measurements is assessed by their comparison with the IGRF model. Second, we assess the quality of the models, which at that time were derived from the data of these two satellites. Third, we propose a new, improved model of the geomagnetic field secular variation based on the scalar measurements of the Kosmos-49 and Kosmos-321 satellites. Graphical Abstract

The ionospheric currents that flow in the E layer, the magnetospheric currents and the induced currents in the lithosphere under the station are the sources of geomagnetic variations in the calm days Sq. There exist several methods for estimating the values corresponding to magnetospheric currents. The magnitude of the induced currents contribution is considered about one third of the measured horizontal variation Sq. In this work, one proceeds to produce the correction for magnetospheric effects by analyzing the ring current index SMR, getting an efficient correction. Subsequently, the values of the north and east components of the surface current densities (KN and KE) above ROMP stations are estimated for calm days with a Kp index less than or equal to 2 in the 2019-2021 interval. It is found that at 14 hs LT, the maximum KN and KE values are recorded at PIL on 12.4.2020, while the minimum KN and KE values are recorded at ORC on 10.19.19 and 11.16.20, respectively.

Abstract The Gravity field and steady-state Ocean Circulation Explorer (GOCE) is part of ESA’s Earth Explorer Program. The satellite carries magnetometers that control the activity of magnetorquers for navigation of the satellite, but are not dedicated as science instruments. However, intrinsic steady states of the instruments can be corrected by alignment and calibration, and artificial perturbations, e.g. from currents, can be removed by their characterisation correlated to housekeeping data. The leftover field then shows the natural evolution and variability of the Earth’s magnetic field. This article describes the pre-processing of input data as well as calibration and characterisation steps performed on GOCE magnetic data, using a high-precision magnetic field model as reference. For geomagnetic quiet times, the standard deviation of the residual is below 13 nT with a median residual of (11.7, 9.6, 10.4) nT for the three magnetic field components (x, y, z). For validation of the calibration and characterisation performance, we selected a geomagnetic storm event in March 2013. GOCE magnetic field data show good agreement with results from a ground magnetic observation network. The GOCE mission overlaps with the dedicated magnetic field satellite mission CHAMP for a short time at the beginning of 2010, but does not overlap with the Swarm mission or any other mission flying at low altitude and carrying high-precision magnetometers. We expect calibrated GOCE magnetic field data to be useful for lithospheric modelling and filling the gap between the dedicated geomagnetic missions CHAMP and Swarm. Graphic Abstract

The Microwave Palaeointensity System at the University of Liverpool has developed, over 30 years, into the current third generation version; a combined 14 GHz microwave resonant cavity and superconducting quantum interference device magnetometer integrated microwave system. The use of microwave energy minimises the bulk temperatures required to demagnetise and remagnetise palaeomagnetic material, thereby limiting the significant problem of thermo-chemical alteration of magnetic minerals. Here we review the microwave palaeointensity approach, including its development, technical details, modern usage and results. We have carried out a comprehensive analysis of 20 palaeointensity studies, published between 2008 and 2022, where data collected using the microwave system may be compared with various other methods at the site level. An assessment of microwave results revealed no statistical bias compared to thermal, and known field data. We also present results from a new controlled experiment which tests the ability of the microwave to accurately recover weak, ancient palaeointensities when strongly overprinted. We conclude that the microwave system can be used for the primary method of determining accurate absolute palaeointensities or as part of a multi-method approach, and is well suited to a wide range of material from archaeomagnetic samples to ancient rocks.

According to the characteristic requirements of Internet of things of intelligent sensor, an autonomous positioning module is developed by using geomagnetic assisted inertial navigation/BDS combined positioning algorithm. The chip selection is based on the principle of low power consumption and localization. The module structure and circuit schematic diagram are introduced. The national production and low-power design are adopted in the hardware design, at the same time, the zero speed correction algorithm, quaternion method and geomagnetic auxiliary correction algorithm are adopted in the software to realize the storage and inversion of the moving trajectory of the intelligent sensor. The test shows that the moving track is highly similar to the actual loop. The measured distance of 378 m loop is 375.01 m, the difference is 2.99 m, and the relative error is 0.8%.

The agonic line, characterized by zero values of geomagnetic declination, has had a westward drift during the last centuries, crossing the location of the Real Observatorio de Madrid at the end of the year 2021. This fact, which was monitored by the Instituto Geográfico Nacional, moves us to study the evolution of the magnetic declination in this emblematic emplacement between the last two crosses of the agonic line. Our results point out that the current westward drift started around the year 1810 and, before this period, the agonic line moved from west to east, crossing the location of the Real Observatorio around 1650–1675.

Abstract The World Magnetic Model (WMM) is a geomagnetic main field model that is widely used for navigation by governments, industry and the general public. In recent years, the model has been derived using high accuracy magnetometer data from the Swarm mission. This study explores the possibility of developing future WMMs in the post-Swarm era using data from the Iridium satellite constellation. Iridium magnetometers are primarily used for attitude control, so they are not designed to produce the same level of accuracy as magnetic data from scientific missions. Iridium magnetometer errors range from 30 nT quantization to hundreds of nT errors due to spacecraft contamination and calibration uncertainty, whereas Swarm measurements are accurate to about 1 nT. The calibration uncertainty in the Iridium measurements is identified as a major error source, and a method is developed to calibrate the spacecraft measurements using data from a subset of the INTERMAGNET observatory network producing quasi-definitive data on a regular basis. After calibration, the Iridium data produced main field models with approximately 20 nT average error and 40 nT maximum error as compared to the CHAOS-7.2 model. For many scientific and precision navigation applications, highly accurate Swarm-like measurements are still necessary, however, the Iridium-based models were shown to meet the WMM error tolerances, indicating that Iridium is a viable data source for future WMMs. Graphical Abstract

This article addresses the further development of the ground-based temperature radiometer TEMPERA, which measures atmospheric microwave radiation in one linear polarization in order to retrieve temperature profiles up to an altitude of 50 km (Stähli et al., 2013). The latest innovation is a new polarimetric receiver, which allows observing the atmosphere simultaneously in left- and right-circular polarization. In combination with an adapted inversion method, the fully polarimetric analysis can improve the accuracy and extends the vertical upper limit of retrieved temperature profiles. Comparisons between single polarization and fully polarimetric retrievals with simulated atmospheric spectra are presented, and the influence of the Earth’s magnetic field is analyzed. In addition, we propose a simple calibration method for fully polarimetric radiometers and present first atmospheric spectra measured with the new TEMPERA-C instrument.

UAVs represent a tremendous opportunity to perform geophysical and repeated experiments, particularly in volcanic contexts. Their ability to be deployed rapidly and fly at various altitudes and the fact that they are easy to operate despite complex field conditions make them attractive for magnetic surveys. Detailed maps of the magnetic field in turn bring key constraints on the rocks’ composition, thermal anomalies, intrusive systems, and crustal contrast evolution. Yet, raw magnetic field measurements require careful processing to minimize directional, positional, and crossover errors. Moreover, stitching together adjacent or overlapping surveys acquired at different times and altitudes is not a trivial task. Therefore, it is challenging in remote areas to directly evaluate the consistency of a survey and to ascertain the success of the field mission. In this paper, we present a fast algorithm allowing for a quick-look modeling of scalar magnetic intensity measurements. The approach relies on rectangular harmonic analysis (RHA). The field measurements are automatically corrected for a global main field. Then, they are projected along this main field and modeled in terms of RHA functions. The software can exploit the quality indices provided with data and a procedure is applied to mitigate the effect of outliers. Maps for the scalar and the vector anomaly fields are readily built on an interpolated regular grid leveled at a constant altitude. In order to assess the modeling and the inversion procedures, analyses are carried out with synthetic measurements derived from a high-resolution global lithospheric magnetic field model estimated on the French aeromagnetic grid and at UAV locations with some added nonrandom noise. These analyses indicate that RHA is efficient for first-order and direct mapping of the crustal magnetic field structures measured by UAVs but that it could be applied on airborne and marine magnetic intensity data covering dense and large geographical extensions.

Abstract We describe the way a global model of the geomagnetic field has been built using vector field data acquired by the absolute scalar magnetometers (ASM) running in vector mode on board the Alpha and Bravo satellites of the European Space Agency (ESA) Swarm mission. This model has been used as a parent model to build a candidate Definitive Geomagnetic Reference Field (DGRF) 2015.0 model to meet the call issued in the context of the recent update of the International Geomagnetic Reference Field (IGRF thirteenth generation). Because small but systematic issues were identified in a previous candidate IGRF 2015.0 model built in the same spirit (also only relying on ASM vector field data) in the context of the previous IGRF update (IGRF twelfth generation), we now also use improved ASM vector field (ASM-V) data. The issue originally affecting the ASM-V data is described, together with the way the improved data are now being produced. The resulting candidate DGRF 2015.0 model is shown to considerably improve on the previous candidate IGRF 2015.0 model (being closer to the final DGRF 2015.0 model by one order of magnitude in spherical harmonic spectral terms). It is also shown to stand among the candidate models closest to the final official DGRF 2015.0 model. Being the only candidate DGRF 2015.0 model entirely and only relying on such ASM-V data, it demonstrates the value of the new ASM-V data for such global geomagnetic field modeling purposes.

