Geomagnetic Field Models Research Articles

A new inclination-based method to evaluate the global geomagnetic configuration and axial dipole moment

The strength and configuration of the geomagnetic field control the average shape of the magnetosphere. The pure dipole assumption and the virtual dipole moment (VDM), determined by individual records, have been widely adopted to evaluate the strength of the geomagnetic field in geological time. However, such an assumption might not be valid during geomagnetic transitions, such as reversals and excursions. The traditional spherical harmonic modeling of the geomagnetic field could be difficult to implement because accurate global records are lacking. Here, we report that an empirical relationship exists between the ratio of the VDM to the true axial dipole moment (VDM/ADM) and the ratio of the power of the axial dipole to that of the non-axial dipole (AD/NAD) based on a new method utilizing globally distributed inclination records. The root mean square global deviation of inclination (RMSΔI) to the standard inclination distribution of the AD was fitted to the AD/NAD with a cubic polynomial by utilizing a large number of geodynamo simulations. Tests with geomagnetic field models showed that the AD/NAD derived from the RMSΔI agreed well with that calculated by using the Gauss coefficients, and the estimated ADM was consistent with the true value. Finally, the application of volcanic records during the Laschamp excursion showed the VDM might overestimate the ADM by a factor of 3. Our new method will be useful in future studies that characterize the configuration of the geomagnetic field and the strength of the axial dipole.

Characterizing the Geomagnetic Field at High Southern Latitudes: Evidence From the Antarctic Peninsula

AbstractDue to a dearth of data from high‐latitude paleomagnetic sites, it is not currently clear if the geocentric axial dipole (GAD) hypothesis accurately describes the long‐term behavior of the geomagnetic field at high latitudes. Here we present new paleomagnetic and paleointensity data from the James Ross Island (JRI) volcanic group, located on the Antarctic Peninsula. This data set addresses a notable lack of data from the 60°–70°S latitude bin and includes 251 samples from 31 sites, spanning 0.99–6.8 Ma in age. We also include positive fold, conglomerate, and baked contact tests. Paleointensity data from three methods (Thellier‐Thellier, pseudo‐Thellier, and Tsunakawa‐Shaw) were collected from all sites. The Thellier‐Thellier method had low yields and produced unreliable data, likely due to sample alteration during heating. Results from the Tsunakawa‐Shaw and pseudo‐Thellier methods were more consistent, and we found a bimodal distribution of paleointensity estimates. Most sites yielded either <15 μT or >40 μT, which together span a range of estimates from long‐term geomagnetic field models, but do not favor any model in particular. Alternating‐field demagnetization of these samples, when combined with preexisting data, yields a revised paleomagnetic pole of −87.5°, 025°, α95 = 3.6° for the Antarctic Peninsula over the last ∼5 Ma, which suggests that the current data set is sufficiently large to “average out” secular variation. Finally, the C2r/C2n transition was probably found at a site on JRI, and further geochronological and paleomagnetic study of these units could refine the age of this reversal.

Global Evolution and Dynamics of the Geomagnetic Field in the 15–70 kyr Period Based on Selected Paleomagnetic Sediment Records

AbstractReconstructions of the geomagnetic field on long time scales are important to understand the geodynamo processes in the Earth's core. The geomagnetic field exhibits a range of variations that vary from normal, dipole‐dominated secular variation to geomagnetic excursions and reversals. These transitional events are associated with significant directional deviations and very low intensities. Here we present a new, global geomagnetic field model spanning the period 70–15 ka (GGFSS70) that includes three excursions: Norwegian‐Greenland Sea, Laschamps, and Mono Lake/Auckland. The model is built from nine globally distributed, high‐resolution, well‐dated, sedimentary paleomagnetic records. The GGFSS70 indicates that the axial‐dipole component changed sign for about 300 years in the middle of the Laschamps excursion (41.25–40.93 ka). The energy comparison at the Earth's surface reveals that the axial‐dipole energy is always higher than the non‐axial‐dipole except over the Laschamps. In the other two excursions, the axial‐dipole is reduced by about one order of magnitude for the Norwegian‐Greenland Sea excursion and less for the Mono Lake/Auckland. At the core‐mantle boundary, the large‐scale non‐axial‐dipole power is comparable to the axial‐dipole power, except over the excursions when the axial‐dipole decreases, though less clearly for the Mono Lake/Auckland excursion. The axial dipole moment over the 15–70 ka varies from 0 to 8 × 1022 Am2, with an average and standard deviation of 5.1 ± 1.5 × 1022Am2. The Laschamps excursion is associated with growth and poleward movement of reversed flux patches and reversed field in the tangent cylinder at the excursion midpoint, which is not the case for the other two excursions.

