Directional spherical multipole wavelets

Hayn, M.; Holschneider, Matthias

doi:10.1063/1.3177198

Cited by 9 publications

(25 citation statements)

References 19 publications

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“…The wavelets we choose for our analysis are the directional Poisson wavelets presented in Hayn & Holschneider (2009). They are defined by taking derivatives of the Poisson kernel of potential fields, which makes them very suitable for potential fields analysis.…”

Section: Directional Continuous Wavelet Analysismentioning

confidence: 99%

“…Here we describe the effect of the normalization of a wavelet spectrum with a background spectrum, and estimate the scaling factor that needs to be applied on the wavelet scales for the case of the backgrounds based on EGM2008 and Gebco oceanic geoids. whereψ n a (l, m) stands for the spherical harmonics coefficient of degree l and order m of the Poisson wavelet ψ n a (Hayn & Holschneider 2009). The wavelet scale in kilometers is given by 20000 a n km, where n is the order of the Poisson wavelet.…”

Section: A P P E N D I X C : S C a L I N G Fa C T O R O F T H E N O Rmentioning

confidence: 99%

“…Here, we revisit the question of the existence and characteristics of the long wavelengths geoid undulations in the light of the new GRACE satellite gravity data by applying a dedicated analysis technique in spherical geometry: a directional wavelet transform with Poisson multipole wavelets (Hayn & Holschneider 2009). This method allows one to analyze the gravity field in two dimensions on the sphere.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Wavelet-based directional analysis of the gravity field: evidence for large-scale undulations

Hayn¹,

Panet²,

Diament³

et al. 2012

Geophysical Journal International

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International audienceIn the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophys-ical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings

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Section: Directional Continuous Wavelet Analysismentioning

confidence: 99%

Section: A P P E N D I X C : S C a L I N G Fa C T O R O F T H E N O Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wavelet-based directional analysis of the gravity field: evidence for large-scale undulations

Hayn¹,

Panet²,

Diament³

et al. 2012

Geophysical Journal International

View full text Add to dashboard Cite

show abstract

“…The idea to construct a not rotation invariant spherical wavelet by a directional derivative of the Poisson kernel was described in [15]. In this case, 'directional derivative' means that the source of the field, or the defining position, is rotated around an axis that is perpendicular to the symmetry axis, and the derivative of this transform is computed.…”

Section: Example: Directional Waveletsmentioning

confidence: 99%

“…Further, the formulas are applied to the second directional derivative of the Poisson wavelet g 1 ρ . This function is an example of directional wavelets, introduced by Hayn and Holschneider in [15] and intended for analyzing of spherical signals with directional features. The result is compared to that obtained for the zonal Poisson wavelets [24] and discussed in view of the general result for zonal wavelets [22].…”

Section: Introductionmentioning

confidence: 99%

On the uncertainty product of spherical functions

Iglewska-Nowak

2021

Applied and Computational Harmonic Analysis

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The uncertainty product of a function is a quantity that measures the trade-off between the space and the frequency localization of the function. Its boundedness from below is the content of various uncertainty principles. In the present paper, functions over the n-dimensional sphere are considered. A formula is derived that expresses the uncertainty product of a continuous function in terms of its Fourier coefficients. It is applied to a directional derivative of a zonal wavelet, and the behavior of the uncertainty product of this function is discussed.

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Poisson Wavelets on $$n$$ n -Dimensional Spheres

Iglewska-Nowak

2014

J Fourier Anal Appl

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In this paper, Poisson wavelets on n-dimensional spheres, derived from Poisson kernel, are introduced and characterized. We compute their Gegenbauer expansion with respect to the origin of the sphere, as well as with respect to the field source. Further, we give recursive formulae for their explicit representations and we show how the wavelets are localized in space. Also their Euclidean limit is calculated explicitly and its space localization is described. We show that Poisson wavelets can be treated as wavelets derived from approximate identities and we give two inversion formulae.

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Directional spherical multipole wavelets

Cited by 9 publications

References 19 publications

Wavelet-based directional analysis of the gravity field: evidence for large-scale undulations

Wavelet-based directional analysis of the gravity field: evidence for large-scale undulations

On the uncertainty product of spherical functions

Poisson Wavelets on $$n$$ n -Dimensional Spheres

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