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The aim of this work is to take full advantage of Spectral Element (SE) and Finite Element (FE) codes by setting up a SEM/FEM co-simulation strategy for soil structure interaction problems, involving a SE code to generate and propagate elastic waves in the soil, while a FE code enables the detailed representation of the studied structure. The spatial coupling is managed by the standard coupling mortar approach, whereas the time integration is dealt with an hybrid (explicit/implicit) asynchronous (different time steps) time integrator. The SEM/FEM co-simulation strategy is set up for linear or nonlinear transient dynamics. A seismic analysis of a concrete dam is considered in order to demonstrate the versatility of the co-simulation approach, assuming a linear rheology or a nonlinear damaging behaviour of the concrete. (C) 2020 Elsevier Ltd. All rights reserved.

International audience; The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

International audience; —The Finite-Element Method (FEM) is routinely used to solve Partial Differential Equations (PDE) in various scientific domains. For seismic waves modeling, the Spectral Element Method (SEM), which is a specific formulation of the classical FEM approach, have gained significant attention for the last two decades. This is explained both from the very good numerical accuracy of this method and from the parallel performance of classical MPI-based implementations that scale up to several tens of thousands computing cores. Nevertheless, the trend for current processors with an increasing level of low-level parallelism requires significant efforts at the shared-memory level. One major bottleneck is coming from the standard FEM assembly phase that leads to significant amount of irregular memory accesses. This prevents any efficient automatic optimizations from the compiler for instance. In this paper, we extract a kernel from a spectral-element application dedicated to earthquake simulations in complex geological medium (EFISPEC code developed at BRGM, the French Geological Survey). We study the intra-node behavior and we propose different levels of optimization (data-layout, manual vectorization, multi-threading) to fully benefit from SIMD units and NUMA architectures. Experiments performed on Intel Broadwell architecture show that the proposed optimizations dramatically improve the intra-node performance of the mini-application. Moreover, our results show a good match with rooflines theoretical performance models. We believe that these optimizations are not specific to this mini-application and may be implemented in different SEM and FEM based solvers as well.

In this paper, we present an optimized implementation of the Finite-Element Methods numerical kernel for SIMD vectorization. A typical application is the modelling of seismic wave propagation. In this case, the computations at the element level are generally based on nested loops where the memory accesses are non-contiguous. Moreover, the back and forth from the element level to the global level (e.g., assembly phase) is a serious brake for automatic vectorization by compilers and for efficient reuse of data at the cache memory levels. This is particularly true when the problem under study relies on an unstructured mesh. The application proxies used for our experiments were extracted from EFISPEC code that implements the spectral finite-element method to solve the elastodynamic equations. We underline that the intra-node performance may be further improved. Additionally, we show that standard compilers such as GNU GCC, Clang and Intel ICC are unable to perform automatic vectorization even when the nested loops were reorganized or when SIMD pragmas were added. Due to the irregular memory access pattern, we introduce a dedicated strategy to squeeze the maximum performance out of the SIMD units. Experiments are carried out on Intel Broadwell and Skylake platforms that respectively offer AVX2 and AVX-512 SIMD units. We believe that our vectorization approach may be generic enough to be adapted to other codes.

We compare different methods to estimate frequency‐domain amplification and duration lengthening of earthquake ground motion in the Mygdonian basin (Greece). Amplification is measured by standard spectral ratios (SSRs) of horizontal component or by single‐station earthquake horizontal‐to‐vertical ratios (EHVRs). Duration lengthening is measured either by the group delay method (Beauval et al. , 2003) and labeled GDDL, or based on the significant duration (Trifunac and Brady, 1975) and labeled TBDL. The methods are applied both to high‐quality recordings of the European experimental site EUROSEISTEST array and to a large set of 3D synthetics computed in a new basin model for 1260 sources regularly distributed in depth, distance, and azimuth from the center of the array. The analysis of the recordings in the center of the basin shows an anticorrelation between amplification and duration lengthening, that is, maxima (resp. minima) of GDDL correspond to minima (resp. maxima) of SSR. The maxima of GDDL are also found to coincide with those of SSR variability. This is confirmed by the analysis of the synthetics, which also reveals a pronounced north–south asymmetry of both amplification and duration lengthening caused by nonisotropic excitation of surface waves at the basin edges. We find that all estimates of site response depend on source location and that EHVR is also strongly sensitive to energy partitioning in the analyzed wavefield. We quantify the source‐related variability of each estimate, discuss the biases in site response estimation using incomplete source catalogs, and investigate whether the azimuthal dependence of site response can be identified in the recordings. Electronic Supplement: Movies of simulated wave propagation, figures of surface‐to‐downhole standard spectral ratio (SSR), group delay duration lengthening (GDDL), earthquake horizontal‐to‐vertical ratio (EHVR), and synthetic waveforms.

