Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves.

Metamaterials are artificially structured media that exibit properties beyond those usually encountered in nature. Typically they are developed for electromagnetic waves at millimetric down to nanometric scales, or for acoustics, at centimeter scales. By applying ideas from transformation optics we can steer Rayleigh-surface waves that are solutions of the vector Navier equations of elastodynamics. As a paradigm of the conformal geophysics that we are creating, we design a square arrangement of Luneburg lenses to reroute Rayleigh waves around a building with the dual aim of protection and minimizing the effect on the wavefront (cloaking). To show that this is practically realisable we deliberately choose to use material parameters readily available and this metalens consists of a composite soil structured with buried pillars made of softer material. The regular lattice of inclusions is homogenized to give an effective material with a radially varying velocity profile and hence varying the refractive index of the lens. We develop the theory and then use full 3D numerical simulations to conclusively demonstrate, at frequencies of seismological relevance 3–10 Hz, and for low-speed sedimentary soil (v(s): 300–500 m/s), that the vibration of a structure is reduced by up to 6 dB at its resonance frequency

Experimental and Numerical Evidence of the Clustering Effect of Structures on Their Response during an Earthquake: A Case Study of Three Identical Towers in the City of Grenoble, France

In this article, interpretation of an equivalent to a macroseismic intensity survey, performed in three identical stand-alone buildings located in Grenoble, France, after an M L 4.1 earthquake, reveals a clustering effect, resulting in different levels of perception of seismic loading by inhabitants. The clustering effect is confirmed using numerical simulation; the variation of the seismic response of the building in the middle of the cluster depends on the azimuth of the seismic source relative to the building cluster. The major effect is the splitting of its resonance frequency, accompanied by a decrease in vibration amplitude. We conclude that clustering has an impact on urban effects, calling into question the validity of seismic design, which considers buildings in urban areas as stand-alone constructions, and the interpretation of macroseismic inten- sity surveys conducted in dense urban areas

The redshift evolution of bias and baryonic matter distribution

We study the distribution of baryonic and luminous matter within the framework of a hierarchical scenario. Using an analytical model for structure formation which has already been checked against observations for galaxies, Lyman-$\alpha$ clouds, clusters and reionization processes, we present its predictions for the bias of these objects. We describe its dependence on the luminosity (for galaxies or quasars) or the column density (for Lyman-$\alpha$ absorbers) of the considered objects. We also study its redshift evolution, which can exhibit an intricate behaviour. These astrophysical objects do not trace the dark matter density field, the Lyman-$\alpha$ forest clouds being undercorrelated and the bright galaxies overcorrelated, while the intermediate class of Lyman-limit systems is seen to sample the matter field quite well. We also present the distribution of baryonic matter over these various objects. We show that light does not trace baryonic mass, since bright galaxies which contain most of the stars only form a small fraction of the mass associated with virialized and cooled halos. We consider two cosmologies: a critical density universe and an open universe. In both cases, our results agree with observations and show that hierarchical scenarios provide a good model for structure formation and can describe a wide range of objects which spans at least the seven orders of magnitude in mass for which data exist. More detailed observations, in particular of the clustering evolution of galaxies, will constrain the astrophysical models involved.Comment: 13 pages, final version published in A&

Arrival angle anomalies of Rayleigh waves observed at a broadband array: a systematic study based on earthquake data, full waveform simulations and noise correlations

Deviation of seismic surface waves from the great-circle between source and receiver is illustrated by the anomalies in the arrival angle, that is the difference between the observed backazimuth of the incident waves and the great-circle. Such arrival angle anomalies have been known for decades, but observations remain scattered. We present a systematic study of arrival angle anomalies of fundamental mode Rayleigh waves (20–100 s period interval) from 289 earthquakes and recorded by a broadband network LAPNET, located in northern Finland. These observations are compared with those of full waveform synthetic seismograms for the same events, calculated in a 3-D Earth and also compared with those of seismograms obtained by ambient noise correlation. The arrival angle anomalies for individual events are complex, and have significant variations with period. On average, the mean absolute deviation decreases from ∼9° at 20 s period to ∼3° at 100 s period. The synthetic seismograms show the same evolution, albeit with somewhat smaller deviations. While the arrival angle anomalies are fairly well simulated at long periods, the deviations at short periods are very poorly modelled, demonstrating the importance of the continuous improvement of global crustal models. At 20–30 s period, both event data and numerical simulations have strong multipathing, and relative amplitude changes between different waves will induced differences in deviations between very closely located events. The source mechanism has only limited influence on the deviations, demonstrating that they are directly linked to propagation effects, including near-field effects in the source area. This observation is confirmed by the comparison with seismic noise correlation records, that is where the surface waves correspond to those emitted by a point source at the surface, as the two types of observations are remarkably similar in the cases where earthquakes are located close to seismic stations. This agreement additionally confirms that the noise correlations capture the complex surface wave propagation

