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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; The objective of this article is to present the nonlinear response of a soft sedimentary site based on a one-dimensional inversion by a genetic algorithm of the shear-wave velocity structure and damping factors of a borehole soil column during the 2005 Fukuoka Prefecture Western Offshore earthquake. First, we confirm that, according to the source rupture mechanism, the major and minor axes in the horizontal plane at the borehole station are the transverse and radial directions, respectively. Then, in order to corroborate in the linear domain the S-wave transfer function of the borehole's logging, we perform time-dependent spectral ratios analyses on small aftershocks. Finally, we show qualitative evidence of nonlinearity during the mainshock associated with a significant shift toward low frequencies of several resonant modes, and we evaluate the degree of nonlinearity by inverting the shear-wave velocity structure and damping factors. Because of a directional effect present only in the major axis around 8 Hz, which prevents the use of the conventional objective function that minimizes the integrated residuals between observed and theoretical ratios, we introduce a simple objective function that depends only on peaks' frequency and amplitude. The efficiency of the objective function and the robustness of the inversion are shown by performing eight independent inversions converging to very similar minima.

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 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.