International audience; A surrogate is proposed to study seismic wave propagation in uncertain medium. The surrogate is based on a double decomposition of the signal: a damped harmonic decomposition coupled with a polynomial chaos (PC) representation of the four coefficients of each harmonic term (amplitude, decay constant, pulsation, and phase). An efficient PC representation of the coefficients are obtained through non-intrusive spectral projections.It requires the resolution of a nonlinear least squares problem for each integration point of the sparse grid. The implementation of the surrogate is illustrated on applications to layered soils with uncertainties in the geological data (geometry, wave velocities, damping factor).Computational tests show that the stochastic signal can be efficiently represented with a low-order PC representation leading to the use of a low-level sparse grid integration. For each test case, a global sensitivity analysis is performed in time and frequency domains to investigatethe relative impact of the random parameters.

International audience; The use of simulation to assess the site effect is often required in low seismicity areas. The "E2VP" project (Euroseistest Verification and Validation Project) launched in 2008 aimed to assess the robustness of simulation methods in complex linear 3D cases. The project E2VP was the framework of various works and advances in simulation practice. The verification step consists in checking that different simulation tools, starting from the same physical problems, lead the same results. Stringent "canonical cases" (but representative of real cases) have been defined and tested by several teams. These tests are now available online for any new team. The validation step (comparison between simulation results and actual data) involved to define their own metrics. Detailed comparisons of the " distance " between the simulations themselves and between simulations and real data have been confronted with the intrinsic variability of seismic ground motions. Simulation tools were also used to understand the physical origin of some source of variability of the site effect, including those related to the back-azimuth. The project helped evolution of the misfit between observations and simulations for different "generations" of geological models, source parameters, the model of "bedrock", and the database version. The project was rich in learnings on the global approach of site effect estimation, beyond the simple numerical simulation. MOTS-CLÉS : effets de site, simulation numérique, Euroseistest, verification, validation.; Le recours à la simulation pour évaluer les effets de site est souvent nécessaire dans les zones à faible sismicité. Le projet « E2VP » (Euroseistest Verification and Validation Project), avait pour but d'évaluer la robustesse des méthodes de simulation dans un cas linéaire 3D complexe. Il a été le cadre de travaux variés et d'avancées dans les pratiques de simulation. L'étape de vérification consiste à vérifier que plusieurs outils de simulation, partant d'un même problème physique, obtiennent les mêmes résultats. Des « cas canoniques » exigeants mais représentatifs de cas réels ont été définis, testés par plusieurs équipes : ces cas tests sont aujourd'hui disponibles pour toute nouvelle équipe. La validation (confrontation entre résultats de simulation et données réelles) a impliqué de définir une métrique propre. Des comparaisons détaillées des « distances » séparant les simulations entre elles et séparant les simulations des données réelles, ont été confrontées à la variabilité intrinsèque des mouvements sismiques. Les outils de simulation ont également permis de comprendre l'origine physique de certaines variabilités de l'effet de site, notamment celles liées au back-azimut des séismes considérés. Le projet a permis de suivre l'évolution du misfit observations / simulations pour différentes « générations » de modèle géologique, des paramètres de source, du modèle « de bedrock », et de la base de données accélérométrique. Le projet s'est révélé riche d'enseignements sur la démarche globale d'estimation des effets de site, en delà de la seule simulation numérique