Analytical solution of the full-range behavior of adhesively bonded FRP-steel joints made with toughened adhesives

Fiber-reinforced polymer (FRP) composites represent an effective solution to strengthen and retrofit existing steel members. Namely, bonded or unbonded carbon FRP (CFRP) plates have been employed to improve the strength, fatigue behavior, and durability of steel bridges. In bonded solutions, the effectiveness of the CFRP reinforcement strongly depends on the adhesive employed to bond the plate, as failure usually occurs due to debonding. Within this framework, the use of toughened adhesives is particularly attractive since they may improve the load carrying capacity of the CFRP-steel interface, also providing a certain ductility. Debonding in CFRP-steel joints was previously studied using a cohesive approach. However, solutions able to describe the full-range behavior of joints with toughened adhesives and finite bonded length are not available in the literature. In this paper, a trapezoidal (trilinear) cohesive material law (CML) is employed to model the bond behavior of pultruded carbon FRP-steel joints made with a rubber-toughened epoxy adhesive, which showed cohesive debonding within the adhesive layer. The analytical solution provided is employed to study the experimental response of nine CFRP-steel joints tested using a single-lap direct shear set-up. Comparisons of analytical and experimental results of joints with three different bonded lengths confirm the effectiveness of the solution proposed

Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales

If one wants to represent the galaxy number density at some point in terms of only the mass density at the same point, there appears the stochasticity in such a relation, which is referred to as ``stochastic bias''. The stochasticity is there because the galaxy number density is not merely a local function of a mass density field, but it is a nonlocal functional, instead. Thus, the phenomenological stochasticity of the bias should be accounted for by nonlocal features of galaxy formation processes. Based on mathematical arguments, we show that there are simple relations between biasing and nonlocality on linear scales of density fluctuations, and that the stochasticity in Fourier space does not exist on linear scales under a certain condition, even if the galaxy formation itself is a complex nonlinear and nonlocal precess. The stochasticity in real space, however, arise from the scale-dependence of bias parameter, $b$. As examples, we derive the stochastic bias parameters of simple nonlocal models of galaxy formation, i.e., the local Lagrangian bias models, the cooperative model, and the peak model. We show that the stochasticity in real space is also weak, except on the scales of nonlocality of the galaxy formation. Therefore, we do not have to worry too much about the stochasticity on linear scales, especially in Fourier space, even if we do not know the details of galaxy formation process.Comment: 24 pages, latex, including 2 figures, ApJ, in pres

Evolution of hierarchical clustering in the CFHTLS-Wide since z~1

We present measurements of higher order clustering of galaxies from the latest release of the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) Wide. We construct a volume-limited sample of galaxies that contains more than one million galaxies in the redshift range 0.2<z<1 distributed over the four independent fields of the CFHTLS. We use a counts in cells technique to measure the variance and the hierarchical moments S_n = /^(n-1) (3<n<5) as a function of redshift and angular scale.The robustness of our measurements if thoroughly tested, and the field-to-field scatter is in very good agreement with analytical predictions. At small scales, corresponding to the highly non-linear regime, we find a suggestion that the hierarchical moments increase with redshift. At large scales, corresponding to the weakly non-linear regime, measurements are fully consistent with perturbation theory predictions for standard LambdaCDM cosmology with a simple linear bias.Comment: 17 pages, 11 figures, submitted to MNRA

A comparison of estimators for the two-point correlation function

Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble Volume simulation cluster catalog. The ``real'' correlation function was determined from the full survey in a 3000Mpc/h periodic cube. The estimators were ranked by the cumulative probability of returning a value within a certain tolerance of the real correlation function. This criterion takes into account bias and variance, and it is independent of the possibly non-Gaussian nature of the error statistics. As a result for astrophysical applications a clear recommendation has emerged: the Landy & Szalay (1993) estimator, in its original or grid version Szapudi & Szalay (1998), are preferred in comparison to the other indicators examined, with a performance almost indistinguishable from the Hamilton (1993) estimator.Comment: aastex, 10 pages, 1 table, 1 figure, revised version, accepted in ApJ