Abstract Geomagnetic disturbances (GMDs) are known to disturb power system equipment performance. The danger is associated with geomagnetically induced currents (GICs) occurring at the Earth's surface during GMD. GICs do not endanger power system operation conditions by themselves. The main challenge posed by GICs to power system states is the change in power system equipment operation conditions provoked by GIC flow. The primary avenue of blackout caused by GMDs is through power transformers. This, in turn, can impair the operation of other power system equipment such as synchronous machines. Modern powerful synchronous machines are not designed and engineered to cope with the negative impacts of GMDs. Moreover, the actual legal norms are inadequate in this case. Enhancing the grid's resiliency to such an event is highly interesting to the industry. The physical processes in synchronous machine windings triggered by GICs and limitations brought to power grid operations are described. First, the idea of the impact of GMDs on the power grid operation is described. The analysis of the impact of GMDs on synchronous machines is performed in the second section. In the end, the power system response under GMDs is studied.

ESA’s Swarm mission is a constellation probing both Earth’s interior and geospace, delivering magnetic and plasma measurements which are used to generate many derived data products. From empirical magnetic field models of the core, crust, ionosphere, and magnetosphere, to multi-point estimates of ionospheric currents and in-situ plasma properties, these are challenging to navigate, process, and visualize. The VirES for Swarm platform (https://vires.services) has been built to tackle this problem, providing tools to increase usability of Swarm data products. The VirES (Virtual environments for Earth Scientists) platform provides both a graphical web interface and an API to access and visualise Swarm data and models. This is extended with a cloud-hosted development environment powered by JupyterHub (the “Virtual Research Environment/VRE”). VirES provides two API’s: the full VirES API for which a dedicated Python client is provided, viresclient, and the more interoperable Heliophysics API (HAPI). The VRE is furnished with a bespoke Python environment containing thematic libraries supporting science with Swarm. This service aims to ease the pathway for scientists writing computer code to analyze Swarm data products, increase opportunities for collaboration, and leverage cloud technologies. Beyond simply providing data and model access to Python users, it is extremely helpful to provide higher-level analysis and visualization tools, and ready-to-use code recipes that people can explore and extend. Critically for space physics, this involves crossover with many other datasets and so it is highly valuable to embed such tools within the wider data and software ecosystems. Through Swarm DISC (Data, Innovation, and Science Cluster), we are tackling this through cookbooks and Python libraries. Cookbooks are built and presented using Jupyter technologies, and tested to work within the VRE. A new library we are building is SwarmPAL, which includes tools for time-frequency analysis and inversion of magnetic field measurements for electric current systems, among others, while relying on the VirES server to provide data portability and other utilities. This paper reviews the current state of these tools and services for Swarm, particularly in the context of the Python in Heliophysics Community, and the wider heliophysics and geospace data environment.

The purpose of this work is to investigate the responses of multiple parameters to the Madoi earthquake preparation. A new method is employed to extract anomalies in a geomagnetic field. The results show that there were abnormal changes in the lithosphere, atmosphere, and ionosphere near the epicenter before the earthquake. Despite the differences in spatial and temporal resolutions, the increase in geomagnetic residuals in the lithosphere exhibits similar temporal characteristics to the enhancement of thermal infrared radiation in the atmosphere. Two high–value regions are present in the ground–based geomagnetic high residuals and the ionospheric disturbances. The northern one is around the epicenter of the Madoi earthquake. Near the southern one, an M6.4 Yangbi earthquake occurred four hours before the Madoi earthquake. In this study, we have observed almost all of the physical phenomena that can occur during the preparation of an earthquake, as predicted using the electrostatic channel model. It can be inferred that the electrostatic channel is a possible mechanism for coupling between the lithosphere, atmosphere, and ionosphere during the Madoi earthquake.

Abstract This paper describes and discusses the preprocessing and calibration of the magnetic data taken by the navigational magnetometers onboard the two GRACE satellites, with focus on the almost 10 years period from January 2008 to the end of the GRACE mission in October 2017 for which 1-Hz magnetic data are available. A calibration of the magnetic data is performed by comparing the raw magnetometer sensor readings with model magnetic vector values as provided by the CHAOS-7 geomagnetic field model for the time and position of the GRACE data. The presented approach also accounts for magnetic disturbances produced by the satellite’s magnetorquer and for temperature effects, which are parametrized by the Sun incident angle. The root-mean-squared error of the difference between the calibrated data and CHAOS-7 model values is about 10 nT, which makes the GRACE magnetometer data relevant for geophysical investigations.

