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.Comment: Third International Symposium on the Effects of Surface Geology on Seismic Motion, Grenoble, 200

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.Comment: 22 pages, 8 figures, submitted to SDE

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

International audienceWe 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

Acoustic response of a rigid frame porous medium slab with a periodic set of inclusions

The acoustic response of a rigid frame porous slab with a periodic set of inclusions is calculated by use of a multipole method. The acoustic properties, in particular the absorption, of such a structure are then derived and studied. Numerical results together with a modal analysis show that the addition of a periodic set of high-contrast inclusions leads to quasi-modes excitation of both the slab and the gratings, and to a large increase of the acoustic absorption of the initial slab, this being partly due to the quasi-modes excitation.Comment: submitted to Journal of Sound and Vibratio

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