Geomagnetic Field Models Research Articles

Archaeomagnetic study of a limekiln in the Les Ferreres Roman aqueduct, World Heritage Site of Tarraco

The aqueduct of Les Ferreres is a major element of the Archaeological Ensemble of Tarraco. Although the ashlars of the aqueduct are stacked without mortar, lime was used in some parts and lime was certainly used in later repairs. Worthy of note is a coating mortar used in a well-documented restoration (1854–1856). In this study, a limekiln found near the Roman aqueduct has been archaeomagnetically dated to determine if it was used for the construction of the aqueduct or in later repairs. The mean values for the measured archaeomagnetic direction from the limekiln were compared with two different archaeomagnetic models (SCHA.DIF.3k and GUMF1), and both indicate that the limekiln is modern with ages only slightly older than the well-documented restoration. The extensive use of the coating mortar in that restoration is consistent with the need of onsite lime production. Additional archaeomagnetic intensity has not contributed to constrain further the obtained archaeomagnetic age but the intensity datum can be added to archaeomagnetic intensity datasets to enhance geomagnetic intensity field models. The paper illustrates how archaeomagnetic dating can be useful to characterize secondary structures of major cultural heritage monuments.

Geomagnetic Field Model Indicates Shrinking Northern Auroral Oval

AbstractPolar cap and auroral oval areas are presented for the period 1900–2015 using a model of the magnetosphere and the International Geomagnetic Reference Field Version 12 (IGRF‐12) model for the geomagnetic field. The effect of the main field long‐term changes is addressed considering steady interplanetary conditions. Until ~1940 both northern and southern polar cap areas increased with time, consistent with the geomagnetic dipole moment decrease during this period. Thereafter, while the southern polar cap area continued to increase steadily, the northern polar cap area has been decreasing rapidly. This hemispherical dichotomy is related to asymmetry in the core field and its secular variation. In the southern polar region the surface field intensity has been decreasing throughout the entire period, whereas in the northern polar region an intensity decrease turned to an increase from 1940 to present day. This recent surface intensity increase stems from intensification of the flux patch below Siberia and cessation of weakening of the flux patch below North America, both on the core‐mantle boundary. The surprising temporal decrease in the area of the northern polar cap has important implications for space weather and communication systems. While the decreasing dipole intensity allows more particles to penetrate the atmosphere, a shrinking northern auroral oval implies an increase in particle precipitation density, resulting in more severe damage to airplanes and ships positioning systems, spacecraft electronic systems and airline passengers when passing above this region. Further study is needed to observationally establish that the northern auroral oval, as defined by optical occurrences of aurora, is indeed shrinking.

CM6: a comprehensive geomagnetic field model derived from both CHAMP and Swarm satellite observations

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 and the lunar diurnal constituent 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.

Residuals to the CHAOS‐6 Geomagnetic Field Model Caused by Magnetospheric Currents During Enhanced Magnetic Activity

AbstractThanks to mapping missions, like Ørsted, CHAMP, and Swarm, we have gained a detailed understanding of the geomagnetic field. High‐resolution models like POMME, GRIMM, or CHAOS are able to describe the main parts of the Earth's magnetic field reliably. These models represent well contributions from the core and crustal fields. But their validity of describing magnetospheric field effects is limited to low activity periods (Kp ~ 0–2). Here, we study the differences between CHAMP magnetic observations and the predictions from CHAOS‐6‐x9, a recent version, outside this validity range. Systematic residuals appear at times of elevated activity. Mean amplitudes at the equator grow up to 12 nT around 20 hr magnetic local time for magnetic activity around Kp = 4.7. Negative residuals are obtained in the evening to midnight sector and positive ones in the morning. A seasonal dependence of the magnetospheric currents causes more negative deflections of the residuals in the winter than in the summer hemisphere. This hemispheric asymmetry cannot be accounted for by a degree 1 spherical harmonics function. A surprising observation is that the residuals show a clear longitude dependent pattern, which changes with local time. The analysis reveals that this feature can be interpreted as a Universal Time dependence of the residuals with a peak‐to‐peak amplitude of about 8 nT and a period of 12 hr at an activity level of Kp = 4.7. All these results call for a better parameterization of the magnetospheric current effects in a geomagnetic field model that is reliable at least up to moderate activity levels.

