Description: This paper concerns the numerical modelling of time-domain mechanical waves in viscoelastic media based on a generalized Zener model. To do so, classically in the literature relaxation mechanisms are introduced, resulting in a set of the so-called memory variables and thus in large computational arrays that need to be stored. A challenge is thus to accurately mimic a given attenuation law using a minimal set of relaxation mechanisms. For this purpose, we replace the classical linear approach of Emmerich & Korn with a nonlinear optimization approach with constraints of positivity. We show that this technique is more accurate than the linear approach. Moreover, it ensures that physically meaningful relaxation times that always honour the constraint of decay of total energy with time are obtained. As a result, these relaxation times can always be used in a stable way in a modelling algorithm, even in the case of very strong attenuation for which the classical linear approach may provide some negative and thus unusable coefficients.

Description: The possibility of applying one explicit finite-difference (FD) scheme to all interior grid points (points not lying on a grid border) no matter what their positions are with respect to the material interface is one of the key factors of the computational efficiency of the FD modelling. Smooth or discontinuous heterogeneity of the medium is accounted for only by values of the effective grid moduli and densities. Accuracy of modelling thus very much depends on how these effective grid parameters are evaluated. We present an orthorhombic representation of a heterogeneous medium for the FD modelling. We numerically demonstrate its superior accuracy. Compared to the harmonic-averaging representation the orthorhombic representation is more accurate mainly in the case of strong surface waves that are especially important in local surface sedimentary basins. The orthorhombic representation is applicable to modelling seismic wave propagation and earthquake motion in isotropic models with material interfaces and smooth heterogeneities using velocity–stress, displacement–stress and displacement FD schemes on staggered, partly staggered, Lebedev and collocated grids.

Description: In a low-seismicity context, the use of numerical simulations becomes essential due to the lack of representative earthquakes for empirical approaches. The goals of the EUROSEISTEST Verification and Validation Project (E2VP) are to provide (1) a quantitative analysis of accuracy of the current, most advanced numerical methods applied to realistic 3D models of sedimentary basins (verification) and (2) a quantitative comparison of the recorded ground motions with their numerical predictions (validation). The target is the EUROSEISTEST site located within the Mygdonian basin, Greece. The site is instrumented with surface and borehole accelerometers, and a 3D model of the medium is available. The simulations are performed up to 4 Hz, beyond the 0.7 Hz fundamental frequency, thus covering a frequency range at which ground motion undergoes significant amplification. The discrete representation of material heterogeneities, the attenuation model, the approximation of the free surface, and nonreflecting boundaries are identified as the main sources of differences among the numerical predictions. The predictions well reproduce some, but not all, features of the actual site effect. The differences between real and predicted ground motions have multiple origins: the accuracy of source parameters (location, hypocentral depth, and focal mechanism), the uncertainties in the description of the geological medium (damping, internal sediment layering structure, and shape of the sediment-basement interface). Overall, the agreement reached among synthetics up to 4 Hz despite the complexity of the basin model, with code-to-code differences much smaller than predictions-to-observations differences, makes it possible to include the numerical simulations in site-specific analysis in the 3D linear case and low-to-intermediate frequency range.

Description: 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 4 Hz. 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.

Description: The ground-motion variability sigma is a fundamental component in probabilistic seismic-hazard assessment because it controls the hazard level at very low probabilities of exceedance. So far, most of the analyses based on empirical ground-motion prediction equations do not consider any distance dependency of sigma. This study aims to analyze the potential distance dependency of ground-motion variability, especially in the near-field region, where the variability is poorly constrained due to the lack of available records. We, therefore, investigate the distance dependency of sigma by performing numerical simulations of ground motion for some strike-slip events. Synthetic velocity seismograms (up to 3 Hz) have been generated from a suite of finite-source rupture models of past earthquakes. Green’s functions were calculated for a 1D velocity structure using a discrete wavenumber technique ( Bouchon, 1981 ). The within-event component of the ground-motion variability was then evaluated from the synthetic data as a function of distance. The simulations reveal that the within-event component of the ground motion shows a distance dependency, subject to the rupture type. For bilateral ruptures, the variability tends to increase with distance. On the contrary, in case of unilateral events, the variability decreases with distance.

Description: 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.

Description: Data Terra’s main mission is to develop a structure for accessing and processing data, data-products and services geared towards observing, understanding and predicting in an integrated manner the history, mechanisms and evolution of the Earth system in response to global changes and extreme events. Data Terra federates four data and services hubs dedicated to the four physical compartments of the Earth System: Aeris for the atmosphere, Odatis for the oceans, Theia for land surfaces and ForM@Ter for the solid Earth. While aimed chiefly at the scientific community, the unique research e-infrastructure also serves public and socio-economic stakeholders and its multi-source data are accessible via coherent, one-stop portals. As a digital infrastructure in the field of earth and environmental science, Data Terra works closely with Earth-observation research infrastructures and space agencies. It is backed by a continuum of distributed and interconnected platforms, proposing services that span the full data cycle from access from repositories to value-added processing, thus enabling inter- and trans-disciplinarity studies as well as exploitation of large volumes of data. At national, European and international levels (EOSC Pillar, Fair impact, Phidias, Copernicus services, …), it is advancing the development of open science, implementation of FAIR approaches, contributing to space missions and applications and to the initiative to generate digital twins of the Earth. Data Terra federates four data and services hubs dedicated to the four physical compartments of the Earth System: Aeris for the atmosphere, Odatis for the oceans, Theia for land surfaces and ForM@Ter for the solid Earth. While aimed chiefly at the scientific community, the unique research e-infrastructure also serves public and socio-economic stakeholders and its multi-source data are accessible via coherent, one-stop portals. Data Terra’s main mission is to develop a structure for accessing and processing data, data-products and services geared towards observing, understanding and predicting in an integrated manner the history, mechanisms and evolution of the Earth system in response to global changes and extreme events. Data Terra federates four data and services hubs dedicated to the four physical compartments of the Earth System: Aeris for the atmosphere, Odatis for the oceans, Theia for land surfaces and ForM@Ter for the solid Earth. While aimed chiefly at the scientific community, the unique research e-infrastructure also serves public and socio-economic stakeholders and its multi-source data are accessible via coherent, one-stop portals. As a digital infrastructure in the field of earth and environmental science, Data Terra works closely with Earth-observation research infrastructures and space agencies. It is backed by a continuum of distributed and interconnected platforms, proposing services that span the full data cycle from access from repositories to value-added processing, thus enabling inter- and trans-disciplinarity studies as well as exploitation of large volumes of data. At national, European and international levels (EOSC Pillar, Fair impact, Phidias, Copernicus services, …), it is advancing the development of open science, implementation of FAIR approaches, contributing to space missions and applications and to the initiative to generate digital twins of the Earth.