98 research outputs found

    Normal modes of layered elastic media and application to diffuse fields

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    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 PP-SVSV waves. The problem is formulated directly in terms of displacements which leads to a 2×22 \times 2 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

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    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

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    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 TT-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 TT-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 TT-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

    Constraints on grain size and stable iron phases in the uppermost Inner Core from multiple scattering modeling of seismic velocity and attenuation

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    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

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    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

    Imagerie de chargements locaux en régime de diffusion multiple

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    Dans les milieux fortement hĂ©tĂ©rogĂšnes, les ondes ne se propagent pas de façon balistique. Elles peuvent interagir de nombreuses fois avec les hĂ©tĂ©rogĂ©nĂ©itĂ©s du milieu et entrer ainsi dans le rĂ©gime de diffusion multiple. Dans ce rĂ©gime, les mĂ©thodes classiques d'imagerie basĂ©es sur les trajets des ondes directes ou simplement diffusĂ©es sont inefficaces. Les formes d'ondes multiplement diffusĂ©es (coda) sont trop complexes pour ĂȘtre modĂ©lisĂ©es exactement mais elles sont parfaitement reproductibles et trĂšs sensibles aux variations du milieu de propagation. Des travaux rĂ©cents ont dĂ©montrĂ© la possibilitĂ© de mesurer de faibles changements de vitesse d'un milieu grĂące aux ondes diffuses, Ă  l'Ă©chelle de la croĂ»te terrestre (coda sismique) comme Ă  l'Ă©chelle des matĂ©riaux (coda ultrasonore). Ces travaux s'intĂ©ressent majoritairement Ă  des changements globaux ou rĂ©gionaux des diffĂ©rents milieux. La problĂ©matique de cette thĂšse concerne la possibilitĂ© d'utiliser la coda pour Ă©tudier des changements locaux du milieu. Deux Ă©tudes complĂ©mentaires sont dĂ©veloppĂ©es : Le problĂšme direct consiste Ă  modĂ©liser les variations de la coda engendrĂ©es par un changement local. Nous distinguons le cas d'un changement local de structure (fort contraste d'impĂ©dance) du cas d'un changement local de vitesse (faible contraste d'impĂ©dance). Le problĂšme inverse consiste Ă  utiliser les mesures de variations de la coda pour tenter de localiser et de caractĂ©riser les changements survenus. Les applications potentielles de ces travaux concernent entre autres le suivi temporel de structures gĂ©ologiques ainsi que le contrĂŽle non destructif de matĂ©riaux hĂ©tĂ©rogĂšnes. Avec cet objectif, les diffĂ©rentes mĂ©thodes dĂ©veloppĂ©es sont illustrĂ©es par des simulations numĂ©riques d'ondes acoustiques et sismiques ainsi que par des expĂ©riences en ultrasons dans des Ă©lĂ©ments en bĂ©ton.In highly heterogeneous media, waves don't propagate ballistically. They can interact several times with the heterogeneities of the medium and enter the multiple scattering regime. In this regime, classical imaging techniques, based on direct or singly scattered waves fail. Multiply scattered waveforms (coda) are too complex for being exactly modeled but are perfectly reproducible and very sensitive to small variations of the medium. Recent works demonstrated the possibility of measuring small velocity variations with diffuse waves, either at the geophysical scale (seismic coda) or at the material scale (ultrasonic coda). These works are mainly focused in monitoring global or regional changes of the medium. The present thesis deals with the possibility of using coda waves to study local changes of the medium. Two complementary studies are developed: The forward problem addresses the modeling of the coda variations generated by a local change. We distinguish the case of a structural change (strong impedance contrast) from the case of a velocity change (small impedance contrast). The inverse problem consists in using the coda variations measurements to locate and characterize the changes that occurred. Potential applications may concern, among others, monitoring of geological structures and non-destructive testing of heterogeneous materials. This in mind, we illustrate the different studies with numerical simulations of acoustic and seismic waves and with ultrasound experiments in concrete blocks.SAVOIE-SCD - Bib.Ă©lectronique (730659901) / SudocGRENOBLE1/INP-Bib.Ă©lectronique (384210012) / SudocGRENOBLE2/3-Bib.Ă©lectronique (384219901) / SudocSudocFranceF