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

There has been longstanding controversy about whether the influence of lateral variations in core-mantle boundary heat flow can be detected in paleomagnetic records of geomagnetic field behavior. Their signature is commonly sought in globally distributed records of virtual geomagnetic pole (VGP) paths that have been claimed to exhibit specific longitudinal preferences during polarity transitions and excursions. These preferences have often been linked to thermal effects from large low seismic velocity areas (LLVPs) in the lowermost mantle, but the results have been contested because of potential sensitivity to sparse temporal and spatial sampling. Recently developed time varying global paleofield models spanning various time intervals in 1–100 ka, three of which include excursions, allow us to complement assessments of spatial distributions of transitional VGP paths with distributions of minimum field intensity. Robustness of the results is evaluated using similar products from four distinct numerical dynamo simulations with and without variable thermal boundary conditions and including stable geomagnetic polarity, excursions and reversals. We determine that VGP distributions are less useful than minimum field intensity in linking the influences of thermal CMB structure to geographical variations in actual paleofield observables, because VGP correlations depend strongly on good spatial sampling of a sufficient number of relatively rare events. These results provide a basis for evaluating comparable observations from four paleofield models. The distribution of VGP locations provide unreliable results given the restricted time span and available data locations. Rough correlations of global distributions of minimum intensity with areas outside the LLVPs give some indications of mantle control during excursions, although the results for the eastern hemisphere are complex, perhaps highlighting uncertainties about the hemispheric balance between thermal and compositional variations in the lowermost mantle. However, access to other geomagnetic properties (such as intensity and radial field at the CMB) provides a strong argument for using extended and improved global paleofield models to resolve the question of mantle influence on the geodynamo from the observational side.

Abstract In December 2019, the 13th revision of the International Geomagnetic Reference Field (IGRF) was released by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. This revision comprises two new spherical harmonic main field models for epochs 2015.0 (DGRF-2015) and 2020.0 (IGRF-2020) and a model of the predicted secular variation for the interval 2020.0 to 2025.0 (SV-2020-2025). The models were produced from candidates submitted by fifteen international teams. These teams were led by the British Geological Survey (UK), China Earthquake Administration (China), Universidad Complutense de Madrid (Spain), University of Colorado Boulder (USA), Technical University of Denmark (Denmark), GFZ German Research Centre for Geosciences (Germany), Institut de physique du globe de Paris (France), Institut des Sciences de la Terre (France), Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (Russia), Kyoto University (Japan), University of Leeds (UK), Max Planck Institute for Solar System Research (Germany), NASA Goddard Space Flight Center (USA), University of Potsdam (Germany), and Université de Strasbourg (France). The candidate models were evaluated individually and compared to all other candidates as well to the mean, median and a robust Huber-weighted model of all candidates. These analyses were used to identify, for example, the variation between the Gauss coefficients or the geographical regions where the candidate models strongly differed. The majority of candidates were sufficiently close that the differences can be explained primarily by individual modeling methodologies and data selection strategies. None of the candidates were so different as to warrant their exclusion from the final IGRF-13. The IAGA V-MOD task force thus voted for two approaches: the median of the Gauss coefficients of the candidates for the DGRF-2015 and IGRF-2020 models and the robust Huber-weighted model for the predictive SV-2020-2025. In this paper, we document the evaluation of the candidate models and provide details of the approach used to derive the final IGRF-13 products. We also perform a retrospective analysis of the IGRF-12 SV candidates over their performance period (2015–2020). Our findings suggest that forecasting secular variation can benefit from combining physics-based core modeling with satellite observations.

Abstract The International Geomagnetic Reference Field (IGRF) is a set of parameters representing the large-scale internal part of Earth’s magnetic field. The 13th generation IGRF requested candidate models for a definitive main field for 2015.0, a provisional main field for 2020.0, and a predictive secular variation covering the period 2020.0–2025.0. The University of Colorado (CU) and the National Centers for Environmental Information (NCEI), part of the National Oceanic and Atmospheric Administration (NOAA), have produced these three candidate models for consideration in IGRF-13. In this paper, we present the methodology used to derive our candidate models. Our candidates were built primarily from Swarm satellite data, and also relied on geomagnetic indices derived from the ground observatory network. The ground observatories played a crucial role as independent data in validating our candidates. This paper also provides a retrospective assessment of the CU/NCEI candidate model to the previous IGRF (IGRF-12) and discusses the impact of differences between candidate and final IGRF models on global model errors.

