296 research outputs found
Normal modes of layered elastic media and application to diffuse fields
The spectral decomposition of the elastic wave operator in a layered
isotropic half-space is derived by means of standard functional analytic
methods. Particular attention is paid to the coupled - waves. The
problem is formulated directly in terms of displacements which leads to a Sturm-Liouville system. The resolvent kernel (Green function) is
expressed in terms of simple plane-wave solutions. Application of Stone's
formula leads naturally to eigenfunction expansions in terms of generalized
eigenvectors with oscillatory behavior at infinity. The generalized normal mode
expansion is employed to define a diffuse field as a white noise process in
modal space. By means of a Wigner transform, we calculate vertical to
horizontal kinetic energy ratios in layered media, as a function of depth and
frequency. Several illustrative examples are considered including energy ratios
near a free surface, in the presence of a soft layer. Numerical comparisons
between the generalized eigenfunction summation and a classical locked-mode
approximation demonstrate the validity of the approach. The impact of the local
velocity structure on the energy partitioning of a diffuse field is
illustrated
Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scattering
In this paper, we present a nonparametric method to estimate the
heterogeneity of a random medium from the angular distribution of intensity
transmitted through a slab of random material. Our approach is based on the
modeling of forward multiple scattering using Compound Poisson Processes on
compact Lie groups. The estimation technique is validated through numerical
simulations based on radiative transfer theory.Comment: 23 pages, 8 figures, 21 reference
Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium
This paper investigates the reconstruction of elastic Green's function from
the cross-correlation of waves excited by random noise in the context of
scattering theory. Using a general operator equation, -the resolvent formula-,
Green's function reconstruction is established when the noise sources satisfy
an equipartition condition. In an inhomogeneous medium, the operator formalism
leads to generalized forms of optical theorem involving the off-shell
-matrix of elastic waves, which describes scattering in the near-field. The
role of temporal absorption in the formulation of the theorem is discussed.
Previously established symmetry and reciprocity relations involving the
on-shell -matrix are recovered in the usual far-field and infinitesimal
absorption limits. The theory is applied to a point scattering model for
elastic waves. The -matrix of the point scatterer incorporating all
recurrent scattering loops is obtained by a regularization procedure. The
physical significance of the point scatterer is discussed. In particular this
model satisfies the off-shell version of the generalized optical theorem. The
link between equipartition and Green's function reconstruction in a scattering
medium is discussed
Density of automorphic points in deformation rings of polarized global Galois representations
Conjecturally, the Galois representations that are attached to essentially
selfdual regular algebraic cuspidal automorphic representations are
Zariski-dense in a polarized Galois deformation ring. We prove new results in
this direction in the context of automorphic forms on definite unitary groups
over totally real fields. This generalizes the infinite fern argument of
Gouvea-Mazur and Chenevier, and relies on the construction of non-classical
-adic automorphic forms, and the computation of the tangent space of the
space of trianguline Galois representations. This boils down to a surprising
statement about the linear envelope of intersections of Borel subalgebras
The Right to Education: A Multi-Faceted Strategy for Litigating before the Inter-American Commission on Human Rights
The Right to Education: A Multi-Faceted Strategy for Litigating before the Inter-American Commission on Human Rights
Constraints on grain size and stable iron phases in the uppermost Inner Core from multiple scattering modeling of seismic velocity and attenuation
International audienceWe propose to model the uppermost inner core as an aggregate of randomly oriented anisotropic ``patches''. A patch is defined as an assemblage of a possibly large number of crystals with identically oriented crystallographic axes. This simple model accounts for the observed velocity isotropy of short period body waves, and offers a reasonable physical interpretation for the scatterers detected at the top of the inner core. From rigorous multiple scattering modeling of seismic wave propagation through the aggregate, we obtain strong constraints on both the size and the elastic constants of iron patches. We perform a systematic search for iron models compatible with measured seismic velocities and attenuations. An iron model is characterized by its symmetry (cubic or hexagonal), elastic constants, and patch size. Independent of the crystal symmetry, we infer a most likely size of patch of the order of 400~m. Recent {\it bcc} iron models from the literature are in very good agreement with the most probable elastic constants of cubic crystals found in our inversion. Our study (1) suggests that the presence of melt may not be required to explain the low shear wavespeeds in the inner core and (2) supports the recent experimental results on the stability of cubic iron in the inner core, at least in its upper part
Locating a weak change using diffuse waves (LOCADIFF) : theoretical approach and inversion procedure
We describe a time-resolved monitoring technique for heterogeneous media. Our
approach is based on the spatial variations of the cross-coherence of coda
waveforms acquired at fixed positions but at different dates. To locate and
characterize a weak change that occurred between successive acquisitions, we
use a maximum likelihood approach combined with a diffusive propagation model.
We illustrate this technique, called LOCADIFF, with numerical simulations. In
several illustrative examples, we show that the change can be located with a
precision of a few wavelengths and its effective scattering cross-section can
be retrieved. The precision of the method depending on the number of source
receiver pairs, time window in the coda, and errors in the propagation model is
investigated. Limits of applications of the technique to real-world experiments
are discussed.Comment: 11 pages, 14 figures, 1 tabl
Quasi Two-dimensional Transfer of Elastic Waves
A theory for multiple scattering of elastic waves is presented in a random
medium bounded by two ideal free surfaces, whose horizontal size is infinite
and whose transverse size is smaller than the mean free path of the waves. This
geometry is relevant for seismic wave propagation in the Earth crust. We derive
a time-dependent, quasi-2D radiative transfer equation, that describes the
coupling of the eigenmodes of the layer (surface Rayleigh waves, SH waves, and
Lamb waves). Expressions are found that relate the small-scale fluctuations to
the life time of the modes and to their coupling rates. We discuss a diffusion
approximation that simplifies the mathematics of this model significantly, and
which should apply at large lapse times. Finally, coherent backscattering is
studied within the quasi-2D radiative transfer equation for different source
and detection configurations.Comment: REVTeX, 36 pages with 10 figures. Submitted to Phys. Rev.
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