Determining the magnetic field in the core-mantle boundary zone by non-harmonic downward continuation

Ballani, L.; Greiner-Mai, H.; Stromeyer, Dietrich

doi:10.1046/j.1365-246x.2002.01655.x

Cited by 15 publications

(37 citation statements)

References 34 publications

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“…Therefore, the field continuation to the CMB must in any case be non-harmonic. In this paper, we will apply the recently developed non-harmonic downward continuation (NHDC) of the geomagnetic field by a rigorous inversion of the induction equation according to Ballani et al (2002), to compute the geomagnetic field at the CMB necessary to calculate the poloidal torque. We will outline this inversion in the following two sections.…”

Section: The Non-harmonic Field Continuation To the Cmbmentioning

confidence: 99%

“…The details of the theory of the inversion method, the used numerical algorithm and the results of some checks of the method for highly conducting shells are given in Ballani et al (2002) and Greiner-Mai et al (2004). Here, we will give an outline to make it understandable how the method works without going too much into details.…”

Section: Inversion Of the Induction Equation -An Outlinementioning

confidence: 99%

“…Because a non-zero conductivity is a precondition for the existence of electric currents, we have to determine the geomagnetic field at the CMB from its observed values at the Earth's surface by a solution of the induction equation of the mantle. Recently, Ballani et al (2002) developed an algorithm for a rigorous inversion of the mantle induction equation to obtain the poloidal geomagnetic field at the CMB, and checked this method also for highly conducting core shells. In this paper, we use this so-called non-harmonic downward continuation (NHDC) instead of the perturbation method of Benton and Whaler (1983) generally used before.…”

Section: Introductionmentioning

confidence: 99%

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Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

et al. 2007

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Axial poloidal electromagnetic core-mantle coupling torque: a re-examination for different conductivity and satellite supported geomagnetic field models ABSTRACTWe investigate the temporal behaviour of the axial component of the electromagnetic coremantle coupling torque that is associated with the poloidal part of the geomagnetic field observable at the Earth surface. For its computation, we use different models of the geomagnetic field, expanded into spherical harmonics (Wardinski and Holme, 2006;Sabaka et al., 2004), and the mantle conductivity. The geomagnetic field, which we have to know at the coremantle boundary for the associated computations, will be inferred from the field at the Earth surface by the non-harmonic field continuation through a conducting mantle shell. The aims of this investigation are (i) to check how sensitive is the computation of the torque with respect to the different geomagnetic field models, (ii) to check its dependence on the spherical harmonic degree n, and (iii) to determine the difference between the mechanical torque derived from the observed length-of-day variations (atmospheric influence subtracted) and the poloidal electromagnetic torque in dependence on the assumed conductivity. To use the non-harmonic field continuation for the torque calculation and to obtain an insight into the influence of the different geomagnetic field models on the EM torques are the major aspects of this paper.

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Section: The Non-harmonic Field Continuation To the Cmbmentioning

confidence: 99%

Section: Inversion Of the Induction Equation -An Outlinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

et al. 2007

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“…The input quantities for the non-harmonic downward continuation method (Ballani et al 2002) are the Gauss coefficients g nm (t), h nm (t). The calculation is done in a separate modelling process (Wardinski & Holme 2003).…”

Section: Global Model Datamentioning

confidence: 99%

“…New global magnetic data -Gauss coefficients up to degree and order 5, monthly values from 1980 to 2000, fitted to global data and partly based on highquality satellite vector data of Magsat and CHAMP/ØRSTED -are processed with a recent non-harmonic downward continuation method (Ballani et al 2002). Using a weakly conducting mantle and the highly conducting fluid in the outer core we investigate the temporal structure of the 1991 jerk below some geomagnetic stations calculating the component dY/dt at the core-mantle boundary and underneath in different depths of the fluid outer core assuming fluid velocity there.…”

mentioning

confidence: 99%

Time Structure of the 1991 Magnetic Jerk in the Core-Mantle Boundary Zone by Inverting Global Magnetic Data Supported by Satellite Measurements

Ballani

Wardinski

Stromeyer

et al.

Earth Observation With CHAMP

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Summary. New global magnetic data -Gauss coefficients up to degree and order 5, monthly values from 1980 to 2000, fitted to global data and partly based on highquality satellite vector data of Magsat and CHAMP/ØRSTED -are processed with a recent non-harmonic downward continuation method (Ballani et al. 2002). Using a weakly conducting mantle and the highly conducting fluid in the outer core we investigate the temporal structure of the 1991 jerk below some geomagnetic stations calculating the component dY/dt at the core-mantle boundary and underneath in different depths of the fluid outer core assuming fluid velocity there. The jerk structure dissolves and differs considerably in magnitude and in phase from the harmonically downward continued component.

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A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

Gribanov

Попов

2021

J. High Energ. Phys.

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In this paper, we propose a new method for obtaining a Born cross section using visible cross section data. It is assumed that the initial state radiation is taken into account in a visible cross section, while in a Born cross section this effect is ommited. Since the equation that connects Born and visible cross sections is an integral equation of the first kind, the problem of finding its numerical solution is ill-posed. Various regularization-based approaches are often used to solve ill-posed problems, since direct methods usually do not lead to an acceptable result. However, in this paper it is shown that a direct method can be successfully used to numerically solve the considered equation under the condition of a small beam energy spread and uncertainty. This naive method is based on finding a numerical solution to the integral equation by reducing it to a system of linear equations. The naive method works well because the kernel of the integral operator is a rapidly decreasing function of the variable x. This property of the kernel leads to the fact that the condition number of the matrix of the system of linear equations is of the order of unity, which makes it possible to neglect the ill-posedness of the problem when the above condition is satisfied. The advantages of the naive method are its model independence and the possibility of obtaining the covariance matrix of a Born cross section in a simple way.It should be noted that there are already a number of methods for obtaining a Born cross section using visible cross section data, which are commonly used in e+e− experiments. However, at least some of these methods have various disadvantages, such as model dependence and relative complexity of obtaining a Born cross section covariance matrix. It should be noted that this paper focuses on the naive method, while conventional methods are hardly covered. The paper also discusses solving the problem using the Tikhonov regularization, so that the reader can better understand the difference between regularized and non-regularized solutions. However, it should be noted that, in contrast to the naive method, regularization methods can hardly be used for precise obtaining of a Born cross section. The reason is that the regularized solution is biased and the covariance matrix of this solution do not represent the correct covariance matrix of a Born cross section.

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Determining the magnetic field in the core-mantle boundary zone by non-harmonic downward continuation

Cited by 15 publications

References 34 publications

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

Time Structure of the 1991 Magnetic Jerk in the Core-Mantle Boundary Zone by Inverting Global Magnetic Data Supported by Satellite Measurements

A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

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