Vincent Lesur

Parent magnetic field models for the IGRF-12GFZ-candidates

We propose candidate models for IGRF-12. These models were derived from parent models built from 10 months of Swarm satellite data and 1.5 years of magnetic observatory data. Using the same parameterisation, a magnetic field model was built from a slightly extended satellite data set. As a result of discrepancies between magnetic field intensity measured by the absolute scalar instrument and that calculated from the vector instrument, we re-calibrated the satellite data. For the calibration, we assumed that the discrepancies resulted from a small perturbing magnetic field carried by the satellite, with a strength and orientation dependent on the Sun’s position relative to the satellite. Scalar and vector data were reconciled using only a limited number of calibration parameters. The data selection process, followed by the joint modelling of the magnetic field and Euler angles, leads to accurate models of the main field and its secular variation around 2014.0. The obtained secular variation model is compared with models based on CHAMP satellite data. The comparison suggests that pulses of magnetic field acceleration that were observed on short time scales average-out over a decade.

An algorithm for deriving core magnetic field models from the Swarm data set

In view of an optimal exploitation of the Swarm data set, we have prepared and tested software dedicated to the determination of accurate core magnetic field models and of the Euler angles between the magnetic sensors and the satellite reference frame. The dedicated core field model estimation is derived directly from the GFZ Reference Internal Magnetic Model (GRIMM) inversion and modeling family. The data selection techniques and the model parameterizations are similar to what were used for the derivation of the second (Lesur et al., 2010) and third versions of GRIMM, although the usage of observatory data is not planned in the framework of the application to Swarm. The regularization technique applied during the inversion process smoothes the magnetic field model in time. The algorithm to estimate the Euler angles is also derived from the CHAMP studies. The inversion scheme includes Euler angle determination with a quaternion representation for describing the rotations. It has been built to handle possible weak time variations of these angles. The modeling approach and software have been initially validated on a simple, noise-free, synthetic data set and on CHAMP vector magnetic field measurements. We present results of test runs applied to the synthetic Swarm test data set.

2-D and 3-D interpretation of electrical tomography measurements, Part 2: The inverse problem

The interpretation of borehole‐to‐borehole electrical measurements requires solving an inverse problem for a given class of model geometries. The usual approach to an inverse problem includes a model dependent task (i.e., forward modeling) and a generic task (i.e., an optimization scheme). We have developed an optimization algorithm using a nonlinear inversion technique. This algorithm allows recovery of a possible resistivity distribution in an investigated zone between two boreholes or in the vicinity of them. This resistivity distribution is defined as a set of 2-D or 3-D volumes of constant resistivity. The inversion procedure minimizes a least‐squares term plus a damping term. This latter term seeks to minimize the roughness of the solution. An improved form of this smoothness term may enhance the spatial resolution of the resistivity image, assuming that the resistivity contrast is known a priori. This reconstruction algorithm has been tested for both 2-D and 3-D geometries. These inversion tests we...

The Earth’s Magnetic Field at the CHAMP Satellite Epoch

Since the Carl-Friedrich Gauss epoch, the Earth’s magnetic field has changed dramatically, its dipole moment decreasing by some 10%. This single observation has raised a large number of questions about a future possible polarity transition, and consequently the possible effects on the Earth’s environment. Here, the progress made over the last few years, when the advent of the satellite era brought a major breakthrough in our understanding of the geomagnetic field at large scales, is summarized. Obtaining good data from observations is a prerequisite, so ground-based and satellite measurements are described. By properly combining these data, information about the characteristics of the geomagnetic field can be retrieved. So, recent global geomagnetic field models based on spherical harmonic analyses are generally discussed. The GRIMM model, as a powerful tool to study the internal geomagnetic field, is discussed in more details. An important and ongoing topic is also the description of the lithospheric contributions, so a large part of this chapter is dedicated to the large and small scales of this field. An outlook to expected future results and unresolved questions is provided in the final part of this chapter.

