Osculations of spectral lines in a layered medium

Kausel, Eduardo; Malischewsky, Peter G.; Barbosa, João Manuel de Oliveira

doi:10.1016/j.wavemoti.2015.01.004

Cited by 19 publications

(13 citation statements)

References 20 publications

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“…Maznev and Every (2011) go beyond normal modes and discuss leaky modes as well. The phenomenon exists in combination with osculation points of dispersion curves (Kausel et al 2015) and according to Maznev and Every (2011) can be partly understood by consideration of mode degeneracy and hybridization. Malischewsky et al (2017) and Malischewsky and Forbriger (2020) report that the condition of a single-valued dispersion relation can as well be violated for simple seismic structures of a layer on top of a half-space.…”

Section: Reported Cases From Engineeringmentioning

confidence: 99%

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

Forbriger

Gao

Malischewsky

et al. 2020

Geophysical Journal International

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SUMMARY Other than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

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Section: Reported Cases From Engineeringmentioning

confidence: 99%

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

Forbriger

Gao

Malischewsky

et al. 2020

Geophysical Journal International

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“…(7,9) and for Eqs. (8,10). Namely, , and Solutions are given by equating the product of the two determinants to zero.…”

Section: Traction-free Platementioning

confidence: 99%

Partial wave basis adapted to exterior boundary conditions of an elastic plate

Cojocaru¹

2021

MJPS

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An approach to describing normal elastic vibration modes in confined systems is presented. In a standard treatment of the problem, the displacement field is represented by a superposition of partial waves of a general form, e.g., plane waves. The unknown coefficients of superposition are then obtained from the equation of motion and the full set of boundary conditions. In the proposed approach, the functional form of partial waves is chosen in such a way as to satisfy the boundary conditions on exterior surfaces identically, i.e., even if the unknown quantities determined by the remaining constraints are found in an approximation, numerically or analytically. Some examples of solutions for composite elastic plates are discussed to illustrate the efficiency of the approach and its relevance for applications.

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“…One notorious characteristic is an extremely high Poisson ratio in the uppermost layers together with a very high impedance contrast between the layers and the subsoil. Investigating the socalled osculations of dispersion curves (Kausel et al, 2015) we have casually discovered unusual higher-mode Rayleigh waves because of the equivocal behaviour of their dispersion curves in a certain frequency range. Following Furumura and Kennett (1998) the dominant seismic phases at regional distances are usually the crustal P g and L g phases and the recorded L g phase can be regarded either as a superposition of multiply reflected S waves in the crust or as a sum of a number of higher surface wave modes sampled at the free surface of the crust.…”

Section: Equivocalness Of Dispersion Curvesmentioning

confidence: 99%

Unusual, equivocal Rayleigh-dispersion curves for simple models taking into account the special propagation conditions in the valley of Mexico City (CDMX) - Preliminary results

Malischewsky¹,

Forbriger

Lomnitz

2017

GeofInt

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Other than commonly assumed in seismology, the phase velocity of Rayleigh waves not necessarily is a single-valued function of frequency. We demonstrate this for the first higher mode in simple models of a homogeneous layer on top of a homogeneous halfspace (LOH), which are used for the subsurface of the Texcoco zone in Mexico City valley in previous studies. In the structure of a homegenous layer with fixed bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-velocity being three times S-velocity (Poisson’s ratio of 0.4375). This type of dispersion is demonstrated and a discussion of their possible fatal consequences for methods customarily used in seismology for dispersion analysis and synthesis of dispersion relations is presented.

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Osculations of spectral lines in a layered medium

Cited by 19 publications

References 20 publications

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

Partial wave basis adapted to exterior boundary conditions of an elastic plate

Unusual, equivocal Rayleigh-dispersion curves for simple models taking into account the special propagation conditions in the valley of Mexico City (CDMX) - Preliminary results

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