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The use of potential field methods for geophysical exploration purposes is nowadays quite common: these techniques consent to retrieve geological knowledge over extended regions and can give complementary information where other invasive or expensive techniques, such as seismic acquisitions, fail (e.g., in the recovery of geometries of geological horizons beneath a thick salt layer). Recent dedicated satellite gravity and magnetic missions, such as GRACE, GOCE and SWARM together with the exploitation of offshore satellite altimetry and airborne/shipborne surveys, have paved the way to the realization of a variety of global models, characterized by spatial resolutions of about 4 km (both for gravity anomaly and lithosphere magnetic anomalies) and high accuracy (about 3-5$3\text{-}5$ mGal and 20 nT). These models are a valuable source of information to study the geological evolution and characterization of the lithosphere structure, especially at a regional scale. In the present work, some preliminary technical aspects related to the use of these models to perform three‐dimensional inversion are discussed, thus defining an empirical but rigorous procedure to set up gravity and magnetic inversion. In particular, we address the questions whether the classical planar approximation is acceptable for regional inversions or if a spherical one is required. We also provide guidance for choosing the best gravity functional (e.g., gravity anomalies or second radial derivative of the anomalous potential) and the optimal sizing of the three‐dimensional volume area to be modelled depending on the specific target investigated. The application of the proposed methods to the Mediterranean case study is also presented. [ABSTRACT FROM AUTHOR]

While devoid of an active magnetic dynamo field today, Mars possesses a remanent magnetic field that may reach several thousand nanoteslas locally. The exact origin and the events that have shaped the crustal magnetization remain largely enigmatic. Three magnetic field data sets from two spacecraft collected over 13 cumulative years have sampled the Martian magnetic field over a range of altitudes from 90 up to 6,000 km: (a) Mars Global Surveyor (MGS) magnetometer (1997–2006), (b) MGS Electron Reflectometer (1999–2006), and (c) Mars Atmosphere and Volatile EvolutioN (MAVEN) magnetometer (2014 to today). In this paper we combine these complementary data sets for the first time to build a new model of the Martian internal magnetic field. This new model improves upon previous ones in several aspects: comprehensive data coverage, refined data selection scheme, modified modeling scheme, discrete‐to‐continuous transformation of the model, and increased model resolution. The new model has a spatial resolution of ∼160 km at the surface, corresponding to spherical harmonic degree 134. It shows small scales and well‐defined features, which can now be associated with geological signatures. Key Points: MGS and MAVEN magnetic field measurements are combined into a high‐resolution magnetic field modelThe new model extends up to SH degree 134, corresponding to 160‐km horizontal resolution at the Martian surfaceIt enables local studies, where geologic and magnetic features can be compared [ABSTRACT FROM AUTHOR]

We derive a lithospheric magnetic field model up to equivalent spherical harmonic degree 1000 over southern Africa. We rely on a joint inversion of satellite, near-surface, and ground magnetic field data. The input data set consists of magnetic field vector measurements from the CHAMP satellite, across-track magnetic field differences from the Swarm mission, the World Digital Magnetic Anomaly Map, and magnetic field measurements from repeat stations and three local INTERMAGNET observatories. For the inversion scheme, we use the revised spherical cap harmonic analysis (R-SCHA), a regional analysis technique able to deal with magnetic field measurements obtained at different altitudes. The model is carefully assessed and displayed at different altitudes and its spectral content is compared to high-resolution global lithospheric field models. By comparing the shape of its spectrum to a statistical power spectrum of Earth's lithospheric magnetic field, we infer the mean magnetic thickness and the mean magnetization over southern Africa. [ABSTRACT FROM AUTHOR]

SUMMARY Many physical characteristics of planets, such as their topography, magnetic and gravitational fields, are routinely detected and measured by spacecrafts. At satellite altitudes, even if little is known about the measured signal, it is possible to separate the large-scale components from other contributions by a spectral analysis carried out along the spacecraft orbit. This procedure, which dates back to the early age of the satellite era, is routinely applied with spherical harmonics analysis for the study of large-scale planetary magnetic fields, particularly those that vary rapidly in time. In this paper, we review the approximations of this procedure for investigating internal and external magnetic fields of planets. We show that the magnetic field analyses along the orbits are limited by a finite frequency resolution that is known to introduce a spectral leakage. This leakage may lead to artificial spatio-temporal variations of the magnetic field, such as an apparent internal field secular variation, an asymmetry of the magnetospheric field and a regional distortion of the lithospheric field structures. We quantify the errors for the Earth's lithospheric field and display its distribution in the spatial and the spectral domains. We also discuss these limits for the Moon and Mars lithospheric magnetic fields. Our analytical results illustrate the pros and cons of the orbit-by-orbit analyses and should allow us to avoid the pitfall of geophysical overinterpretation of some artificial magnetic field variations. [ABSTRACT FROM AUTHOR]

