Geomagnetic Potential Research Articles

Correlation Based Time Evolution of the Archeomagnetic Field

AbstractIn a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, https://doi.org/10.1093/gji/ggaa336). By assuming a Gaussian process for the geomagnetic potential, a correlation‐based algorithm was presented, which incorporates a closed‐form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space‐time correlation kernel is constructed from the tensor product of the closed‐form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.

Evidence for an Effective Gravitational Constant from the Laboratory Measurements

We consider, within the framework of an improved $$5D$$ Kaluza-Klein theory (KK $$\psi$$ ), the set of twenty most precise values ever published of Earth-based gravitational constant measurements. We take into account the possibility of a jump discontinuity into the geomagnetic potential in connection with the spin crossover of the iron (III) complex ions migrating from the Earth’s outer core into the deep Earth mantle as well as the spin crossover of the copper (III) complex ions migrating downwards within either the Earth’s crust or deep in the Earth’s mantle. Moreover, it turns out that the boundary conditions assigned to both internal, $$\phi$$ , and external, $$\psi$$ , scalar fields are sensitive to the aforementioned jump discontinuity too. Again, the fits to the experimental data are found in good agreement with the predictions of the linearized KK $$\psi$$ theory. An estimate around the vacuum expectation values $$\psi=v$$ and $$\phi=1$$ of the second derivatives $${\partial^{2}f_{\textrm{EM}}}/{\partial\phi^{2}}(v,1)$$ , $${\partial^{2}f_{\textrm{EM}}}/{\partial\phi\partial\psi}(v,1)$$ and $${\partial^{2}f_{\textrm{EM}}}/{\partial\psi^{2}}(v,1)$$ of the coupling function, $$f_{\textrm{EM}}(\psi,\phi)$$ , of the electromagnetic field (EM) with $$\psi$$ and $$\phi$$ , is provided for the first time, thereby enabling the determination of the product $$v\times f_{\textrm{EM}}(v,\phi)$$ and $$v\times f_{\textrm{EM}}(\psi,1)$$ in the second-order approximation from the experimental data.

Correlation based snapshot models of the archeomagnetic field

SUMMARY For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective a priori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. A priori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.

Modeling of regional magnetic field applying spherical functions: practical aspect

Observation of geomagnetic field, measurement of its components values and establishment on their base models of geomagnetic field as well as geomagnetic mapping are the main trend of geomagnetic studies. Analytical model of geomagnetic field allows calculating the value of any component of geomagnetic field at any point of near-earth space and on the Earth. A new method has been proposed for construction of geomagnetic potential regional model. In accordance with Gauss’ fundamental studies, classical concept of geomagnetic potential became its record as endless series of Legeandre functions. A program of writing the series of geomagnetic potentials according to their spherical or ellipsoidal functions is used for most cases for modeling of global (normal) geomagnetic field with the length of a series equal to 9—13 harmonics. However in case when the sphere is not complete and only its part (a segment of the sphere or its trapezium) is taken into account the spherical Legeandre functions lose their orthogonality. In this connection for elaboration of regional field models different modifications of spherical harmonic analysis with application of spherical Legeandre functions even grade and real order are used. Such functions form an orthogonal by weight system of functions on arbitrary spherical trapezium but do not have recurrent correlation therefore we are to use for their calculation an arrangement as hypergeometric series. The area of determination of such functions is spherical segment. Working formulae have been obtained for constructing the model mentioned above. As front-end data for constructing a model of regional magnetic field the values of its components obtained at geomagnetic observatories have been used. It has also been suggested to make calculations of regional model of geomagnetic potential by a method proposed within the limits of a procedure deletion-computing-restoration. Initially a systematic product of components is found using a global model of geomagnetic field. Then abnormal values of components are calculated. A model of regional abnormal geomagnetic field is computed using basic functions. A parameter of Tikhonov’s regularizing is introduced to stabilize the solution.

Analysis of the Hypothesis of a Giant Gaussian Process as a Means for Describing Secular Variations of the Geomagnetic Field Vector

The consistency of the empirical data on the paleointensity and paleoinclinations contained in the BOROKPINT paleointensity world database with the Geocentric Axial Dipole (GAD) hypothesis and the Giant Gaussian Process (GGP) model describing the geomagnetic field variations in the Brunhes epoch is tested. The calculation procedure is based on the representation of the geomagnetic field potential by the sum of the spherical functions of a spatial coordinate with random coefficients, which enables the computer simulation of the data that correspond to the given statistical characteristics of the coefficients. The estimation shows that according to the Kolmogorov–Smirnov and Anderson–Darling tests, the GAD hypothesis in its canonical form should be rejected. The extension of GAD to GGD with nonzero time-average quadrupole and octupole terms brings the paleointensity and paleoinclination data into agreement with the GGP model realizations; however, these models turn out to be mutually exclusive because their parameters are inconsistent with each other. Testing the paleoinclination data against GDP model demonstrates the necessity of introducing a small correction to the purely dipole component of the geomagnetic field. At the same time, the analysis of the paleointensity data shows that these data with a very high probability agree with the GGP models with a high quadrupole contribution making up 1/3 of the dipole coefficient, which is strongly at odds with the parameters of the model corresponding to the paleoinclination data. This inconsistency is most probably caused by the artifacts due to the incorrect determinations of paleointensity; however, this interpretation leaves unsolved the question about the causes of such a strong latitudinal dependence of the intensity of the Virtual Axial Dipole Moment (VADM) what follows from the empirical data.