Enhanced magnetic fields within a stratified layer

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

Persistent westward drift of the geomagnetic field at the core–mantle boundary linked to recurrent high-latitude weak/reverse flux patches

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

Taylor Polynomial Model of the Geomagnetic Field in an Underground Gas Storage Area

The study of normal geomagnetic background fields is the premise and basis for obtaining local geomagnetic anomalies caused by changes in underground pressure during gas injection and extraction in an underground gas storage (UGS) area. Measurements of the total magnetic field in an array consisting of sixty-three stations were acquired at a UGS and its surrounding areas. We completed field measurements at the stations using proton precession magnetometers (PPMs) with a sensitivity of 0.15 nT @ 1 Hz in April 2017 and March 2018. The geomagnetic background field model of the UGS area is calculated using the Taylor polynomial fitting method based on the data of all measured stations. A fourth-order Taylor polynomial model is appropriate for the UGS area according to a comprehensive comparative analysis of the mean square error and boundary distortion effect. The geomagnetic field distribution in the core area of the UGS can be better described by enlarging the network of repeat stations. The results provide a reference model for extracting the variations in the local magnetic field (LMF) caused by the underground pressure variations in the UGS area.

Combinatory Attitude Determination Method for High Rotational Speed Rigid-Body Aircraft

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.

Magnetic observations from CryoSat-2: calibration and processing of satellite platform magnetometer data

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).

Archaeomagnetic investigations in Bolgar (Tatarstan)

The objective of this study is to provide a well-dated point for a future palaeosecular variation (PSV) reference curve for western Russia. For this purpose archaeomagnetic and magnetic property analyses were carried out on a pottery kiln unearthed at the UNESCO World Heritage site of ancient Bolgar, having a rather precise age dating. The archaeological context provided an age between 1340 and 1360 C.E. The characteristic remanence vector was determined through alternating field demagnetisation and Thellier-Thellier palaeointensity experiments. Some innovations were introduced regarding palaeointensity. The check testing the equality of blocking and unblocking temperature was redefined. This allowed waiving the commonly used additional zero-field cooling steps during the Thellier-Thellier experiment. Another innovation concerns the calculation of archaeointensity at structure level. A Bayesian approach was introduced for averaging individual specimen archaeointensities using a prior probability distribution of unknown uncertainties. Next, an additional prior probability distribution was used to correct for cooling rate effects. This resulted in a lower uncertainty compared to common practice and in eluding time consuming cooling rate experiments. The complex magnetic mineralogy consists of maghaemite, multi-domain haematite and Al-substituted haematite. Some samples contained also some non-stoichiometric magnetite. The magnetic mineralogy was determined through hysteresis loops, backfield and remanence decay curves, measurements of the frequency dependence of magnetic susceptibility and through low temperature magnetisation curves. Accompanying high-temperature thermomagnetic analyses revealed an excellent thermo-chemical stability of the studied specimens. Directions obtained from alternating field demagnetisation and those extracted from archaeointensity experiments are congruent and have low uncertainties. The obtained archaeomagnetic results are fairly in agreement with global geomagnetic field models and contemporary PSV data of the wider area. The geomagnetic field vector obtained for ancient Bolgar is of high quality, deserving thus its inclusion in a future PSV reference curve for European Russia.

Archaeomagnetic dating of vitrified Broborg hillfort in southeast Uppsala, Sweden

Hundreds of European hillforts from the Bronze and Iron Ages show evidence of extreme heating of the stone ramparts, which has caused melting of the rocks which partially turned to glass on cooling. The cause and age of wall vitrification at these hillforts has long been debated in the archaeological community. This work aims to determine the age of vitrification at the Broborg hillfort (Uppsala, Sweden) using archaeomagnetic dating. Rock magnetic investigations verified the suitability of the vitrified materials for such studies, with titanomagnetites being the major magnetic signal carriers. Despite the challenges involved in sample collection at the Broborg site, a total of eight oriented samples (five vitrified, three non-vitrified) were collected and used in this study. The mean paleodirection and paleointensity results were combined to compare with a geomagnetic field model for Europe. Three possible archaeomagnetic age intervals for Broborg vitrification were found: 389–579 CE, 602–752 CE, and 965–1300 CE, among which the 389–579 CE date range is the most consistent with the published 14C ages and known historical context of the site. This study shows that paleointensity data alone could be used to date such sites, requiring smaller unoriented samples, potentially removing some of the barriers to sample acquisition at some archaeological sites.

New constraints on the medieval repopulation process in the northern Iberian plateau from the full vector archaeomagnetic dating of two hearths at La Pudia site (Caleruega, Burgos, Spain)

The progressive southward reoccupation of territories of the Iberian Peninsula by the Christian kingdom against the Muslims from the eighth century AD onwards is a well-known process. However, there are few well-dated sites of this period, especially in the northern plateau of Spain. Here we report the full vector archaeomagnetic dating of two hearths from the archaeological site of La Pudia I (Caleruega, Castile-and-Leon, Spain). Both hearths were archaeomagnetically investigated in order to date their last use linked to the abandonment of the site. The archaeomagnetic direction was analysed through thermal (TH) and stepwise alternating field (AF) demagnetization of the natural remanent magnetization (NRM). Pseudo-single domain slightly substituted magnetite was identified as the main magnetic carrier. Thellier–Coe type absolute archaeointensity determinations were carried out on 48 samples from both hearths. The mean directions obtained were independently analysed both at sample and at specimen levels yielding very similar results but statistically distinguishable at 95% confidence level. The archaeomagnetic dating was carried out by comparing the mean directions and archaeointensity values of both hearths with the SHA.DIF.14k geomagnetic field model. The results obtained are in agreement with the archaeological context, suggesting that the abandonment of the archaeological site took place between the end of ninth century and the first half of the eleventh century AD. These results provide one of the first evidences of independently well-dated sites of the Christian conquest in the Iberian northern plateau at the onset of the Early–High Middle Ages.