    Multimethod Characterization of the French-Pyrenean Valley of BagnĂšres-de-Bigorre for Seismic-Hazard Evaluation: Observations and Models

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    International audienceA narrow rectilinear valley in the French Pyrenees, affected in the past by damaging earthquakes, has been chosen as a test site for soil response characteriza- tion. The main purpose of this initiative was to compare experimental and numerical approaches. A temporary network of 10 stations has been deployed along and across the valley during two years; parallel various experiments have been conducted, in particular ambient noise recording, and seismic profiles with active sources for struc- ture determination at the 10 sites. Classical observables have been measured for site amplification evaluation, such as spectral ratios of horizontal or vertical motions between site and reference stations using direct S waves and S coda, and spectral ratios between horizontal and vertical (H/V) motions at single stations using noise and S-coda records. Vertical shear-velocity profiles at the stations have first been obtained from a joint inversion of Rayleigh wave dispersion curves and ellipticity. They have subsequently been used to model the H/V spectral ratios of noise data from synthetic seismograms, the H/V ratio of S-coda waves based on equipartition theory, and the 3D seismic response of the basin using the spectral element method. General good agreement is found between simulations and observations. The 3D simulation reveals that topography has a much lower contribution to site effects than sedimentary filling, except at the narrow ridge crests. We find clear evidence of a basin edge effect, with an increase of the amplitude of ground motion at some distance from the edge inside the basin and a decrease immediately at the slope foot

    Lunar Seismology: An Update on Interior Structure Models

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    An international team of researchers gathered, with the support of the Interna- tional Space Science Institute (ISSI), (1) to review seismological investigations of the lunar interior from the Apollo-era and up until the present and (2) to re-assess our level of knowl- edge and uncertainty on the interior structure of the Moon. A companion paper (Nunn et al. in Space Sci. Rev., submitted) reviews and discusses the Apollo lunar seismic data with the aim of creating a new reference seismic data set for future use by the community. In this study, we first review information pertinent to the interior of the Moon that has become available since the Apollo lunar landings, particularly in the past ten years, from orbiting spacecraft, continuing measurements, modeling studies, and laboratory experiments. Fol- lowing this, we discuss and compare a set of recent published models of the lunar interior, including a detailed review of attenuation and scattering properties of the Moon. Common features and discrepancies between models and moonquake locations provide a first esti- mate of the error bars on the various seismic parameters. Eventually, to assess the influence of model parameterisation and error propagation on inverted seismic velocity models, an inversion test is presented where three different parameterisations are considered. For this purpose, we employ the travel time data set gathered in our companion paper (Nunn et al. in Space Sci. Rev., submitted). The error bars of the inverted seismic velocity models demon- strate that the Apollo lunar seismic data mainly constrain the upper- and mid-mantle struc- ture to a depth of ∌1200 km. While variable, there is some indication for an upper mantle low-velocity zone (depth range 100–250 km), which is compatible with a temperature gradi- ◩ent around 1.7 C/km. This upper mantle thermal gradient could be related to the presence of the thermally anomalous region known as the Procellarum Kreep Terrane, which contains a large amount of heat producing elements

    The Polarization of Ambient Noise on Mars

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    Seismic noise recorded at the surface of Mars has been monitored since February 2019, using the InSight seismometers. This noise can reach −200 dB. It is 500 times lower than on Earth at night and it increases of 30 dB during the day. We analyze its polarization as a function of time and frequency in the band 0.03–1 Hz. We use the degree of polarization to extract signals with stable polarization independent of their amplitude and type of polarization. We detect polarized signals at all frequencies and all times. Glitches correspond to linear polarized signals which are more abundant during the night. For signals with elliptical polarization, the ellipse is in the horizontal plane below 0.3 Hz. In the 0.3-1Hz high frequency band (HF) and except in the evening, the ellipse is in the vertical plane and the major axis is tilted. While polarization azimuths are different in the two frequency bands, they both vary as a function of local hour and season. They are also correlated with wind direction, particularly during the daytime. We investigate possible aseismic and seismic origins of the polarized signals. Lander or tether noise can be discarded. Pressure fluctuations transported by wind may explain part of the HF polarization but not the tilt of the ellipse. This tilt can be obtained if the source is an acoustic emission coming from high altitude at critical angle. Finally, in the evening when the wind is low, the measured polarized signals may correspond to the seismic wavefield of the Mars background noise