May Rayleigh waves propagate with group- and phase-velocities of opposite sign in the valley of Mexico City?

On the basis of the group-velocity formula the occurrence of negative group velocities of Rayleigh waves is theoretically discussed for simplified models of Mexico City\u27s basin by using results of a preceding article of the authors

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

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 $k_l(\omega)$ for the $l$-th Rayleigh mode to be a single-valued function of frequency $\omega$. 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

Surface optomechanics: Calculating optically excited acoustical whispering gallery modes in microspheres

Stimulated Brillouin scattering recently allowed experimental excitation of surface acoustic resonances in micro-devices, enabling vibration at rates in the range of 50 MHz to 12 GHz. The experimental availability of such mechanical whispering gallery modes in photonic-MEMS raises questions on their structure and spectral distribution. Here we calculate the form and frequency of such vibrational surface whispering gallery modes, revealing diverse types of surface vibrations including longitudinal, transverse, and Rayleigh-type deformations. We parametrically investigate these various modes by changing their orders in the azimuthal, radial, and polar directions to reveal different vibrational structures including mechanical resonances that are localized near the interface with the environment where they can sense changes in the surroundings.Comment: 10 pages, 5 figures, 1 table; journal paper - Optics Express, Accepted for pub. as of 20 Jun 201

Energy partition of seismic coda waves in layered media: theory and application to Pinyon Flats Observatory

We have studied the partition of shear, compressional and kinetic energies in the coda of ten earthquakes recorded on a dense array, located at Pinyon Flats Observatory (PFO), California. We observe a clear stabilization of the shear to compressional ($W^s/W^p$) energy ratio in the coda, with an average value of about 2.8. The ratio between the vertical and horizontal kinetic energies ($V^2/H^2$) can be measured from 5 to 25Hz and shows an abrupt transitionfrom 0.1 in the 5-10Hz band, to about 0.8 in the 15-25Hz band. These measured values are in sharp contrast with the theoretical prediction for equipartitioned elastic waves in a homogeneous half-space. To explain these observations, we have developed a theory of equipartition in a layered elastic half-space. Using a rigorous spectral decomposition of the elastic wave equation, we define equipartition as a white noise distributed over the complete set of eigenfunctions. The theory predicts that close to the resonance frequency of a low-velocity layer, the ratio between shear and compressional energies strongly decreases. Using a detailed model of the subsurface at PFO, this conterintuitive result is found to be in good qualitative and quantitative agreement with the observations

Ultrasonic evaluation of the hydration degree of the orange peel

The elastic parameters of fruit and vegetables are normally monitored in quality control processes as there is a good correlation to the degrees of firmness, turgidity and humidity. These parameters have been traditionally measured by means of penetration tests, which are destructive. This has resulted in the increased attention recently given to ultrasonic techniques applied to the quality evaluation of horticultural commodities. Nevertheless, since most of the fruit and vegetables display a viscoelastic behavior, the penetration test should be considered to be quasi-static, especially when compared with the speeds associated with the ultrasonic tests. Both methods should provide different values for the elastic parameters. The aim of this work is to study this discrepancy in the values of the elastic parameters and interpret the elastodynamic behavior of the vegetable tissue under an ultrasound test. Thus, the paper presents an ultrasonic nondestructive method to evaluate the elastic parameters of the sweet orange peel at 40. kHz. The complete dehydration process of two sets of oranges (Navelina and Ortanique) was monitored for 2. months. A linear elastic solid model with viscous losses was numerically solved using a simulation scheme based on a 3D-Spherical FDTD method (Finite-Difference Time-Domain) in order to interpret the results, which proved that the elastic parameters obtained by penetration and ultrasonic tests differ. The method provides an empirical relation between the hydration state and the elastic parameters of the orange peel. Therefore, the proposed ultrasonic test reported in this work is capable of determining the hydration state of the orange simply by measuring the propagation speed of the Rayleigh waves on the orange peel, and hence, can be used as a fruit quality index during postharvest processes. © 2012 Elsevier B.V.This study was supported by the Programa de Apoyo a la Investigacion y Desarrollo (PAID-05-09-002-618), (PAID-06-10-002-295) of Universidad Politecnica de Valencia. The authors would like to thank K. Y. Foo, from the University of Birmingham and P. Malischewsky from the University Friedrich-Schiller at Jena, for the fruitful discussions regarding surface acoustic waves.Jimenez, N.; Picó Vila, R.; Camarena Femenia, F.; Redondo, J.; Roig, B. (2012). Ultrasonic evaluation of the hydration degree of the orange peel. Postharvest Biology and Technology. 67:130-137. https://doi.org/10.1016/j.postharvbio.2011.12.020S1301376

a review and some new issues on the theory of the h v technique for ambient vibrations

In spite of the Horizontal-to-Vertical Spectral Ratio (HVSR or H/V) technique obtained by the ambient vibrations is a very popular tool, a full theoretical explanation of it has been not reached yet. A short excursus is here presented on the theoretical models explaining the H/V spectral ratio that have been development in last decades. It leads to the present two main research lines: one aims at describing the H/V curve by taking in account the whole ambient-vibration wavefield, and another just studies the Rayleigh ellipticity. For the first theoretical branch, a comparison between the most recent two models of the ambient-vibration wavefield is presented, which are the Distributed Surface Sources (DSS) one and the Diffuse Field Approach (DFA). A mention is done of the current developments of these models and of the use of the DSS for comparing the H/V spectral ratio definitions present in literature. For the second research branch, some insights about the connection between the so-called osculation points of the Rayleigh dispersion curves and the behaviour of the H/V curve are discussed

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

Explicit asymptotic formulations are derived for Rayleigh and Rayleigh-type interfacial and edge waves. The hyperbolic–elliptic duality of surface and interfacial waves is established, along with the parabolic–elliptic duality of the dispersive edge wave on a Kirchhoff plate. The effects of anisotropy, piezoelectricity, thin elastic coatings, and mixed boundary conditions are taken into consideration. The advantages of the developed approach are illustrated by steady-state and transient problems for a moving load on an elastic half-space

Application of Surface wave methods for seismic site characterization

Surface-wave dispersion analysis is widely used in geophysics to infer a shear wave velocity model of the subsoil for a wide variety of applications. A shear-wave velocity model is obtained from the solution of an inverse problem based on the surface wave dispersive propagation in vertically heterogeneous media. The analysis can be based either on active source measurements or on seismic noise recordings. This paper discusses the most typical choices for collection and interpretation of experimental data, providing a state of the art on the different steps involved in surface wave surveys. In particular, the different strategies for processing experimental data and to solve the inverse problem are presented, along with their advantages and disadvantages. Also, some issues related to the characteristics of passive surface wave data and their use in H/V spectral ratio technique are discussed as additional information to be used independently or in conjunction with dispersion analysis. Finally, some recommendations for the use of surface wave methods are presented, while also outlining future trends in the research of this topic