New Paleointensity Data From Aniakchak Volcano, Alaska, USA

AbstractThis study presents the first set of Holocene, high‐quality absolute paleointensity data from Alaska, USA. Existing paleointensity data for the Holocene are generally located at mid‐northern latitudes in North America, Europe, the Middle East, and eastern Asia. Relatively few data are from the Alaska region. IZZI‐modified paleointensity experiments were conducted on glassy volcanic materials from Aniakchak volcano, a mid‐ to high‐latitude composite volcano on the Alaska‐Aleutian arc. The CCRIT selection criteria were applied to the paleointensity results. A total of 30 specimens from six samples with estimated ages ranging from 1931 CE to 2,300 years before present passed all selection criteria. The sample‐mean paleointensities ranged from 49.5 to 68.0 microTesla (μT). The sample‐mean paleointensity results are comparable to modeled intensities, however all except for one sample‐mean paleointensity are lower than those predicted by geomagnetic field models. The paleointensity estimate for the historical 1931 CE eruption was about 15 μT greater than the expected field strength. This overestimate may result from unrecognized alteration or non‐ideal remanence carriers in this sample. Further evaluation of samples from the 1931 CE eruption using a Bayesian estimation method resulted in a paleointensity estimate that encompasses the historical field strength within uncertainty. These new paleointensity results are a valuable contribution to the mid‐ to high‐northern latitude paleomagnetic data set. Incorporation of these data into future geomagnetic field models will improve the predictions of geomagnetic field behavior in the Alaska region.

Towards Understanding the Interconnection between Celestial Pole Motion and Earth's Magnetic Field Using Space Geodetic Techniques.

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core–mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time–frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF’s contribution to the Earth’s rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

Empirical Modeling of Ionospheric Current Using Empirical Orthogonal Function Analysis and Artificial Neural Network

AbstractGiven the potential importance of solar quiet (Sq) ionospheric current in geomagnetic field modeling, it is vital to obtain accurate parameters characterizing its variations, particularly the spatial and temporal variations. In this paper, we derived the Sq current function based on the spherical harmonic analysis (SHA) technique using a 14‐year (2006–2019) quiet geomagnetic field record over the American sector. The empirical orthogonal function (EOF) analysis was then applied to deduce temporal and spatial variations of the Sq current. It is observed that the first EOF mode of the Sq current function is dominated by solar activity, while the second and third EOF modes exhibit annual and semiannual variations, respectively. Also, the artificial neural network (ANN) model of Sq current function was constructed to validate the EOF model predictions. While the Sq current intensity predicted by the ANN model is underestimated by 2.83%, the EOF model underpredicted the Sq current intensity by 1.92% relative to the observation. The root mean square error (RMSE) of the EOF model is 0.64 kA. This RMSE is about 79% smaller than that of the ANN model. In addition, both the EOF and ANN models capture the variation of the total Sq current (Jtotal) intensity with respect to solar activity. In principle, the EOF model had an optimal performance at nearly 98% accuracy, with the ANN model exhibiting almost the same degree of accuracy, which appears to be a reference point for ionospheric conditions when looking for space weather applications.