Abstract The International Geomagnetic Reference Field (IGRF) model is a combination of the several models developed by independent groups of scientists using different approaches for the selection of input data and methods for calculating harmonic coefficients. This approach allows for mutual comparison of individual models and for their combination to obtain the most reliable values of the harmonic coefficients. This letter provides a brief description of methods for building the IZMIRAN Earth’s main magnetic field model, submitted to the IAGA Working Group V-MOD for creating IGRF-13. Special efforts were made to obtain as uniform coverage of the entire Earth’s surface as possible with observations. The surface was divided into a grid of approximately equal cells. Then the data for geomagnetically quiet intervals were placed in the corresponding cells and a median filter was applied to select the data in each cell. Spherical harmonic coefficients up to degree 13 were calculated for the interval 2014-Jan to 2019-Aug with a time step of 10 days and extrapolated to 01.01.2010.

Abstract Using magnetic field data from the China Seismo-Electromagnetic Satellite (CSES) mission, we derive a global geomagnetic field model, which we call the CSES Global Geomagnetic Field Model (CGGM). This model describes the Earth’s magnetic main field and its linear temporal evolution over the time period between March 2018 and September 2019. As the CSES mission was not originally designed for main field modelling, we carefully assess the ability of the CSES orbits and data to provide relevant data for such a purpose. A number of issues are identified, and an appropriate modelling approach is found to mitigate these. The resulting CGGM model appears to be of high enough quality, and it is next used as a parent model to produce a main field model extrapolated to epoch 2020.0, which was eventually submitted on October 1, 2019 as one of the IGRF-13 2020 candidate models. This CGGM candidate model, the first ever produced by a Chinese-led team, is also the only one relying on a data set completely independent from that used by all other candidate models. A successful validation of this candidate model is performed by comparison with the final (now published) IGRF-13 2020 model and all other candidate models. Comparisons of the secular variation predicted by the CGGM parent model with the final IGRF-13 2020–2025 predictive secular variation also reveal a remarkable agreement. This shows that, despite their current limitations, CSES magnetic data can already be used to produce useful IGRF 2020 and 2020–2025 secular variation candidate models to contribute to the official IGRF-13 2020 and predictive secular variation models for the coming 2020–2025 time period. These very encouraging results show that additional efforts to improve the CSES magnetic data quality could make these data very useful for long-term monitoring of the main field and possibly other magnetic field sources, in complement to the data provided by missions such as the ESA Swarm mission.

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

Abstract The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission carries magnetometers that are dedicated to enhance the satellite’s navigation. After appropriate calibration and characterisation of artificial magnetic disturbances, these observations are valuable assets to characterise the natural variability of Earth’s magnetic field. We describe the data pre-processing, the calibration, and characterisation strategy against a high-precision magnetic field model applied to the GRACE-FO magnetic data. During times of geomagnetic quiet conditions, the mean residual to the magnetic model is around 1 nT with standard deviations below 10 nT. The mean difference to data of ESA’s Swarm mission, which is dedicated to monitor the Earth’s magnetic field, is mainly within ± 10 nT during conjunctions. The performance of GRACE-FO magnetic data is further discussed on selected scientific examples. During a magnetic storm event in August 2018, GRACE-FO reveals the local time dependence of the magnetospheric ring current signature, which is in good agreement with results from a network of ground magnetic observations. Also, derived field-aligned currents (FACs) are applied to monitor auroral FACs that compare well in amplitude and statistical behaviour for local time, hemisphere, and solar wind conditions to approved earlier findings from other missions including Swarm. On a case event, it is demonstrated that the dual-satellite constellation of GRACE-FO is most suitable to derive the persistence of auroral FACs with scale lengths of 180 km or longer. Due to a relatively larger noise level compared to dedicated magnetic missions, GRACE-FO is especially suitable for high-amplitude event studies. However, GRACE-FO is also sensitive to ionospheric signatures even below the noise level within statistical approaches. The combination with data of dedicated magnetic field missions and other missions carrying non-dedicated magnetometers greatly enhances related scientific perspectives.

Abstract In December 2019, the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group (V-MOD) adopted the thirteenth generation of the International Geomagnetic Reference Field (IGRF). This IGRF updates the previous generation with a definitive main field model for epoch 2015.0, a main field model for epoch 2020.0, and a predictive linear secular variation for 2020.0 to 2025.0. This letter provides the equations defining the IGRF, the spherical harmonic coefficients for this thirteenth generation model, maps of magnetic declination, inclination and total field intensity for the epoch 2020.0, and maps of their predicted rate of change for the 2020.0 to 2025.0 time period.