We show how a 3-D, self-consistent numerical model of the geodynamo can be used as the subjective prior information for the determination of Earth's core surface flows from the geomagnetic field and its secular variation. This is achieved by estimating those parts of the numerical model state vector hidden from the observations, through a standard Kalman filtering (or stochastic inverse) procedure, where the Kalman gain matrix is based on the multivariate statistics of the geodynamo model. To allow for a direct comparison with observations, the field variables entering these statistics are scaled following two of the scaling laws that have recently come to the fore in numerical dynamo modelling, which express the dependency of the secular variation timescale and the magnetic energy density on their respective control parameters. We perform test experiments with noisy synthetic data, showing good to excellent recovery of the hidden parts of the state vector. A geomagnetic field model parent to a candidate model to the 2010 release of IGRF is then used for a core surface flow estimation. The estimated flow confirms the presence of convective columns underneath America, whereas exhibiting a high level of equatorial symmetry. We suggest that the discrete state estimation problem considered here (in connection with the classical core flow problem) could be used generically as a means to assess the degree of geophysical realism of a given geodynamo model. More generally, this study opens the way to using scaling laws and multivariate statistics from numerical models in the broader context of geomagnetic data assimilation. [ABSTRACT FROM AUTHOR]

Abstract: The current morphology of the martian lithospheric magnetic field results from magnetization and demagnetization processes, both of which shaped the planet. The largest martian impact craters, Hellas, Argyre, Isidis and Utopia, are not associated with intense magnetic fields at spacecraft altitude. This is usually interpreted as locally non- or de-magnetized areas, as large impactors may have reset the magnetization of the pre-impact material. We study the effects of impacts on the magnetic field. First, a careful analysis is performed to compute the impact demagnetization effects. We assume that the pre-impact lithosphere acquired its magnetization while cooling in the presence of a global, centered and mainly dipolar magnetic field, and that the subsequent demagnetization is restricted to the excavation area created by large craters, between 50- and 500-km diameter. Depth-to-diameter ratio of the transient craters is set to 0.1, consistent with observed telluric bodies. Associated magnetic field is computed between 100- and 500-km altitude. For a single-impact event, the maximum magnetic field anomaly associated with a crater located over the magnetic pole is maximum above the crater. A 200-km diameter crater presents a close-to-1-nT magnetic field anomaly at 400-km altitude, while a 100-km diameter crater has a similar signature at 200-km altitude. Second, we statistically study the 400-km altitude Mars Global Surveyor magnetic measurements modelled locally over the visible impact craters. This approach offers a local estimate of the confidence to which the magnetic field can be computed from real measurements. We conclude that currently craters down to a diameter of 200km can be characterized. There is a slight anti-correlation of −0.23 between magnetic field intensity and impact crater diameters, although we show that this result may be fortuitous. A complete low-altitude magnetic field mapping is needed. New data will allow predicted weak anomalies above craters to be better characterized, and will bring new constraints on the timing of the martian dynamo and on Mars’ evolution. [Copyright &y& Elsevier]

The Earth's magnetic field is mainly produced within the Earth's liquid and electrically conducting core, as a result of a process known as the geodynamo. Many other sources also contribute to the magnetic signal accessible to observation at the Earth's surface, partly obscuring the main core magnetic field signal. Thanks to a series of very successful satellites and to advances in magnetic field modelling techniques, considerable progress has, however, been made in the recent years toward better identifying the signal of each of these sources. In particular, temporal changes in the field of internal origin happen to be detectable now in spherical harmonic degrees up to, perhaps, 16. All of these changes are usually attributed to changes in the core field itself, the secular variation, on the ground that the lithospheric magnetization cannot produce such signals. It has, however, been pointed out, on empirical grounds, that temporal changes in the field of internal origin produced by the induced part of the lithospheric magnetization could dominate the core field signal beyond degree 22. This short note revisits this issue by taking advantage of our improved knowledge of the small-scale field changes and of the likely sources of the lithospheric field. We rely on a simple extrapolation of the observed spatial spectrum of the field changes beyond degree 16 and use a forward approach based on a recent geological model of lithospheric magnetization. This leads us to confirm that the main cause of the observed changes in the field of internal origin up to some critical degree, NC, is indeed likely to be the secular variation of the core field, but that the signal produced by the time-varying lithospheric field is bound to dominate and conceal the time-varying core signal beyond that critical degree, in very much the same way the permanent component of the lithospheric field dominates and conceals the permanent component of the core field beyond degree 14. All uncertainties taken into account, we estimate NC to lie between 22 and 24. We, however, also note that in practice, the main limitation to the observation of the core field small-scale secular variation is not so much its concealing by the field of lithospheric origin but its fast changing nature and small magnitude. This leads us to conclude that whereas cumulative small-scale lithospheric field changes might be detected some day, detection of core-field secular variation beyond degree 18 is likely to remain a severe challenge for some time. [ABSTRACT FROM AUTHOR]