A Holocene paleomagnetic record from Küçükçekmece Lagoon, NW Turkey

Lake sediments are very useful for providing high-resolution records of geomagnetic field variations, especially for the Holocene period. We present high-resolution paleomagnetic records from three cores (KCL12P1, P2, and P3) recovered from Küçükçekmece Lagoon, located at the northern shoreline of the Sea of Marmara, Turkey. The cores were subjected to a comprehensive paleomagnetic and rock magnetic investigation using oriented samples. According to the age-depth model, based on radiocarbon dating and X-ray fluorescence-derived Ca/Ti element ratios, tuned to available oxygen isotope records based on an absolute calendar-year time-scale, we obtained a new paleomagnetic record for the last 3800 years. Low paleointensities were found during 1500-2000 BP. Stacked paleomagnetic directions from Küçükçekmece Lagoon were correlated to regional geomagnetic field models. This correlation proved that the paleomagnetic records (paleointensity, inclination) obtained from the Küçükçekmece Lagoon sediments considerably agree with the data from the surrounding region over the past 3800 years.

Further Evidence of High Intensity During the Levantine Iron Age Anomaly in Southwestern Europe: Full Vector Archeomagnetic Dating of an Early Iron Age Dwelling From Western Spain

AbstractWe report an archeomagnetic study from the Early Iron Age archeological site of Cerro de San Vicente (Salamanca, Spain). The studied materials were sampled from one roundhouse and its central fireplace, a surrounding burnt floor, and slags with a twofold objective. First, to archeomagnetically determine the last use of the central fireplace, because dating with other methods was imprecise. Second, to retrieve information about the Earth's magnetic field in Western Europe from a period when the Levantine Iron Age Anomaly (LIAA) has been occasionally reported. This study includes mineralogical, archeomagnetic directional analyses, and multimethod archeointensity determinations. Paleomagnetic analyses of the central fireplace yield a mean direction: declination D = 15.1°, inclination I = 52.5°; k = 477.1, and α95 = 5.6°. Archeointensity determinations yield a mean anisotropy‐corrected archeointensity of 72.4 ± 2.0 μT (74.7 ± 4.3 μT if a pTRM‐check correction is applied) on the central fireplace and 48.2 ± 2.0 μT on slags. A full‐vector archeomagnetic dating was performed with the SHA.DIF.4k geomagnetic field model which yielded an age interval of last use of the central fireplace between 644 and 575 BCE (654–575 BCE with the pTRM‐check corrected data) at 95% confidence level. This date agrees with the archeological context. Results allows to place the high paleointensity obtained near the maximum observed in Iberia at this age, confirming the existence of this peak related to the LIAA in Western Europe where records of this feature are still scarce.

Magnetometer Calibration Based on the CHAOS-7 Model

We describe a method for the in-orbit calibration of body-mounted magnetometers based on the CHAOS-7 geomagnetic field model. The code is designed to find the true calibration parameters autonomously by using only the onboard magnetometer data and the corresponding CHAOS outputs. As the model output and satellite data have different coordinate systems, they are first transformed to a Star Tracker Coordinate (STC). Then, non-linear optimization processes are run to minimize the differences between the CHAOS-7 model and satellite data in the STC. The process finally searches out a suite of calibration parameters that can maximize the model-data agreement. These parameters include the instrument gain, offset, axis orthogonality, and Euler rotation matrices between the magnetometer frame and the STC. To validate the performance of the Python code, we first produce pseudo satellite data by convoluting CHAOS-7 model outputs with a prescribed set of the ‘true’ calibration parameters. Then, we let the code autonomously undistort the pseudo satellite data through optimization processes, which ultimately track down the initially prescribed calibration parameters. The reconstructed parameters are in good agreement with the prescribed (true) ones, which demonstrates that the code can be used for actual instrument data calibration. This study is performed using Python 3.8.5, NumPy 1.19.2, SciPy 1.6, AstroPy 4.2, SpacePy 0.2.1, and ChaosmagPy 0.5 including the CHAOS-7.6 geomagnetic field model. This code will be utilized for processing NextSat-1 and Small scale magNetospheric and Ionospheric Plasma Experiment (SNIPE) data in the future.

