arXiv subjects

Armand Wirgin

Publications and source records attributed to Armand Wirgin.

29 records · Page 2Linked to original sources

arXiv2006

Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half space: I. Finite set of blocks

We address the problem of the response to a seismic wave of an urban site consisting of $N$ non-identical, non-equispaced blocks overlying a soft layer underlain by a hard substratum. The results of a theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite element (FE) technique. The two methods are shown to give rise to the same prediction of the seismic response for N=1 and N=2 blocks. The mechanism of the interaction between blocks and the ground, as well as that of the mutual interaction between blocks, are studied. It is shown that the presence of a small number of blocks modifies the seismic disturbance in a manner which evokes qualitatively, but not quantitatively, what was observed during the 1985 Michoacan earthquake in Mexico City. Disturbances at a much greater level, induced by a large number of blocks (in fact, a periodic set) are studied in the companion paper.

physics.geo-ph↗

arXiv2006

Amplification and Increased Duration of Earthquake Motion on Uneven Stress-Free Ground

When a flat stress-free surface (i.e., the ground in seismological applications) separating air from a isotropic, homogeneous or horizontally-layered, solid substratum is solicited by a SH plane body wave incident in the substratum, the response in the substratum is a single specularly-reflected body wave. When the stress-free condition, equivalent to vanishing surface impedance, is relaxed by the introduction of a {spatially- constant, non- vanishing surface impedance}, the response in the substratum is again a single reflected body wave whose amplitude is less than the one in the situation of a stress-free ground. When the stress-free condition is relaxed by the introduction of a a {spatially-modulated surface impedance}, which simulates the action of an uneven (i.e., not entirely-flat) ground, the frequency-domain response takes the form of a spectrum of {plane body waves} and {surface waves} and {resonances} are produced at the frequencies of which one or several surface wave amplitudes can become large. It is shown, that at resonance, the amplitude of one, or of several, components of the motion on the surface can be amplified with respect to the situation in which the surface impedance is either constant or vanishes. Also, when the solicitation is pulse-like, the integrated time history of the square of surface displacement and of the square of velocity can be larger, and the duration of the signal can be considerably longer, for a spatially-modulated impedance surface than for a constant, or vanishing, impedance surface.

physics.class-ph↗

arXiv2006

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab.

physics.comp-ph↗

arXiv2006

Synthesis of unilateral radiators

A radiator is typically a parabolic mirror illuminated by an electromagnetic source, or a cylindrical transducer of resonant vibrations. Both of these devices are designed to radiate either a beam of parallel rays or a (focused) beam that converges to a point or a line. Consequently, at the worst, the radiation pattern is largely restricted to a {\it half space}, and at the best, to a cone or cylinder-like subspace of this half space. Such devices can therefore be termed unilateral radiators. This study is devoted to the synthesis of the sources that can give rise to such radiation, the underlying motivation being the removal of the material presence of the mirror or transducer casing from which waves coming from other boundaries could reflect or diffract.

physics.class-ph↗

arXiv2006

Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid

The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous layer with a sudden change in physical properties is studied. A simple wave equation is derived and solved for this system. The reflection and transmission coefficients are calculated numerically using a wave splitting-Green's function approach (WS-GF). The reflected and transmitted wave time histories are also simulated. Experimental results obtained for materials saturated by air are compared to the results given by this approach and to those of the classical transfer matrix method (TMM).

physics.flu-dyn↗

arXiv2006

Three methods for the description of the temporal response to a SH plane impulsive seismic wave in a soft elastic layer overlying a hard elastic substratum