Differential Spontaneous Photon Emissions from Cerebral Hemispheres of Fixed Human Brains: Asymmetric Coupling to Geomagnetic Activity and Potentials for Examining Post-Mortem Intrinsic Photon Information

The emissions of biophotons have been considered a ubiquitous property of living systems and their components. We measured the “spontaneous” photon emissions from fixed whole and sectioned human brains within hyper-dark settings. Significant differences in photon counts were measured from different spatial planes. The flux densities were in the order of 2 × 10-12 W per m2. The right hemispheres but not the left hemispheres displayed more photon emissions whose spectral power density profiles exhibited a conspicuous amplitude peak between 7.9 and 8 Hz. Brains measured in the hyperdark (~10-12 W·m2) after removal from the typical lighting of the laboratory emitted more photons than those that had been maintained in the hyperdark for one week. The significant correlation between the numbers of photons emitted from the left hemisphere (but not the right) and global geomagnetic activity also exhibited energy equivalence between the photon flux densities and the geomagnetic shift within the cerebral volumes. These results indicate that what has been assumed to be fixed unresponsive human brain tissue still emits small numbers of photons that may be residuals from ambient light and can potentially interact with global geomagnetic activity. The medical implications for post-mortem intrinsic photonic information based upon the anisotropic microstructures within the hemispheres of the human cerebrum are discussed.

Multipole models of the geomagnetic field: Construction of the Nth approximation

The fact that the geomagnetic potential, as well as magnetic induction and its gradient, can be represented with an arbitrary accuracy in the scope of multipole models has been justified programmatically and analytically. The obtained expressions are brief and can be utilized in analytical and computer-based studies using methods of computer algebra and numerical computations. Previously unknown analytical expressions for the components of the first seven multipole tensors, expressed in terms of the Gaussian coefficients, have been obtained for applied problems of space dynamics. An algorithm that makes it possible to construct analytical expressions for the arbitrary-order multipole tensor and magnetic induction vector components in any finite approximation has been developed.

Two geomagnetic regional models for Albania and south-east Italy from 1990 to 2010 with prediction to 2012 and comparison with IGRF-11

Here we present a revised geomagnetic reference model for the region comprising Albanian territory, southeast part of Italian Peninsula and Ionian Sea from 1990 to 2010 with prediction to 2012. This study is based on the datasets of magnetic measurements taken during different campaigns in Albania and Italy in the time of concern, together with a total intensity data set from the ∅rsted and CHAMP satellite missions. The model is designed to represent the Cartesian components, X, Y, Z and the total intensity F of the main geomagnetic field (and its secular variation SV) for the period of interest. To develop the model, we applied a Spherical Cap Harmonic Analysis (SCHA) of the geomagnetic potential over a 16° cap with most of the observations concentrated in the central 4° half-angle. The use of a larger cap than that containing the data was made to reduce the typical problems in SV modelling over small regions. Also a new technique, called “Radially Simplified Spherical Cap Harmonic Analysis” (RS-SCHA), was developed to improve the model especially in the radial variation of the geomagnetic field components. Both these models provide an optimal representation of the geomagnetic field in the considered region compared with the International Geomagnetic Reference Field model (IGRF-11) and can be used as reference models to reduce magnetic surveys undertaken in the area during the time of validity of the model, or to extrapolate the field till 2012.

Local time variation of the amplitude of geomagnetic sudden commencements (SC) and SC-associated polar cap potential

Abstract Local time (LT) variations of the averaged H-component amplitude of geomagnetic sudden commencements (SCs) observed at Memambetsu (geomagnetic latitude 35.4°) are derived separately for the summer and winter season. The amplitude was found to be higher at nighttime than daytime in both seasons, and the LT variations showed a good agreement with calculated LT variations of the resultant magnetic field due to a pair of fieldaligned currents (FACs) and ionospheric currents produced by the FACs. The DL- and DP-component of the disturbance field of SC can be separated based on a comparison of the observed and calculated LT variations. A method is introduced by which we can estimate the potential voltage difference associated with the FACs in the polar cap.

Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earth’s oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellite’s rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.

Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.

Aikitu Tanakadate and the Controversy over Vertical Electrical Currents in Geomagnetic Research

Aikitu Tanakadate (1856-1952) was a pioneer in geomagnetic research in Japan. This paper focuses on Tanakadale's investigation of vertical, electrical currents between the Earth and his atmosphere and his role in a controversy over these currents. This controversy arose after Adolf Schmidt (1860-1944) hypothesized these vertical currents in 1895. Debate was aroused over this question for two reasons: firstly it might upset the premise of the Gaussian theory of geomagnetic potential; and secondly it seemed to provide a key to revealing the mechanism of geomagnetism. Tanakadale did not doubt the existence of such currents, but he was skeptical about the method with which the hypothesis was tested. After 1939 the controversy died down, but never ended. The recent solution of this problem in 1992 shows that Tanakadate was far-sighted in criticizing the validity of the method which others used to test the hypothesis.