Magnetometer-based autonomous orbit determination via a measurement differencing extended Kalman filter during geomagnetic storms

PurposeThe main reason for the low accuracy of magnetometer-based autonomous orbit determination is the coarse accuracy of the geomagnetic field model. Furthermore, the geomagnetic field model error increases obviously during geomagnetic storms, which can still further reduce the navigation accuracy. The purpose of this paper is to improve the accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms.Design/methodology/approachIn this paper, magnetometer-based autonomous orbit determination via a measurement differencing extended Kalman filter (MDEKF) is studied. The MDEKF algorithm can effectively remove the time-correlated portion of the measurement error and thus can evidently improve the accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms. Real flight data from Swarm A are used to evaluate the performance of the MDEKF algorithm presented in this study. A performance comparison between the MDEKF algorithm and an extended Kalman filter (EKF) algorithm is investigated for different geomagnetic storms and sampling intervals.FindingsThe simulation results show that the MDEKF algorithm is superior to the EKF algorithm in terms of estimation accuracy and stability with a short sampling interval during geomagnetic storms. In addition, as the size of the geomagnetic storm increases, the advantages of the MDEKF algorithm over the EKF algorithm become more obvious.Originality/valueThe algorithm in this paper can improve the real-time accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms with a low computational burden and is very suitable for low-orbit micro- and nano-satellites.

The impact of second-order ionospheric delays on the ZWD estimation with GPS and BDS measurements

Since millimeter accuracy is required in many GNSS applications such as real-time zenith wet delay (ZWD) estimation, the higher-order ionospheric delays on GNSS signals are no longer negligible. We calculated the second-order ionospheric delays ($$I_{2}$$) and analyzed the impact on the ZWD estimation with GPS-only and combined GPS/BDS observations. The undifferenced PPP model with fixed coordinates was used to estimate the ZWD and horizontal gradients. The method of blockwise sequential least squares was utilized to eliminate the receiver clock biases and compute the $$I_{2}$$ impact on the ZWDs. The $$I_{2}$$ delays on each GNSS satellite observations were calculated with the CODE final TEC map and the 12th generation of the international geomagnetic reference field (IGRF-12) model. The statistical results with the actual observation geometry show that the $$I_{2}$$ delays can reach over 10 mm during the daytime, and the corresponding impact on the estimated ZWD can reach up to several millimeters. At station HKWS, the maximum $$I_{2}$$ impact with GPS only reaches up to 3.1 mm and is still 2.4 mm when both GPS and BDS observations are used. The simulated $$I_{2}$$ impact on the ZWD could reach several millimeters, even though the TEC and geomagnetic values were calculated from relatively moderate background models. Compared with the 5–10 mm precision of real-time ZWD estimation, the $$I_{2}$$ delays must not be ignored, especially during high VTEC periods.

Recent geomagnetic variations and the force balance in Earth’s core

SUMMARY The nature of the force balance that governs the geodynamo is debated. Recent theoretical analyses and numerical simulations support a quasigeotrophic (QG), magneto-Archimedes-Coriolis (MAC) balance in Earth’s core, where the Coriolis and pressure forces equilibrate at leading order in amplitude, and where the buoyancy, Lorentz and ageostrophic Coriolis forces equilibrate at the next order. In contrast, earlier theoretical expectations have favoured a magnetostrophic regime where the Lorentz force would reach leading order at the system scale. The dominant driver (buoyant or magnetic) for the general circulation in Earth’s core is equally debated. In this study, these questions are explored in the light of the high-quality geomagnetic data recently acquired by satellites and at magnetic ground observatories. The analysis involves inverse geodynamo modelling, a method that uses multivariate statistics extracted from a numerical geodynamo model to infer the state of Earth’s core from a geomagnetic field model interpretation of the main field and secular variation data. To test the QG-MAC dynamic hypothesis against the data, the framework is extended in order to explicitly prescribe this force balance into the inverse problem solved at the core surface. The resulting inverse solutions achieve a quantitatively adequate fit to the data while ensuring deviations from the QG-MAC balance (which amount to an inertial driving of the flow) lower than each of the leading forces. The general circulation imaged within the core over the past two decades confirms the existence of a planetary-scale, eccentric, axially columnar gyre that comprises an intense, equatorially symmetric jet at high latitudes in the Pacific hemisphere. The dominant driver of this circulation is shown to be of buoyant nature, through a thermal wind balance with a longitudinally hemispheric buoyancy anomaly distribution. Geomagnetic forecasts initiated with the inverted core states are systematically more accurate against the true interannual geomagnetic field evolution when enforcing the QG-MAC constraint. This force balance is therefore consistent with the geomagnetic data at the large scales of Earth’s core that can be imaged by the method.