Observed Auroral Ovals Secular Variation Inferred from Auroral Boundary Data

We analyze the auroral boundary corrected geomagnetic latitude provided by the Auroral Boundary Index (ABI) database to estimate long-term changes of core origin in the area enclosed by this boundary during 1983–2016. We design a four-step filtering process to minimize the solar contribution to the auroral boundary temporal variation for the northern and southern hemispheres. This process includes filtering geomagnetic and solar activity effects, removal of high-frequency signal, and additional removal of a ~20–30-year dominant solar periodicity. Comparison of our results with the secular change of auroral plus polar cap areas obtained using a simple model of the magnetosphere and a geomagnetic core field model reveals a decent agreement, with area increase/decrease in the southern/northern hemisphere respectively for both observations and model. This encouraging agreement provides observational evidence for the surprising recent decrease of the auroral zone area.

Multispacecraft Current Density Estimates in the Low‐ and Mid‐Latitude F‐Region Ionosphere Using the Swarm Constellation

AbstractWe present a new application of a multispacecraft method which provides estimates of the full electric current density vector in the ionospheric low‐ and mid‐latitude F region. The method uses the three satellites of the Swarm constellation in configurations when they were close to each other. The current density is calculated inside triangular prisms defined by the satellite positions. The technique is inspired by similar approaches such as the curlometer. Here, we propose an alternative mathematical treatment, which involves the use of the well‐known curl‐B technique and a least squares minimization. The proposed formalism provides a rigorous way to propagate the errors through the problem and special care is taken to validate the algorithm and assess the relevance of the derived currents. Such techniques are powerful tools to study the F‐region ionosphere currents as they naturally exclude all the other contributions outside the considered volumes. The F region is known to host currents with a complex spatiotemporal variability. Besides the intrinsic interest of this system itself, understanding the dynamics of these currents is also critical for global geomagnetic field modeling as they are an important source of error in the models. In this paper, we present the full algorithm and test the method on both synthetic and real Swarm satellite data on February 15, 2014. Several sources of error are investigated. Additionally, the results reveal expected characteristics of F‐region interhemispheric field‐aligned currents. Some new characteristics of F‐region currents, potentially associated with dynamo and pressure currents, are also observed.

A quantitative study on the effects of external geomagnetic fields by using the GeoMagSphere back-tracing code

Evaluation of cosmic ray trajectories and penetration inside the Earth environment is mandatory for estimation of flux by on-orbit detectors as well as of radiation damage on electronics devices and biological tissues, like those of astronauts onboard the International Space Station. We studied the impact of the external magnetic field on the calculation of some parameters like the rigidity cut-off, by a quantitative comparison among several geomagnetic field models. For this purpose we used GeoMagSphere back-tracing code, performing the particle trajectory reconstruction back-in-time from the chosen position and time up to the borders of the magnetosphere. The analysis done points out the need to combine an external magnetic field model with the internal one (usually IGRF). Several external field models have a different impact on the accuracy as well as on the time needed for calculation, important in case of a large amount of back-traced particles. We also studied cosmic ray propagation inside the magnetosphere, separately for quiet and disturbed solar activity periods. We found that during highly disturbed periods and during magnetic storms, rigidity cut-off, as well as cosmic ray flux, can be appropriately evaluated only by using external field models, like that one proposed by Tsyganenko and Sitnov (2005), well describing those particular conditions.

Probabilistic approach to geomagnetic field modelling of data with age uncertainties and post-depositional magnetisations

Holocene geomagnetic field models are used to study processes in Earth's core, millennial scale variations in solar activity and to relatively date geological and archaeological archives. Constructing models from magnetic field directions and intensities stored in archaeological artefacts, igneous rocks and sediment records is challenging due to the sparse data distribution and the large chronological and magnetic uncertainties associated with the data. In addition, data from sediment records are further complicated by the effects of post-depositional remanent magnetisations (pDRMs) that lead to a magnetic signal which is smoothed and offset in time. Here we present a new probabilistic modelling approach that addresses these problems by co-estimating the geomagnetic field and the age of the data as well as accounting for the effects of pDRM and systematic directional errors in the sedimentary data. The use of a flexible Student's t-distribution in the likelihood function removes the need for outlier rejection which may otherwise lead to excessive smoothing of the model when applied to data with uncertain ages. A final ensemble of models is obtained through Hamiltonian Monte Carlo simulation of the posterior distribution. The modelling approach is tested and evaluated using synthetic data generated from the prior with an equivalent spatial and temporal distribution to the real data and corrupted with realistic noise.