Aeromagnetic and Marine Measurements

Modern magnetic measurements have been acquired since the 1940s over land and the 1950s over oceans. Such measurements are collected using magnetometer sensors rigidly fixed to the airframe or towed in a bird for airborne or in a fish in marine surveys using a cable long enough to avoid the ship/airplane magnetic effect. Positioning problems have been considerably reduced by the Global Positioning System (GPS). Considerable progress has been made in geomagnetic instrumentation increasing the accuracy from ∼10 nT or better in the 1960s to ∼0.1 nT or more nowadays. Scalar magnetometers, less sensitive to orientation problems than the fluxgate vector instruments, are the most commnonly used for total-field intensity measurement. Optical pumping alkali vapor magnetometers with high sampling rate and high sensitivity are generally used aboard airframes whereas proton precession magnetometers (including Overhauser) are favored at sea. Scalar magnetic anomalies are calculated by subtraction of global core field models like the International Geomagnetic Reference Field (IGRF) after subtraction of an external magnetic field estimate using magnetic observatories or temporary magnetic stations. The external field correction using an auxiliary station is often not possible in marine measurements. However comprehensive models such as CM4 can be used to provide adequate core and external magnetic fields, particularly for almost all early magnetic measurements which were not corrected for the external field. In the case of airborne measurements such global models help to define a reference level for global mapping of the anomaly field. The current marine dataset adequately covers most of the Northern Hemisphere oceanic areas while major gaps are observed in the southern Indian and Pacific oceans. Airborne measurements cover all the world, except oceanic areas and large part of Antarctica. Data are however often not available when owned by private companies. The data released are mainly owned by governmental agencies. The derived airborne/marine magnetic anomaly maps combined with long-wavelength satellite maps help scientists to better understand the structure and the evolution of the lithosphere at local, regional and global scales. Marine magnetic observations are also made at depth, near the seafloor, in order to access shorter wavelengths of the magnetic field for high resolution studies. Airborne High Resolution Anomaly Maps (HRAM) are also nowadays the new trends pushing towards the generalisation of the Unmanned Aerial Vehicles (UAV) or Autonomous Underwater Vehicles (AUV) or Remotely Operated Vehicles (ROV) magnetic surveys.

Geomagnetic secular variation violating the frozen-flux condition at the core surface

We consider a method to extract the part of a given geomagnetic secular variation (SV) model that is not consistent with a frozen-flux condition. This condition is usually derived from the diffusionless radial induction equation at the core-mantle boundary (CMB), and is defined explicitly in the spatial domain: radial flux changes within closed null-flux curves at the core surface are not allowed at any instant. We study here this condition in the spherical harmonic (SH) domain, relying on the SH expansion of the diffusionless equation. SV models at a certain epoch are separated into advective and non-advective parts. The advective (resp. non-advective) part satisfies (resp. does not satisfy) the frozen-flux condition redefined in the SH domain. We show that this separation is not unique. In this work, we achieve a unique separation by assuming the orthogonality of the two parts in terms of the radial SV energy at the CMB. From the recent geomagnetic models, GRIMM and CM4, we find that the non-advective part shows up mainly in the small reverse patches of the radial magnetic field at the CMB. However, non-advective behaviors are also observed outside these patches. As far as no restriction is imposed on core flow configuration, time variations of the non-advective part are not correlated to those of the SV models. However, if the flow is restricted to be tangentially geostrophic, time variations of the SV models have to be partly non-advective. Furthermore, for this flow configuration, the secular decrease of the axial dipole has to be largely non-advective.

Geomagnetic field evolution. Changes on the way

ow, mantle conductivity and lithospheric composition to the dynamics of the ionospheric and magnetospheric currents. Therefore, in this paper a case is presented for the necessity of continuous monitoring of geomagnetic eld from ground and space. This contribution is mainly based on some recent work and