International audience; The E2VP-1 international benchmark ( EUROSEISTEST Verification and Validation Project , 2005-2008) aimed at (i) evaluating accuracy of the numerical methods for seismic simulations of realistic 2D/3D basin models, and (ii) quantitatively comparing the recorded and numerically simulated earthquake ground motions. In this framework, the EUROSEISTEST located in the Mygdonian basin of the Volvi area, near Thessaloniki (Northern Greece) was chosen as target site. In this paper, we present the results obtained for the 2D linear case, for three different numerical schemes finite elements, spectral elements, and finite differences methods. We also compare the 2D results with linear and nonlinear 1D results obtained for soil columns extracted in the middle and the edge of the 2D basin profile.; Le benchmark international E2VP-1 (« EUROSEISTEST Verification and Validation Project », 2005-2008) avaitpour principaux objectifs d’évaluer la précision des méthodes numériques pour simuler la réponse sismique 2D/3D debassins sédimentaires, en comparant de manière quantitative, les réponses enregistrées et calculées. Dans ce cadre, il a étéchoisi d’utiliser le site EUROSEISTEST situé dans le bassin Mygdonien de la région de Volvi, proche de Thessalonique(Grèce). Dans cet article, nous présentons les résultats obtenus pour le cas linéaire 2D, avec 3 méthodes numériques :différences finies, éléments finis et éléments spectraux. Nous comparons également les résultats 2D avec les résultatslinéaires et non linéaires 1D obtenus sur 2 colonnes de sol extraites en bord et milieu du profil 2D

International audience; Long period (0.1-2 Hz) events are frequently observed on active volcanoes and are often related to fluid and gas movements inside the edifice. Understanding the physical mechanism beyond their generation would improve our ability to detect volcanic unrest and define a more accurate state of the activity of the volcano. Nowadays full moment tensor (F-MT) inversions are usually carried out under the assumption of a point source. This assumption resides in the way classical F-MT inversions are performed: a grid search inside a specific volume of investigation. However source dimension of LP events may involve finiteness. We first carry out full moment tensor inversion to constrain a possible crack plane. Many sources along the identified plane are supposed to act simultaneously. Probability weights based on the pseudo-algorithm proposed by Zhang et al. (JGR, 2014) are given to each source to minimize the misfit between observed and retrieved signals. Subsequent iterations are continued until the best matching solution is obtained. Each point of the possible finite source gets different scaling factors, contributing to the synthetics. Sources with the low scaling factors are removed and we finally obtain a set of preferable sources which could act simultaneously (or time-shifted). We test this methodology on synthetic signals computed in a 3D realistic velocity model of Etna volcano (Italy) with topography and a source grid spacing of 40 meters. We generate synthetics for: a point source; a finite source (250m. wide with 5 sources acting at a delayed time of 0.2 s) both representing a horizontal crack. First results show how misfit values are very high for the point source solution (0.75) while the finite source shows a lower value (0.35). The point source solution doesn’t offer enough resolution, with many possible sources acting at the same time, and is rejected. The finite source solution gives an image of a finite source of the same dimensions of the real one but slightly shifted. This shift could come from some limitations of resolution due to the low frequencies of interest. These results suggest that this approach could be potentially applicable to volcanic LP events.

International audience; SUMMARY Differences between 3-D numerical predictions of earthquake ground motion in the Mygdonian basin near Thessaloniki, Greece, led us to define four canonical stringent models derived from the complex realistic 3-D model of the Mygdonian basin. Sediments atop an elastic bedrock are modelled in the 1D-sharp and 1D-smooth models using three homogeneous layers and smooth velocity distribution, respectively. The 2D-sharp and 2D-smooth models are extensions of the 1-D models to an asymmetric sedimentary valley. In all cases, 3-D wavefields include strongly dispersive surface waves in the sediments. We compared simulations by the Fourier pseudo-spectral method (FPSM), the Legendre spectral-element method (SEM) and two formulations of the finite-difference method (FDM-S and FDM-C) up to 4Hz. The accuracy of individual solutions and level of agreement between solutions vary with type of seismic waves and depend on the smoothness of the velocity model. The level of accuracy is high for the body waves in all solutions. However, it strongly depends on the discrete representation of the material interfaces (at which material parameters change discontinuously) for the surface waves in the sharp models. An improper discrete representation of the interfaces can cause inaccurate numerical modelling of surface waves. For all the numerical methods considered , except SEM with mesh of elements following the interfaces, a proper implementation of interfaces requires definition of an effective medium consistent with the interface boundary conditions. An orthorhombic effective medium is shown to significantly improve accuracy and preserve the computational efficiency of modelling. The conclusions drawn from the analysis of the results of the canonical cases greatly help to explain differences between numerical predictions of ground motion in realistic models of the Mygdonian basin. We recommend that any numerical method and code that is intended for numerical prediction of earthquake ground motion should be verified through stringent models that would make it possible to test the most important aspects of accuracy.