Dating a medieval pottery workshop of the city of Burgos (Spain): Archaeomagnetic and archaeological evidences

Here we report a detailed archaeomagnetic and rock-magnetic study of a pottery kiln from Burgos (Spain) to reconstruct its burning conditions and date its last use and abandonment age. During the course of a rescue archaeological excavation carried out in 2015 in the center of Burgos city, a medieval pottery workshop was discovered. Two well-preserved kilns appeared and archaeomagnetic analyses were performed on one of them. In addition to a large amount of pottery remains, some numismatic and documental evidences provided a general chronological estimation, but the abandonment age of the workshop remains unknown. On the basis of the existing archaeological information we carried out an archaeomagnetic study in order to date its last use. 69 archaeomagnetic samples were collected from the combustion chamber and the kiln's fire tunnel. Stepwise alternating field and thermal demagnetization of the natural remanent magnetization (NRM) were carried out to retrieve the mean direction. Additional experiments consisted in the acquisition of isothermal remanence (IRM), low-field magnetic susceptibility and its anisotropy as well as thermomagnetic curves. Despite the high temperatures expected in the combustion chamber, it appeared that the bricks´ samples from the fire tunnel exhibit the most successful directional results. Magnetite and variable contributions of hematite are the main ferromagnetic minerals observed in the thermomagnetic curves. The type of lithology studied, its previous magnetic history and their location in the kiln strongly condition the observed directional and rock-magnetic results. Additionally, AMS data revealed the manufacturing fabric of the fire tunnel's bricks, showing moderately high anisotropy degrees, but not enough to casts doubts on the directional NRM record. In order to test the reproducibility of the dating results, archaeomagnetic dating was carried out using different geomagnetic field models and the Iberian paleosecular variation curve. The small differences observed in the dating results are mainly due to the density and type of input data of these records. The combination of the archaeomagnetic analyses with the archaeological and documental suggests that last kiln's usage took place during the first half of the XVIth century CE. Overall, this paper illustrates how the combination of archaeological data and archaeomagnetic analyses may improve our understanding about the manufacturing processes, use and age of abandonment of archaeological combustion structures.

Magnetometer-Based Orbit Determination via Fast Reconstruction of Three-Dimensional Decoupled Geomagnetic Field Model

In this paper, magnetometer-based orbit determination via the fast reconstruction of a 3-D decoupled geomagnetic field (TDGF) model is examined. For the TDGF model, the three components of the geomagnetic field vector at a certain point are calculated separately with three different independent sets of Gauss coefficients rather than one identical set. The fast reconstruction algorithm is based on a recursive least-squares algorithm with a low computational burden. According to the orbit determination accuracy requirements for near-Earth satellites with communication systems that must be operational to update the TDGF model, the on-orbit model update interval can be appropriately selected so that the orbit determination accuracy can be effectively maintained. The simulation results of real flight data from magnetic survey satellites and simulated data show that the robustness of the proposed algorithm for different values of the measurement noise covariance matrices makes the algorithm more practical and that the position estimation error achieved by the proposed algorithm can meet the requirements of low- and medium-precision missions for near-Earth micro- and nanosatellites. In this way, both the autonomy and the orbit determination accuracy of satellites are considered simultaneously at the expense of some unnecessary autonomous capabilities for satellite tasks.