Modelling the magnetic field at a regional scale has always been challenging. Several techniques were proposed in the past but few solve Laplace equation and meet the requirements of potential theory. Among the regional techniques, the Spherical Cap Harmonic Analysis (SCHA) that solve Laplace equation has become widespread. However, recognizing the inherent difficulties of SCHA to represent the main field over a small spherical cap, a revision of this technique the R-SCHA was proposed to deal with multilevel magnetic measurements. For the reasons explained in this paper, R-SCHA is not suitable either when data are available at one surface only. The present paper proposes an alternative to SCHA and R-SCHA, named R-SCHA2D, that is suitable for modelling geomagnetic data available at a quasi-constant altitude. The efficiency of R-SCHA2D is successfully tested on a set of repeat station data. The magnetic field over France and its secular variation are reliably represented between 1965 and 2007.5. The regional parameters are obtained from the joint inversion in space and time of 29 metropolitan repeat stations and 1 observatory vector data using time power series as a temporal basis function. This approach does not require additional constraints like adding synthetic data, regularizing the inverse problem, or removing a trend prior to the inversion to be stable. It is shown that the geomagnetic jerks over France are detected in the regional parameters themselves and that it is possible to estimate the crustal bias. Considering the real data distribution in space and time, and the parameters used for this modelling, the R-SCHA2D model compared with the CM4 comprehensive model showed no indisputable evidence proving the existence of a secular variation anomaly over France. The main field and the secular variation are sketched for various epochs, in particular for epoch 2007.5. The present approach does neither address the problem of internal/external fields separation nor the upward continuation of the model to satellite altitudes. [ABSTRACT FROM AUTHOR]

Study of induced magnetic field is a powerful way to sound Earth internal structure. This work presents a full analysis and interpretation in terms of electrical conductivity and temperature of vector magnetic field measurements from Swarm Level1b data product from 26/11/2013 to 31/12/2019. Time series of the Gauss coefficients associated with the induced and inducing magnetic field are obtained from the data after removal of the core and lithospheric fields models and data selection. A Bayesian inversion of the induced field Gauss coefficients is then performed to obtain a new estimate of Earth's 1D mantle electrical conductivity down to 2000 km depth. This profile is fully compatible with the profiles derived from satellite and ground magnetic observatories data but does not present in the lower mantle the increase predicted by laboratory-based conductivity profile associated to classical mantle composition and temperature profile. Using the most recent database to model the electrical conductivity of all mineral mantle phases, two different methods are used to interpret Swarm data in terms of temperature for a given composition and water content. The first one is based on an interpretation of the conductivity estimates in terms of temperature by classical numerical root search. The second one consists in inferring a temperature probability density function from a Bayesian inversion of the Gauss coefficients associated to the induced magnetic field. Our results show that the later provide more reliable estimates of mantle temperatures, in relation to more physically grounded prior values. This second method provides also tighter constraints on the electrical conductivity estimates of the lower mantle. [Display omitted] • Full analysis and interpretation of Swarm vector magnetic field measurements. • Use of laboratory-based database to model mantle electrical conductivity • Estimation of new electrical conductivity profile for the Earth's mantle. • Estimation of new temperature profile for the Earth's mantle. [ABSTRACT FROM AUTHOR]

Nineteen new archeointensity results were obtained from the analysis of groups of French pottery fragments dated to the Early Middle Ages (6th to 10th centuries AD). They are from several medieval ceramic production sites, excavated mainly in Saran (Central France), and their precise dating was established based on typo-chronological characteristics. Intensity measurements were performed using the Triaxe protocol, which takes into account the effects on the intensity determinations of both thermoremanent magnetization anisotropy and cooling rate. Intensity analyses were also carried out on modern pottery produced at Saran during an experimental firing. The results show very good agreement with the geomagnetic field intensity directly measured inside and around the kiln, thus reasserting the reliability of the Triaxe protocol and the relevance of the quality criteria used. They further demonstrate the potential of the Saran pottery production for archeomagnetism. The new archeointensity results allow a precise and coherent description of the geomagnetic field intensity variations in Western Europe during the Early Medieval period, which was until now poorly documented. They show a significant increase in intensity during the 6th century AD, high intensity values from the 7th to the 9th century, with a minimum of small amplitude at the transition between the 7th and the 8th centuries and finally an important decrease until the beginning of the 11th century. Together with published intensity results available within a radius of 700 km around Paris, the new data were used to compute a master curve of the Western European geomagnetic intensity variations over the past 1500 years. This curve clearly exhibits five intensity maxima: at the transition between the 6th and 7th century AD, at the middle of the 9th century, during the 12th century, in the second part of the 14th century and at the very beginning of the 17th century AD. Some of these peaks are smoothed, or nearly absent when the selection of the data is extended to a 1250 km radius around Paris. The apparent regularity in the occurrence of intensity maxima, with a recurrence of ∼250 years, is particularly intriguing and might reflect a new characteristic of the secular variation, at least in Western Europe. It clearly requires further investigation and in particular the acquisition of new data from older periods. [ABSTRACT FROM AUTHOR]

Highlights: [•] Ensembles of time-varying archeomagnetic field models are introduced. [•] Three such ensembles of low degree models covering the past three millennia are built. [•] These models rely on archeomagnetic, volcanic and sedimentary data. [•] Model uncertainties and model prediction errors are extensively discussed. [•] These model ensembles, with their matlab toolkit, are freely available to users. [Copyright &y& Elsevier]