This article investigates the impact of 2D and 3D geometric effects (i.e., topography and nonhorizontal‐layering effects) on Green’s functions and spectral ratios inside vertical arrays by using numerical simulations. All simulations are carefully performed by a spectral‐element method of order six and are valid in the frequency range 0.05–10 Hz. Analysis reveals that a surface‐to‐downhole spectral ratio is a very sensitive physical variable with respect to problem’s geometry; and, consequently, it should be analysed with care. We found that a small change in the waveform relative to the 1D theory can strongly affect the resonant modes. For the configuration of our 2D and 3D wave propagation problems, we show the cause of this sensitivity is mainly due to the downhole Green’s function that is more affected by the geometry than the free surface Green’s function. As a result, both amplitude and frequency of a resonant mode can deviate from the 1D theory because of 2D/3D geometric effects. We also found the amplitude of resonant modes was mostly lower relative to the 1D theory because of geometric scattering. As a consequence, the quality factors inverted so far from spectral ratios based on 1D theory are expected to be underestimated. Because the resonant frequencies are also affected by geometric effects, the S ‐wave velocity of soil layers inverted from 1D theory can be biased as well. For example, we show that the fundamental frequencies computed around small hills sometimes underestimate, sometimes overestimate the fundamental frequency of a 1D problem. Online Material: Animations showing 2D and 3D geometric effects on wave propagation.

Horizontal‐to‐vertical (H/V) spectral ratios of microtremors (HVRM) have been traditionally interpreted as representing either the S ‐wave amplification directly or the Rayleigh‐wave ellipticity for a horizontally layered structure. However, based on the diffuse field theory, we have derived an alternative theoretical basis that HVRM corresponds to the square root of the ratio between the imaginary part of the horizontal Green’s function and that of the vertical one. Under that condition, the 1D horizontal layering assumption is not needed to interpret HVRM. As observational evidence of such non‐1D HVRM, we discovered significant directional dependency at a site on the Uji campus, Kyoto University, Japan. The observed microtremor north–south/vertical spectral ratios are quite stable and have only one peak around 0.5 Hz. On the other hand, the east–west/vertical spectral ratios are smaller in amplitude and have higher peak frequencies and sometimes two separated peaks. The directional dependency of observed HVRM is aligned to the axis of the 2D basin structure. We performed numerical analyses by spectral element method using a unit load on the surface to examine the effect of the 2D basin structure on the imaginary parts of the Green’s functions. We found that the 2D basin structure clearly changes the characteristics of the H/V spectral ratios in both perpendicular and parallel directions relative to the basin axis. Thus, we succeeded in theoretically simulating the qualitative difference between the H/V spectral ratios for two orthogonal horizontal components of the HVRM observed on the Uji campus. Online Material: Snapshots and animations of wave propagation.

International audience; This paper presents the inversion of linear and equivalent linear soil profile (i.e., S-wave velocity and damping factor) at the KiK-net station MYGH10 during the Great Tohoku Earthquake, 2011. Due to possible strong 2D or 3D topographic effects at the station located close to mountainous areas, we carefully select weak motions that present few of those effects. Among 50 weak motions, only 5 are selected to check the linear profile of the site. Then, the equivalent linear soil profile during the main shock is inverted, showing very interesting nonlinear effects, such as bedrock nonlinearity.

International audience; This article presents the verification of a spectral-element method (SEM) code using the so-called layer over half-space 3 (LOH.3) benchmark model of the Southern California Earthquake Center to 7 Hz with a minimum S-wave velocity of 2000 m/s. First, the approach of Liu and Archuleta (2006) is successfully implemented in an explicit SEM, then, it is shown that the SEM code displays excellent goodness of fits (GOFs) with five Gauss-Lobatto-Legendre (GLL) nodes per wavelength at 7 Hz. A parametric study on the influence of the number of GLL nodes per wavelength shows that more than five GLL nodes per minimum wavelength do not significantly increase the accuracy; however, a decrease of the accuracy starts to be seen from four GLL nodes. A parametric study of the influence of the number of relaxation mechanism on the accuracy of the numerical response shows that, for this specific case, six to eight relaxation mechanisms are sufficient to reproduce the reference solution, whereas below six the viscoelastic response is strongly affected and tends to an elastic response when using two relaxation mechanisms only.