A novel geomagnetic assimilation method of vector geomagnetic data

Geomagnetic field has important applications in Earth Science, earthquake prediction, aerospace, national defense construction and other areas. Therefore, accurate modeling of regional geomagnetic field is very important. Geomagnetic assimilation method can effectively improve the accuracy of regional vector geomagnetic data, and then promote the establishment of high-precision geomagnetic regional model. The geomagnetic stations at different latitudes and longitudes have different influences on the geomagnetic assimilation of vector geomagnetic data. However, traditional geomagnetic assimilation methods do not take into account the differences in latitude and longitude, which result in low accuracy of the geomagnetic assimilation of vector geomagnetic data. To solve the problem, this paper proposes a new geomagnetic assimilation method based on the three weighting factors of direction, distance and a parameter k. In this method, the longitude differences and latitude differences of different stations are taken as the weight elements to participate in the weight determination, and parameter k is set to further modify the weight, so as to achieve the high precision geomagnetic assimilation to regional vector geomagnetic data. Based on the real observation data of five stations in the European region of station network in the world data center (WDC), this paper conducted geomagnetic assimilation of the vector geomagnetic data of different stations. The experimental results show that at five stations which include some central stations and some marginal stations, for the F, H, D and I geomagnetic elements, the geomagnetic assimilation accuracy of the proposed method is better than that of the method based on the distance weighting method both on magnetically quiet day and on magnetically disturbed day. In addition, the results also show that the geomagnetic assimilation accuracy of FUR station, which is a marginal station, is significantly improved by the proposed method. On magnetically disturbed day, the error of F component is reduced by 0.6 nT, and the error of H component is reduced by 1 nT. On magnetically quiet day, the error of F component is reduced by 0.4 nT, and the error of H component is reduced by 0.1 nT. The above results prove the effectiveness and feasibility of the proposed method in the geomagnetic assimilation of vector geomagnetic data, especially for the vector geomagnetic data of marginal area.

Obtaining archaeointensity data from British Neolithic pottery: A feasibility study

There is a significant lack of geomagnetic field strength (archaeointensity) measurements for many archaeological time periods in the United Kingdom (UK). This not only makes past geomagnetic secular variation difficult to model but also limits the development of archaeointensity dating. This paper presents the first archaeointensity study on UK Neolithic material. In this study, twenty-five sherds of Neolithic Grooved Ware pottery from the Ness of Brodgar, Orkney, UK, some with direct radiocarbon dates, were subjected to a full archaeomagnetic investigation with the aim of increasing the amount of archaeointensity data for the UK. Both thermal Thellier and microwave palaeointensity experiments were used to determine which technique would be most suitable for British Neolithic pottery. Three successful archaeointensity results between 35 and 40μT were obtained using thermal Thellier method, which is consistent with the limited data available within a 15° radius and geomagnetic field model predictions from the same time. We separated the results into four different types with an intention of explaining the behaviours that determine the likelihood of achieving an acceptable archaeointensity estimate. The feasibility of obtaining geomagnetic field strength information during the UK Neolithic from ceramics has been demonstrated and the results provide a solid basis for improving our knowledge of geomagnetic secular variation during archaeological time in Britain.

Magnetometer data from the GRACE satellite duo

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.

Tetrahedral satellite formation: Geomagnetic measurements exchange and interpolation

This note presents a study of a four-satellite tetrahedral formation to collect, process, and exchange multipoint measurements of geomagnetic field in a near-polar orbit. The study is conducted as a series of numerical experiments based on simulated spacecraft orbits and corresponding geomagnetic field models output. The four satellites are assumed to move in near-circular orbits specifically chosen to maintain the tetrahedron quality. The satellites exchange their simulated magnetometers readings and the collected multipoint measurements are processed on board of any of them thus creating an instantaneous interpolated map of the geomagnetic field in the interior of the tetrahedron. Interpolation is carried out with the use of Kriging algorithms, known in geostatistics for capturing spatial correlation of the data and taking into account statistical properties of the interpolated variables. We propose a concept of a servicing formation, and analyze interpolation accuracy for different formation sizes. It is then discussed how the processed multipoint measurements can be provided as a service to other nearby satellites. Finally, we show that using the existing COTS magnetometers it is possible to obtain real-time interpolation data, which are more precise at a given point and time than a conventional onboard magnetic field model, thus ensuring better attitude determination routines performance in the serviced spacecraft.

Geomagnetic Virtual Observatories: monitoring geomagnetic secular variation with the Swarm satellites

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.