Are External Magnetic Disturbances Suppressed by Magnetometer Noise when Estimating a Nanosatellite’s Rotational Motion?

In this study, a three-axis magnetometer based attitude estimation algorithm that includes external magnetic field model is presented. The magnetic fields from the external sources are considered in the geomagnetic field model used in the attitude estimation algorithm and not treated as error sources on the magnetometer. By this way, it was aimed to model the magnetometer better by taking into account the effects of the space environment and perform a higher accuracy in the estimation of the rotational motion of the satellite. However, a problem arose such that the magnetometer sensor noise levels used in the attitude estimations appear to mask the effects of the external magnetic field. The fact that with the developing technologies in micro-electro-mechanical systems, the magnetometer noise might be keep decreasing, led us to investigate the magnitude of the noise level that would suppress the external field.

Palaeosecular variations of the geomagnetic field in Africa during the Holocene: a review

Abstract The importance of the full understanding of the Holocene geomagnetic field spans from human history and archaeology, to palaeoclimatic changes and engineering, to geomagnetic field modelling and unravelling of the geomagnetic field characteristics and anomalies. Unfortunately, the dearth of data from large under-covered areas such as oceans, the African and South American continents, and the southern hemisphere (only 4–6% of the global datasets) dramatically limits our knowledge of the temporal and spatial evolution of the geomagnetic field and its application. Here, a review of all data from the African continent is presented in order to encourage and motivate a new generation of palaeomagnetic and archaeomagnetic studies. New data will sharpen the palaeomagnetism as a dating tool, improve our knowledge of local/global geomagnetic features, and will help to finally answer some of the fundamental questions in palaeomagnetism, like the temporal and spatial distribution of the palaeointensity peaks described, and the origin and evolution of the South Atlantic Anomaly.

Evolution of the Large-Scale Geomagnetic Field over the Last 12 000 Years

Abstract—The ERDA and IGRF-12 geomagnetic field models are used to study the behavior of Earth’s large-scale magnetic field. The unusualness of the modern field’s behavior is studied from the viewpoint of the appearance of a new reversal. Estimates are given for the change in energy of the potential magnetic field on the Earth’s surface and of the liquid core, as well as Joule dissipation in the liquid core over 12 000 years. Both values increase sharply for the modern field, which is associated with an increase in the resolution of observations. Various methods for describing geomagnetic field reversals are considered. It is shown that the estimate for the duration of the reversal may depend on the method. It is demonstrated how erroneous reversal predictions may be, based on short time series, in particular, over the last century.

The cone of acceptance and magnetic rigidity cutoff of galactic cosmic ray particles for different models of the International Geomagnetic Reference Field from 1965-2015 in the Deblin airport, Poland

We present the results of computations of the trajectories (the asymptotic latitude and asymptotic longitude) and the magnetic cutoff rigidity of galactic cosmic ray (GCR) particles for the airport Deblin, Poland (geographical latitude 51°33′32′′ N, geographical longitude 21°50′53′′ E) based on the numerical integration of equations of motion of charged particles of cosmic rays in the Earth’s magnetic field. The set of allowed trajectories at a given site on the surface of the Earth is called the asymptotic cone of acceptance The initial distance from the center of the Earth was taken to be 20 km above the Earth’s surface. At about this altitude, most cosmic rays undergo nuclear collisions. Calculations were made for different of models of the International Geomagnetic Reference Field (IGRF) from 1965–2015. The IGRF is an internationally agreed and widely used mathematical model of the Earth’s magnetic field of internal origin. Each constituent model of the IGRF is a set of spherical harmonics of degree n and order m, representing a solution to Laplace’s equation for the magnetic potential arising from sources inside the Earth at a given epoch. In all asymptotic direction calculations, we used sixth-degree expansion of geomagnetic field model. Schmidt normalized spherical harmonic coefficients were taken for the epochs from 1965 to 2015. Knowledge of asymptotic directions and the magnetic rigidity cutoff is important from the point of view of study different classes of cosmic rays variations intensity and anisotropy.

Influence of geomagnetic field models on analytical propagator for SPIN stabilized satellites

Influence of geomagnetic field models on analytical propagator for SPIN stabilized satellites