Nonlinear behaviour of soft soils observed during strong ground motions is now well established and the deployment of vertical arrays (i.e., borehole stations) has contributed to detailed wave propagation analyses and the assessment for quantitative physical parameters such as shear-wave velocity, pressure-wave velocity and damping factors with respect to shear strain levels. Despite the growing numbers of studies on this phenomenon, its knowledge is still recent and researches on borehole station data remains an important step toward the understanding of the complex in-situ behaviour of soft sediments subjected to strong ground motions. The purpose of this work is threefold. First, an inversion code by genetic algorithm is developed in order to inverse borehole stations data via the Thomson-Haskell propagator matrix method. This technique allows us to validate the one-dimensional (1D) structure (e.g., shear-wave velocity, damping factors) of a borehole in the linear elastic domain and to show quantitative evidence of the nonlinear behaviour of the soft sediments during the 2005 Fukuoka Prefecture western offshore earthquake, Japan. Second, the results of the inversion are used in order to test a simple and an advanced constitutive law using the Finite Elements Method. The results clearly show that the bi-linear assumption of the simple constitutive law produces unrealistic velocity and acceleration time histories. The used of the advanced constitutive law leads to better results; however, the number of parameters to be tuned in order to obtain results consistent with the observation is an unavoidable obstacle. Third, in order to extend the study of site effects to higher dimensions, 2D and 3D codes of the very efficient Spectral Elements Method are developed and validated by comparing their results in the linear domain with those obtained theoretically or with other numerical methods.; Le comportement non-linéaire des sols observé lors des mouvements sismiques forts est maintenant bien établi et le déploiement des puits accélérométriques a permis des analyses détaillés de la propagation des ondes ainsi qu'une évaluation quantitative des paramètres physiques tels que la vitesse de cisaillement et de compression des ondes et les facteurs d'amortissements en fonction de la déformation. En dépit du nombre grandissant d'´etudes sur ce phénomène, sa connaissance est encore récente et les recherches sur les données de puits accélérométriques restent une étape importante vers la compréhension du comportement complexe in-situ des sédiments soumis à des mouvements sismiques forts. L'objectif de ces travaux est triple. Premièrement, un code d'inversion par algorithme génétique est développé afin d'inverser des données de puits accélérométriques via la théorie des matrices de propagation de Thomson- Haskell. Cette technique nous permet dans un premier temps de valider la structure en une dimension (1D) (e.g., vitesse des ondes de cisaillement, facteurs d' amortissements) d'un puits accélérométrique dans le domaine linéaire et dans un second temps de mettre en évidence de manière quantitative le comportement non-linéaire des sédiments lors du séisme de Fukuoka, 2005, Japon. Deuxièmement, les résultats de l'inversion sont utilisés pour tester des lois de comportement simples et avancées en utilisant la Méthode des Eléments Finis. Les résultats montrent clairement que l'hypothèse bilinéaire de la loi de comportement simple produit des séries temporelles non réalistes en vitesse et en accélération. L'utilisation d'une loi de comportement avancée mène à de meilleurs résultats, cependant, le nombre de paramètres ajustables pour obtenir des résultats consistants avec l'observation est un obstacle inévitable. Troisièmement, afin d'étendre l'étude des effets de site à des dimensions supérieures, des codes 2D et 3D de la Méthode en Eléments Spectraux sont développés et validés en comparant leurs résultats dans le domaine linéaire avec ceux obtenus théoriquement ou via d'autres méthodes numériques.

International audience; We present finite-element numerical simulations of seismic wave propagation in non linear inelastic geologicalmedia. We demonstrate the feasibility of large scale modeling based on an implicit numerical scheme and a nonlinear constitutive model. We illustrate our methodology with an application to regional scale modeling in the French Riviera, which is prone to earthquakes. The PaStiX direct solver is used to handle large matrix numerical factorizations based on hybrid parallelism to reduce memory overhead. A specific methodology is introduced for the parallel assembly in the context of soil nonlinearity. We analyse the scaling of the parallel algorithms on large-scale configurations and we discuss the physical results.

International audience; A specific approach is studied to couple two well-known numerical methods, a finite difference method (FDM) and a finite element method (FEM) for simulating regional seismic wave propagation to local site response. This coupling uses a technique of the “paraxial approximation” in order to input in the FEM the seismic wave generated in the FDM. The main advantage of this approach is to locally extract an area of interest where non-linear soil response or complex geometry is important from the regional wave propagation in a relatively simple medium. This result in taking advantage of both methods: the portability of the FDM and the flexibility of the FEM. This paper presents a theoretical framework of the paraxial approximation, through which the coupling is realized between the FDM and the FEM, and demonstrates some examples for the validation of the proposed coupling technique as well as its possible applications.