IGRF, 1991 Revision

The International Geomagnetic Reference Field (IGRF) is a series of mathematical models of the main geomagnetic field and its secular variation. Each model consists of a set of spherical harmonic (or Gauss) coefficients, the g's and h's in a series expansion of the following geomagnetic potential.

International Geomagnetic Reference Field, 1991 revision: International Association of Geomagnetism and Aeronomy (IAGA) Division V, Working Group 8: Analysis of the main field and secular variation

The International Geomagnetic Reference Field (IGRF) is a series of mathematical models of the main geomagnetic field and its secular variation. Each model consists of a set of spherical harmonic (or Gauss) coefficients, g and h in a series expansion of the geomagnetic potential V=a∑n=1N∑m=0n(a/r)n+1[gnmcosmϕ+hnmsinmϕ]Pnm(cosθ), where a is the mean radius of the Earth (6371.2 km); r the radial distance from the center of the Earth; ϕ the east longitude measured from Greenwich; θ the geocentric colatitude; and Pnm(cosθ) the associated Legendre function of degree n and order m, normalized according to the convention of Schmidt [see, e.g., Langel (1987)]. In principle, N should be ∞ but the Working Group is of the opinion that in practice the available data for most epochs do not justify N greater than 10. This value is chosen to maintain consistency between models at different epochs. The coefficients are in units of nanotesla (nT).

A preliminary study on variations in the Gauss coefficients of the geomagnetic potential over several hundred years

Geomagnetic secular variations are examined in terms of time variation in the Gauss coefficients. Major parts of the variations over several hundred years can be represented by a two mode model which consists of a standing and a drifting field. When the Gauss coefficients are plotted on a diagram with g n m in the abscissa and h n m in the ordinate, the drifting component describes a circle. However, some of the observed coefficients depict an elliptical trajectory rather than a circular one. Improvement of the model is attempted in two different ways. One is to assume time variability of the amplitude of the drifting component. The other is to introduce another drifting mode. Selecting a few spherical harmonic terms, variations in the Gauss coefficients since A.D. 1600 are analysed. When the amplitude of the drifting field is assumed to vary, the observed nature of the elliptical trajectory is well represented. In this case, phase velocity also changes with time. It is large while the amplitude is small, and it is small while the amplitude is large. Three mode models, in which an eastward drifting mode is incorporated, approximate the observed variations as well, not only for the period over several hundred years but also for the last several decades. In this model the westward drifting mode dominates the eastward mode.

Simplified theory of series for the gravitational and geomagnetic potential

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Bumps on the core—mantle boundary: geomagnetic and gravitational evidence revisited

Evidence for the presence of undulations or temperature variations, or both, at the core-mantle boundary comes from the remarkably high correlation between the pattern of long-wavelength gravitational anomalies and the corresponding pattern of anomalies in the geomagnetic potential when the latter is rotated in longitude. Since gravitational anomalies originate at or above the core surface and the magnetic anomalies originate within the core, the correlation, if statistically significant, must be a manifestation of processes occurring at the core-mantle interface and has important implications for the structure and dynamics of the Earth’s deep interior. Indeed, the discovery of the correlation stemmed from considerations of interactions between motions in the core and mantle and can be regarded as evidence in favour of deep mantle convection. The large value for the correlation coefficient is now accepted but, notwithstanding our published statistical tests to the contrary, opinions are often expressed in the literature that any low-order convergent field might be expected to show a high correlation with gravity when rotated to the optimum position. Here we reiterate that this is not so, and illustrate our argument with a number of randomly generated field models that have correlation coefficients from 0.2 to 0.8.

Uniqueness probems in the spherical harmonic analysis of the geomagnetic field direction data.

It is shown that if the field directions (inclination and declination, or other combination of two independent angles) are completely known on the surface of the earth, the geomagnetic potential can be determined uniquely except an arbitrary multiplicative constant. On the other hand, when declinations only are specified on the surface there are infinitely many potentials which satisfy exactly the same boundary conditions. Such non-uniqueness seems also to be present for the cases of other incomplete data set composed of one angle only. The uniqueness theorem serves as the basis for spherical harmonic analyses of the paleomagnetic field.

Geomagnetic potential in offset dipole coordinates

Abstract : The geomagnetic potential (IGRF 1965.0) is converted into the spherical coordinates of an optimally offset and inclined dipole by means of a least-squares fit to the 'transformed' Schmidt coefficients. Time derivatives of the resulting spherical-harmonic expansion coefficients are obtained by taking symmetric first differences (1966.0 vs 1964.0). (Author)

Density perturbations in the earth's core due to hydromagnetic oscillations

The equation for density perturbation induced by plane hydromagnetic waves (responsible for geomagnetic secular variation) has been derived based on β-plane formulation. It is deduced that for the usual physical properties of the earth's core such a density perturbation would be small and would not be, in the main, responsible for the recently discovered correlation between gravitation and geomagnetic potentials.