Abstract We present geomagnetic main field and secular variation time series, at 300 equal-area distributed locations and at 490 km altitude, derived from magnetic field measurements collected by the three Swarm satellites. These Geomagnetic Virtual Observatory (GVO) series provide a convenient means to globally monitor and analyze long-term variations of the geomagnetic field from low-Earth orbit. The series are obtained by robust fits of local Cartesian potential field models to along-track and East–West sums and differences of Swarm satellite data collected within a radius of 700 km of the GVO locations during either 1-monthly or 4-monthly time windows. We describe two GVO data products: (1) ‘Observed Field’ GVO time series, where all observed sources contribute to the estimated values, without any data selection or correction, and (2) ‘Core Field’ GVO time series, where additional data selection is carried out, then de-noising schemes and epoch-by-epoch spherical harmonic analysis are applied to reduce contamination by magnetospheric and ionospheric signals. Secular variation series are provided as annual differences of the Core Field GVOs. We present examples of the resulting Swarm GVO series, assessing their quality through comparisons with ground observatories and geomagnetic field models. In benchmark comparisons with six high-quality mid-to-low latitude ground observatories we find the secular variation of the Core Field GVO field intensities, calculated using annual differences, agrees to an rms of 1.8 nT/yr and 1.2 nT/yr for the 1-monthly and 4-monthly versions, respectively. Regular sampling in space and time, and the availability of data error estimates, makes the GVO series well suited for users wishing to perform data assimilation studies of core dynamics, or to study long-period magnetospheric and ionospheric signals and their induced counterparts. The Swarm GVO time series will be regularly updated, approximately every four months, allowing ready access to the latest secular variation data from the Swarm satellites.

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

The NW Iberian margin is a hyperextended continental margin, formed during the opening of the North Atlantic Ocean, where a subsequent partial tectonic inversion has undergone during the Alpine Orogeny. This succession of tectonic episodes determines the magnetic signature of the margin. The Spanish Exclusive Economic Zone Project has carried out seven one-month cruises between 2001 and 2009. To extend and densify the spatial coverage, we have used data from the World Digital Magnetic Anomaly Map. Here, we describe the methodology used for the acquisition and data processing of the magnetic field data. The use of diverse instrumentation, a non-complete external field’s cancelation, and the use of different magnetic core field models, contributed to the total error budget. To reduce it, we have used a leveling algorithm which minimizes all these contributions. Finally, a statistical analysis was applied using crossover residuals, showing a resolution better than 28 nT.

The article addresses the problem of the connection of earthquakes with geomagnetic phenomena. We have carried out an experimental study using a method based, firstly, on the separation of periods of geomagnetic activity into extremely quiet and disturbed, and, secondly, on the description of seismic activity with an index called the global daily magnitude (GDM). By analyzing the NEIC earthquake catalog of the US Geological Survey over a 20-year period from 1980 to 1999, we have shown that the planetary activity of earthquakes under extremely quiet geomagnetic conditions is noticeably higher than under disturbed conditions. The detected tendency for seismic activity to increase in extremely quiet periods of geomagnetic activity has indirectly been confirmed by the analysis of 35 earthquakes with magnitude 8 and higher, which occurred on Earth from 1980 to 2019. We have found that in extremely quiet geomagnetic conditions, the probability of the occurrence of strong earthquakes is noticeably higher. The result qualitatively confirms the assumption of a change in the regime of seismic activity due to the influence of alternating magnetic fields on the ductility of rocks.

Abstract We present the CHAOS-7 model of the time-dependent near-Earth geomagnetic field between 1999 and 2020 based on magnetic field observations collected by the low-Earth orbit satellites Swarm, CryoSat-2, CHAMP, SAC-C and Ørsted, and on annual differences of monthly means of ground observatory measurements. The CHAOS-7 model consists of a time-dependent internal field up to spherical harmonic degree 20, a static internal field which merges to the LCS-1 lithospheric field model above degree 25, a model of the magnetospheric field and its induced counterpart, estimates of Euler angles describing the alignment of satellite vector magnetometers, and magnetometer calibration parameters for CryoSat-2. Only data from dark regions satisfying strict geomagnetic quiet-time criteria (including conditions on IMF $$B_z$$ B z and $$B_y$$ B y at all latitudes) were used in the field estimation. Model parameters were estimated using an iteratively reweighted regularized least-squares procedure; regularization of the time-dependent internal field was relaxed at high spherical harmonic degree compared with previous versions of the CHAOS model. We use CHAOS-7 to investigate recent changes in the geomagnetic field, studying the evolution of the South Atlantic weak field anomaly and rapid field changes in the Pacific region since 2014. At Earth’s surface a secondary minimum of the South Atlantic Anomaly is now evident to the south west of Africa. Green’s functions relating the core–mantle boundary radial field to the surface intensity show this feature is connected with the movement and evolution of a reversed flux feature under South Africa. The continuing growth in size and weakening of the main anomaly is linked to the westward motion and gathering of reversed flux under South America. In the Pacific region at Earth’s surface between 2015 and 2018 a sign change has occurred in the second time derivative (acceleration) of the radial component of the field. This acceleration change took the form of a localized, east–west oriented, dipole. It was clearly recorded on ground, for example at the magnetic observatory at Honolulu, and was seen in Swarm observations over an extended region in the central and western Pacific. Downward continuing to the core–mantle boundary, we find this event originated in field acceleration changes at low latitudes beneath the central and western Pacific in 2017.

