Generalized eigenfunctions of layered elastic media and application to diffuse fields

Margerin, Ludovic

doi:10.1121/1.3021312

Cited by 23 publications

(30 citation statements)

References 22 publications

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“…(3) is bounded between 0 and 1, which is advantageous for a quantitative fit (Nakahara and Margerin, 2011). In the bulk of a homogeneous half-space, the partition ratio PE hr of a wavefield composed of an equipartition mixture of body waves is theoretically equal to 0.67 (Margerin, 2009). The horizontal-to-vertical amplitude ratio H/V(t) is defined in the time domain as:…”

Section: Methods Of Analysismentioning

confidence: 99%

“…The observations at depth reveal that energy equipartition among body waves applies for frequencies higher than 6 Hz. In the lower frequency range 0.2-2 Hz, frequency-dependent energy partitioning ratios measured in the coda are modeled with the spectral technique developed by Margerin (2009) to constrain the depth-dependent seismic velocity structure at Underseis.…”

Section: Introductionmentioning

confidence: 99%

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Attenuation and velocity structure from diffuse coda waves: Constraints from underground array data

Galluzzo

Rocca

Margerin³

et al. 2015

Physics of the Earth and Planetary Interiors

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Section: Methods Of Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Attenuation and velocity structure from diffuse coda waves: Constraints from underground array data

Galluzzo

Rocca

Margerin³

et al. 2015

Physics of the Earth and Planetary Interiors

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“…From a mathematical point of view, leaky modes are complex poles that do not belong to the proper eigenvalue spectrum because such poles are located on a forbidden Riemann sheet [11,1]. These modes constitute a discrete set which is actually not part of the complete modal set constituted by the discrete set of trapped modes and the continuous spectrum of radiation modes representing the contribution of body waves [4,12,5,13]. However, leaky modes have the potential to give a good representation of the continuum over an area close to the core or the surface of the waveguide.…”

Section: Context and Objectivesmentioning

confidence: 99%

“…They constitute a continuous spectrum of standing waves [4,5]. This continuum is intrinsic to the unbounded nature of the cross-section of the waveguide.…”

Section: Context and Objectivesmentioning

confidence: 99%

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Treyssède¹,

Nguyen²,

Bonnet-Bendhia³

et al. 2014

Wave Motion

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Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In numerous applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded in the transverse directions. The physics of waves in such an open waveguide significantly differs from a closed waveguide, i.e. for a bounded cross-section. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes. These leaky modes have often been considered in non destructive testing applications, which require waves of low attenuation in order to maximize the inspection distance. The main difficulty with numerical modeling of open waveguides lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. A simple numerical procedure consists in using absorbing layers of artificially growing viscoelasticity, but large layers may be required. The goal of this paper is to explore another approach for the computation of trapped and leaky modes in open waveguides. The approach combines the so-called semi-analytical finite element method and a perfectly matched layer technique. Such an approach has already been successfully applied in scalar acoustics and electromagnetism. It is extended here to open elastic waveguides, which raises specific difficulties. In this paper, two-dimensional stratified waveguides are considered. As it reveals a rich structure, the numerical eigenvalue spectrum is analyzed in a first step. This allows to clarify the spectral objects calculated with the method, including radiation modes, and their dependency on the perfectly matched layer parameters. In a second step, numerical dispersion curves of trapped and leaky modes are compared to analytical results.

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“…The connection with 2D elasticity was pointed out by Sánchez-Sesma and Campillo (2006). It has been proposed that the coda of earthquakes can be seen as a realization of a diffuse field (Shapiro et al 2000;Hennino et al 2001;Margerin 2009). In several instances, the ASN allows Green's function retrieval from the average of cross-correlation between two receivers within a diffuse seismic field.…”

Section: Introductionmentioning

confidence: 99%

Application of a simplified calculation for full-wave microtremor H/V spectral ratio based on the diffuse field approximation to identify underground velocity structures

Masaki

Irikura

et al. 2017

Earth Planets Space

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Under the diffuse field approximation, the full-wave (FW) microtremor H/V spectral ratio (H/V) is modeled as the square root of the ratio of the sum of imaginary parts of the Green's function of the horizontal components to that of the vertical one. For a given layered medium, the FW H/V can be well approximated with only surface waves (SW) H/V of the "cap-layered" medium which consists of the given layered medium and a new larger velocity half-space (cap layer) at large depth. Because the contribution of surface waves can be simply obtained by the residue theorem, the computation of SW H/V of cap-layered medium is faster than that of FW H/V evaluated by discrete wavenumber method and contour integration method. The simplified computation of SW H/V was then applied to identify the underground velocity structures at six KiK-net strong-motion stations. The inverted underground velocity structures were used to evaluate FW H/Vs which were consistent with the SW H/Vs of corresponding cap-layered media. The previous study on surface waves H/Vs proposed with the distributed surface sources assumption and a fixed Rayleighto-Love waves amplitude ratio for horizontal motions showed a good agreement with the SW H/Vs of our study. The consistency between observed and theoretical spectral ratios, such as the earthquake motions of H/V spectral ratio and spectral ratio of horizontal motions between surface and bottom of borehole, indicated that the underground velocity structures identified from SW H/V of cap-layered medium were well resolved by the new method.

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Generalized eigenfunctions of layered elastic media and application to diffuse fields

Cited by 23 publications

References 22 publications

Attenuation and velocity structure from diffuse coda waves: Constraints from underground array data

Attenuation and velocity structure from diffuse coda waves: Constraints from underground array data

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Application of a simplified calculation for full-wave microtremor H/V spectral ratio based on the diffuse field approximation to identify underground velocity structures

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