We treat the case of a flat stress-free surface (i.e., the ground in seismological applications) separating air from a homogeneous, isotropic, solid substratum overlain by a homogeneous, isotropic, solid layer (in contact with the ground) solicited by a SH plane body wave incident in the substratum. The analysis is first carried out in the frequency domain and subsequently in the time domain. The frequency domain response is {\it normal} in that no resonances are excited (a resonance is here understood to be a situation in which the response is infinite in the absence of dissipation). The translation of this in the time domain is that the scattered pulse is of relatively-short duration. The duration of the pulse is shown to be largely governed by radiation damping which shows up in the imaginary parts of the complex eigenfrequencies of the configuration. Three methods are elaborated for the computation of the time history and give rise to the same numerical solutions for a large variety of configurations of interest in the geophysical setting under the hypothesis of non-dissipative, dispersionless media. The method appealing to the complex eigenfrequency representation is shown to be the simplest and most physically-explicit way of obtaining the time history (under the same hypothesis). Moreover, it is particularly suited for the case in which modes can be excited as occurs when the incident wave is not plane or the boundary condition is not of the stress-free variety for all transverse coordinates on the ground plane.

physics.class-ph↗

arXiv2005

Acoustic identification of a poroelastic cylinder

We show how to cope with the acoustic identification of poroelastic materials when the specimen is in the form of a cylinder. We apply our formulation, based on the Biot model, approximated by the equivalent elastic solid model, to a long bone-like or borehole sample specimen probed by low frequency sound.

physics.class-ph↗

arXiv2004

Simulation of seismic response in a city-like environment

We study the seismic response of idealized 2D cities, constituted by non equally-spaced, non equally-sized homogenized blocks anchored in a soft layer overlying a hard half space. The blocks and soft layer are occupied by dissipative media. To simulate such response, we use an approximation of the viscoelastic modulus by a low-order rational function of frequency and incorporate this approximation into a first-order-in-time scheme. Our results display spatially-variable, strong, long-duration responses inside the blocks and on the ground, which qualitatively match the responses observed in some earthquake-prone cities of Mexico, France, the USA, etc.

physics.comp-ph↗

arXiv2004

The inverse crime

The inverse crime occurs when the same (or very nearly the same) theoretical ingredients are employed to synthesize as well as to invert data in an inverse problem. This act has been qualified as trivial and therefore to be avoided by Colton and Kress.

math-ph↗

arXiv2004

2D ground motion at a soft viscoelastic layer/hard substratum site in response to SH cylindrical seismic waves radiated by deep and shallow line sources

We show, essentially by theoretical means, that for a site with the chosen simple geometry and mechanical properties (horizontal, homogeneous, soft viscoelastic layer of infinite lateral extent overlying, and in welded contact with, a homogeneous, hard elastic substratum of half-infinite radial extent, shear-horizontal motion): 1) coupling to Love modes is all the weaker the farther the seismic source (modeled as a line, assumed to lie in the substratum) is from the lower boundary of the soft layer, 2) for a line source close to the lower boundary of the soft layer, the ground response is characterized by possible beating phenomena, and is of significantly-longer duration than for excitation by cylindrical waves radiated by deep sources. Numerical applications of the theory show, for instance, that a line source, located 40m below the lower boundary of a 60m thick soft layer in a hypothetical Mexico City-like site, radiating a SH pulse of 4s duration, produces substantial ground motion during 200s, with marked beating, at an epicentral distance of 3km. This response is in some respects similar to that observed in real cities located at soft-soil sites so that the model employed herein may help to establish the causes and pinpoint the major contributing factors of the devastating effects of earthquakes in such cities.

physics.geo-ph↗

arXiv2003

Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields

The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. It is shown that to second order in $k_{0}a$ ($k_{0}$ the wavenumber in the host medium, $a$ the radius of the cylinder), only the first three terms (i.e., of orders 0, -1 and +1) in the partial wave representation of the scattered field are non-vanishing, and the material parameters enter into these terms in explicit manner. Moreover, the zeroth-order term contains only two of the unknown material constants (i.e., the real and imaginary parts of complex compressibility of the cylinder $κ_{1}$) whereas the $\pm 1$ order terms contain the other material constant (i.e., the density of the cylinder $ρ_{1}$). A method, relying on the knowledge of the totality of the far-zone scattered field and resulting in explicit expressions for $ρ_{1}$ and $κ_{1}$, is devised and shown to give highly-accurate estimates of these quantities even for frequencies such that $k_{0}a$ is as large as 0.1.

physics.class-ph↗