Abstract Earth’s internal magnetic field is generated through motion of the electrically conductive iron-alloy fluid comprising its outer core. Temporal variability of this magnetic field, termed secular variation (SV), results from two processes: one is the interaction between core fluid motion and the magnetic field, the other is magnetic diffusion. As diffusion is widely thought to take place over relatively long, millennial time scales, it is common to disregard it when considering yearly to decadal field changes; in this frozen-flux approximation, core fluid motion may be inferred on the core–mantle boundary (CMB) using observations of SV at Earth’s surface. Such flow models have been used to forecast variation in the magnetic field. However, recent work suggests that diffusion may also contribute significantly to SV on short time scales provided that the radial length scale of the magnetic field structure within the core is sufficiently short. In this work, we introduce a hybrid method to forecast field evolution that considers a model based on both a steady flow and diffusion, in which we adopt a two-step process: first fitting the SV to a steady flow, and then fitting the residual by magnetic diffusion. We assess this approach by hindcasting the evolution for 2010–2015, based on fitting the models to CHAOS-6 using time windows prior to 2010. We find that including diffusion yields a reduction of up to 25% in the global hindcast error at Earth’s surface; at the CMB this error reduction can be in excess of 77%. We show that fitting the model over the shortest window that we consider, 2009–2010, yields the lowest hindcast error. Based on our hindcast tests, we present a candidate model for the SV over 2020–2025 for IGRF-13, fit over the time window 2018.3–2019.3. Our forecasts indicate that over the next decade the axial dipole will continue to decay, reversed-flux patches will increase in both area and intensity, and the north magnetic (dip) pole will continue to migrate towards Siberia.

Abstract From the launch of the Ørsted satellite in 1999, through the CHAMP mission from 2000 to 2010, and now with the Swarm constellation mission starting in 2013, satellite magnetometry has provided excellent monitoring of the near-Earth magnetic field regime. The advanced Comprehensive Inversion scheme has been applied to data before Swarm and to the Swarm data itself, but now for the first time to all the satellite data in this new era, culminating in the CM6 model. The highlights of this model include not only a continuous core magnetic field description over the entire time period 1999 to 2019.5 in good agreement with the CHAOS model series, but the addition of two new oceanic tidal magnetic sources: the larger lunar elliptic semi-diurnal constituent $$N_2$$ N 2 and the lunar diurnal constituent $$O_1$$ O 1 . CM6 is also the parent model of the NASA/GSFC candidates for the DGRF2015 and IGRF2020 in response to the IGRF-13 call. This paper provides a full report on the development of CM6.

Abstract We describe and discuss the preprocessing and calibration steps applied to the magnetic data measured by the three “platform magnetometers” on-board the CryoSat-2 satellite. The calibration is performed by comparing the magnetometer sensor readings with magnetic field values for the time and position of the satellite as given by the CHAOS-6 geomagnetic field model. We allow for slow temporal variations of the calibration parameters by solving for scale values, offsets, and non-orthogonalities in monthly bins, and account for non-linearities as well as the magnetic disturbances caused by battery, solar panel and magnetorquer currents. Fully calibrated magnetic vector data, together with time and position, are provided as daily files in CDF data format at swarm-diss.eo.esa.int. The data show good agreement with Swarm satellite magnetic measurements during close encounters (rms difference between 1 and 5 nT for inter-satellite distances below 300 km).

Abstract For the past 20 years, state of the art geomagnetic core field models have relied heavily on magnetic measurements made from space-based instrumentation. These models have revealed rapid global magnetic field variations on sub-decadal timescales originating in Earth’s core. With the end of the CHAMP mission in 2010 and the launch of Swarm in late 2013, there has been a 3-year gap in high-quality satellite measurements of the geomagnetic field. Geomagnetic field models have therefore relied on ground observatory data to fill in this gap period. However, ground observatories are unable to provide a truly global picture of the core field and its temporal changes. Many satellites in operation carry vector fluxgate “platform” magnetometers for attitude control, which can offer an alternative to relying on ground observatory measurements during the gap period. However, these instruments need to be carefully calibrated in order to provide meaningful information on Earth’s core field. Some previous studies attempted to calibrate such instruments with a priori geomagnetic field models. This approach has several disadvantages: (1) errors in the model will introduce errors in the calibration parameters, and (2) relying on an a priori model may not be feasible in the post-Swarm era. In this paper, we develop a novel approach to build a time-dependent geomagnetic field model from platform magnetometer data, by co-estimating their calibration parameters with the internal field parameters. This method does not require an a priori geomagnetic field model, but does require a dataset of previously calibrated data. We use CHAMP, Swarm, and ground observatory measurements to supply this dataset, and incorporate platform magnetic measurements from DMSP and Cryosat-2 during the gap years. We find that the calibration parameters of DMSP and Cryosat-2 can be reliably estimated, and these missions provide meaningful information on rapid core field variations during the gap period.

