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

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.

Autocorrelation of the Ground Vibrations Recorded by the SEIS‐InSight Seismometer on Mars

Since early February 2019, the SEIS (Seismic Experiment for Interior Structure) seismometer deployed at the surface of Mars in the framework of the InSight mission has been continuously recording the ground motion at Elysium Planitia. In this study, we take advantage of this exceptional data set to put constraints on the crustal properties of Mars using seismic interferometry (SI). To carry out this task, we first examine the continuous records from the very broadband seismometer. Several deterministic sources of environmental noise are identified and specific preprocessing strategies are presented to mitigate their influence. Applying the principles of SI to the single-station configuration of InSight, we compute, for each Sol and each hour of the martian day, the diagonal elements of the time-domain correlation tensor of random ambient vibrations recorded by SEIS. A similar computation is performed on the diffuse waveforms generated by more than a hundred Marsquakes. A careful signal- to-noise ratio analysis and an inter-comparison between the two datasets suggest that the results from SI are most reliable in a narrow frequency band around 2.4 Hz, where an amplification of both ambient vibrations and seismic events is observed. The average autocorrelation functions (ACFs) contain well identifiable seismic arrivals, that are very consistent between the two datasets. Interpreting the vertical and horizontal ACFs as, respectively, the P- and S- seismic reflectivity below InSight, we propose a simple stratified velocity model of the crust, which is mostly compatible with previous results from receiver function analysis. Our results are discussed and compared to recent works from the literature

The interior of Mars as seen by InSight (Invited)

InSight is the first planetary mission dedicated to exploring the whole interior of a planet using geophysical methods, specifically seismology and geodesy. To this end, we observed seismic waves of distant marsquakes and inverted for interior models using differential travel times of phases reflected at the surface (PP, SS...) or the core mantle-boundary (ScS), as well as those converted at crustal interfaces. Compared to previous orbital observations1-3, the seismic data added decisive new insights with consequences for the formation of Mars: The global average crustal thickness of 24-75 km is at the low end of pre-mission estimates5. Together with the the thick lithosphere of 450-600 km5, this requires an enrichment of heat-producing elements in the crust by a factor of 13-20, compared to the primitive mantle. The iron-rich liquid core is 1790-1870 km in radius6, which rules out the existence of an insulating bridgmanite-dominated lower mantle on Mars. The large, and therefore low-density core needs a high amount of light elements. Given the geochemical boundary conditions, Sulfur alone cannot explain the estimated density of ~6 g/cm3 and volatile elements, such as oxygen, carbon or hydrogen are needed in significant amounts. This observation is difficult to reconcile with classical models of late formation from the same material as Earth. We also give an overview of open questions after three years of InSight operation on the surface of Mars, such as the potential existence of an inner core or compositional layers above the CM

Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data

Mars’s seismic activity and noise have been monitored since January 2019 by the seismometer of the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) lander. At night, Mars is extremely quiet; seismic noise is about 500 times lower than Earth’s microseismic noise at periods between 4 s and 30 s. The recorded seismic noise increases during the day due to ground deformations induced by convective atmospheric vortices and ground-transferred wind-generated lander noise. Here we constrain properties of the crust beneath InSight, using signals from atmospheric vortices and from the hammering of InSight’s Heat Flow and Physical Properties (HP3) instrument, as well as the three largest Marsquakes detected as of September 2019. From receiver function analysis, we infer that the uppermost 8–11 km of the crust is highly altered and/ or fractured. We measure the crustal diffusivity and intrinsic attenuation using multiscattering analysis and find that seismic attenuation is about three times larger than on the Moon, which suggests that the crust contains small amounts of volatiles

Inférence statistique sur la fonction de phase des milieux aléatoires par diffusion multiple des ondes

National audienc

Statistical inference for random media phase-function by multiple scattering of waves

Nous proposons un modele de type Processus de Poisson sur un groupe de Lie compact pour la description et l'etude de la diffusion multiple dans les milieuax aleatoires. Cette approche permet d'inferer sur le milieu et en particulier d'estimer la fonction de phase du milieu qui donne acces au spectre d'heterogeneite, grendeur caracteristique du milieu. La technique d'inference proposee consiste en une decomposition du processus de Poisson modelisant le phenomene de diffusion multiple. Nous validons la technique proposee en testant les estimateurs sur des donnees de simulation Monte Carlo

Decompounding on compact Lie groups

International audienc

Dépistage de la trisomie 21 (information, consentement et satisfaction des patientes)

LILLE2-BU Santé-Recherche (593502101) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF