Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth's gravitational field at satellite height

Michel, Volker

doi:10.1088/0266-5611/21/3/013

Cited by 52 publications

(37 citation statements)

References 19 publications

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“…Last, it should be noted that the inversion of the magnetic potential V [m] from (1.2) is closely related to the gravimetric problem (see, e.g. [10,11] and references therein). However, while the gravimetric problem is unique when restricted to harmonic mass densities, the vectorial nature of the inverse magnetization problem causes the described non-uniqueness issues.…”

Section: M(x) = Q(x)mentioning

confidence: 99%

On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

Gerhards

2018

Inverse Problems in Science and Engineering

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Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e. the magnetization is described by a scalar susceptibility and the dipole direction). Here, we investigate the situation under the additional constraint that the susceptibility is either spatially localized in a subregion of the sphere or that it is band-limited. If the dipole direction is known, then the susceptibility is uniquely determined under the spatial localization constraint while it is only determined up to a constant under the assumption of bandlimitedness. If the dipole direction is not known, uniqueness is lost again. However, we show that all dipole directions that could possibly generate the measured magnetic potential need to be zeros of a certain polynomial which can be computed from the given potential. We provide examples of non-uniqueness of the dipole direction and examples on how to find admissible candidates for the dipole direction under the spatial localization constraint. ARTICLE HISTORY

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Section: M(x) = Q(x)mentioning

confidence: 99%

On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

Gerhards

2018

Inverse Problems in Science and Engineering

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“…A completely different way to solve the gravitational inverse problem (GIP) (and the GCIP) has been suggested by Michel (2005), who derives the harmonic part C of the density from gravity observations.…”

Section: Mass and Mass Redistributionmentioning

confidence: 99%

Time-Variable Gravity Field and Global Deformation of the Earth

Kusche¹

2013

Handbook of Geomathematics

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The analysis of the Earth's time-variable gravity field and its changing patterns of deformation plays an important role in Earth system research. These two observables provide, for the first time, a direct measurement of the amount of mass that is redistributed at or near the surface of the Earth by oceanic and atmospheric circulation and through the hydrological cycle. In this chapter, we will first reconsider the relations between gravity and mass change. We will in particular discuss the role of the hypothetical surface mass change that is commonly used to facilitate the inversion of gravity change to density. Then, after a brief discussion of the elastic properties of the Earth, the relation between surface mass change and the three-dimensional deformation field is considered. Both types of observables are then discussed in the framework of inversion. None of our findings are entirely new; we merely aim at a systematic compilation and discuss some frequently made assumptions. Finally, some directions for future research are pointed out.

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“…The corresponding formulae were derived in and [Michel, 2005a]. The expansion of in terms of the basis of type I has the advantage that it yields an obvious characterisation of the non-uniqueness.…”

Section: Theorem 2 Let V : R 3 \B → R Given By (2) Satisfy the Conditmentioning

confidence: 99%

On Mathematical Aspects of a Combined Inversion of Gravity and Normal Mode Variations by a Spline Method

Berkel

Michel

2010

Math Geosci

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This paper provides a brief overview of two linear inverse problems concerned with the determination of the Earth's interior: inverse gravimetry and normal mode tomography. Moreover, a vector spline method is proposed for a combined solution of both problems. This method uses localised basis functions, which are based on reproducing kernels, and is related to approaches which have been successfully applied to the inverse gravimetric problem and the seismic traveltime tomography separately.

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Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth's gravitational field at satellite height

Cited by 52 publications

References 19 publications

On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

Time-Variable Gravity Field and Global Deformation of the Earth

On Mathematical Aspects of a Combined Inversion of Gravity and Normal Mode Variations by a Spline Method

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