For positioning tasks of mobile robots in indoor environments, the emerging positioning technique based on visual inertial odometry (VIO) is heavily influenced by light and suffers from cumulative errors, which cannot meet the requirements of long-term navigation and positioning. In contrast, positioning techniques that rely on indoor signal sources such as 5G and geomagnetism can provide drift-free global positioning results, but their overall positioning accuracy is low. In order to obtain higher precision and more reliable positioning, this paper proposes a fused 5G/geomagnetism/VIO indoor localization method. Firstly, the error back propagation neural network (BPNN) model is used to fuse 5G and geomagnetic signals to obtain more reliable global positioning results; secondly, the conversion relationship from VIO local positioning results to the global coordinate system is established through the least squares principle; and finally, a fused 5G/geomagnetism/VIO localization system based on the error state extended Kalman filter (ES-EKF) is constructed. The experimental results show that the 5G/geomagnetism fusion localization method overcomes the problem of low accuracy of single sensor localization and can provide more accurate global localization results. Additionally, after fusing the local and global positioning results, the average positioning error of the mobile robot in the two scenarios is 0.61 m and 0.72 m. Compared with the VINS-mono algorithm, our approach improves the average positioning accuracy in indoor environments by 69.0% and 67.2%, respectively.

Abstract The extensive lava piles of Iceland contain a unique record of geomagnetic field variations spanning the past ~ 16 Ma. Since the 1950s, palaeomagnetic data have been obtained from over 9400 Icelandic lavas. We have compiled all palaeomagnetic data currently available and developed a publicly accessible database (http://www.icepmag.org). The data within the database are primarily palaeodirections, with a relatively smaller number of palaeointensity data (8936 entries contain direction only, 218 intensity only, and 337 both direction and intensity). In addition, the database contains a wide range of metadata, including geochronological information, site details, and laboratory methods. The search interface of the database allows users to search for data using a range of customisable filters (e.g. by publication, geological age, location, laboratory method, palaeomagnetic statistics) and to quickly visualise and download the matching search results. The data within the database have significant potential for understanding long-term palaeomagnetic field variations at high latitude, the behaviour of excursions and reversals, and geological mapping on Iceland.

Abstract Characterization of Earth's magnetic field is key to understanding dynamics of the core. We assess whether Iridium Communications magnetometer data can be used for this purpose since. The 66 Iridium satellites are in 86° inclination, 780 km altitude, circular orbits, with 11 satellites in each of six orbit planes. In one day the constellation returns 300,000 measurements spanning the globe with

Palaeointensity information enables us to define the strength of Earth’s magnetic field over geological time, providing a window into Earth’s deep interior. The difficulties in acquiring reliable measurements are substantial, particularly from older rocks. Two of the most significant causes of experimental failure are laboratory induced alteration of the magnetic remanence carriers and effects relating to multidomain magnetic carriers. One method that has been claimed to overcome both of these problems is the Shaw method. Here we detail and evaluate the method, comparing various selection criteria in a controlled experiment performed on a large, non-ideal dataset of mainly Precambrian rocks. Monte Carlo analyses are used to determine an optimal set of selection criteria; the end result is a new, improved experimental protocol that lends itself very well to the automated Rapid 2G magnetometer system enabling experiments to be carried out expeditiously and with greater accuracy.

Ferromagnetism in 3d metals is re-examined in a simple band model. It is shown that the molecular field model cannot account for the low values of coercive field in ferromagnetic pure metals, and that the standard Stoner theory of band ferromagnetism incorrectly evaluates the total electronic energy and cannot predict reasonable Curie temperatures. A simple band model for magnetism is formulated, yielding a criterion for ferromagnetism even in absence of a Hubbard term, involving only the density of states (DOS) at the Fermi level, its derivative and the filling of the 3d band. By introducing a double-peaked DOS, one may explain the occurrence of ferromagnetism in bcc Fe, hcp-fcc Co and fcc Ni, the stabilization of fcc-hcp or bcc structures across all 3d elements, the occurrence of antiferromagnetism in chromium, and derive reasonable Curie temperatures. ‘Re-entrant’ ferromagnetism is predicted at ultrahigh temperatures, suggesting an alternate origin for the geomagnetic field.