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  • 1
    Electronic Resource
    Electronic Resource
    Blind prediction of the site effects at Ashigara Valley, Japan, and its comparison with reality (1994)
    Springer
    Natural hazards 10 (1994), S. 149-170 
    Details
    ISSN: 1573-0840
    Keywords: Finite-difference method ; numerical predictions ; site effects ; earthquake ground motions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Weak and strong ground motions were numerically predicted for three stations of the Ashigara Valley test site. The prediction was based on the records from a rock-outcrop station, one weak-motion record from a surface-sediments station, and the standard geotechnical model. The data were provided by the Japanese Working Group on the Effects of Surface Geology as a part of an international experiment. The finite-difference method for SH waves in a 2-D linear viscoelastic medium (a causalQ model) was employed. Comparison with the real records shows that at two stations the predictions fit better than at the third one. Strangely, the two better predictions were for stations situated at larger distances from the reference rock station (one station was on the surface, the other in a borehole). The strong ground motion (the peak acceleration of about 200 cm s−2) was not predicted qualitatively worse than the weak motion (8 cm s−2). A less sophisticated second prediction (not submitted during the experiment), in which we did not attempt to fit the available weak-motion record at the sedimentary station, agrees with the reality significantly better.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00643449
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    Paper (German National Licenses)
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  • 2
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    Earthquake Ground Motion in the Mygdonian Basin, Greece: The E2VP Verification and Validation of 3D Numerical Simulation up to 4 Hz (2015)
    Seismological Society of America (SSA)
    Details
    Publication Date: 2015-06-09
    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.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
    Published by Seismological Society of America (SSA)
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  • 3
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    Choice of regularization in adjoint tomography based on two-dimensional synthetic tests (2015)
    Oxford University Press
    Details
    Publication Date: 2015-05-31
    Description: We present synthetic tests of 2-D adjoint tomography of surface wave traveltimes obtained by the ambient noise cross-correlation analysis across the Czech Republic. The data coverage may be considered perfect for tomography due to the density of the station distribution. Nevertheless, artefacts in the inferred velocity models arising from the data noise may be still observed when weak regularization (Gaussian smoothing of the misfit gradient) or too many iterations are considered. To examine the effect of the regularization and iteration number on the performance of the tomography in more detail we performed extensive synthetic tests. Instead of the typically used (although criticized) checkerboard test, we propose to carry out the tests with two different target models—simple smooth and complex realistic models. The first test reveals the sensitivity of the result on the data noise, while the second helps to analyse the resolving power of the data set. For various noise and Gaussian smoothing levels, we analysed the convergence towards (or divergence from) the target model with increasing number of iterations. Based on the tests we identified the optimal regularization, which we then employed in the inversion of 16 and 20 s Love-wave group traveltimes.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 4
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    A discrete representation of a heterogeneous viscoelastic medium for the finite-difference modelling of seismic wave propagation (2019)
    Oxford University Press
    Details
    Publication Date: 2019
    Description: 〈span〉〈div〉Summary〈/div〉The accuracy and efficiency of numerical simulations of seismic wave propagation and earthquake ground motion in realistic models strongly depend on discrete grid representation of the material heterogeneity and attenuation. We present a generalization of the orthorhombic representation of the elastic medium (Kristek 〈span〉et al.〈/span〉 2017) to the viscoelastic medium to make it possible to account for a realistic attenuation in a heterogeneous viscoelastic medium with material interfaces. An interface is represented by an averaged orthorhombic medium with rheology of the Generalized Maxwell body (GMB-EK, equivalent to the Generalized Zener body). The representation is important for the possibility of applying one explicit finite-difference 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. This is one of the key factors of the computational efficiency of the finite-difference modelling. Smooth or discontinuous heterogeneity of the medium is accounted for only by values of the effective (i.e. representing reasonably averaged medium) grid moduli and densities. Accuracy of modelling thus very much depends on how the medium heterogeneity is represented/averaged. We numerically demonstrate accuracy of the developed orthorhombic representation. The orthorhombic representation neither changes the structure of calculating stress-tensor components nor increases the number of arithmetic operations compared to a smooth weakly heterogeneous viscoelastic medium. It is applicable to the velocity-stress, displacement-stress and displacement FD schemes on staggered, partly-staggered, Lebedev and collocated grids. We also present an optimal procedure for a joint determination of the relaxation frequencies and anelastic coefficients.〈/span〉
    Print ISSN: 2051-1965
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 5
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    3-D numerical simulations of earthquake ground motion in sedimentary basins: testing accuracy through stringent models (2015)
    Oxford University Press
    Details
    Publication Date: 2015-02-12
    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.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 6
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    A no-cost improved velocity-stress staggered-grid finite-difference scheme for modelling seismic wave propagation (2016)
    Oxford University Press
    Details
    Publication Date: 2016-09-03
    Description: We investigate the problem of finite-difference approximations of the velocity–stress formulation of the equation of motion and constitutive law on the staggered grid (SG) and collocated grid (CG). For approximating the first spatial and temporal derivatives, we use three approaches: Taylor expansion (TE), dispersion-relation preserving (DRP), and combined TE-DRP. The TE and DRP approaches represent two fundamental extremes. We derive useful formulae for DRP and TE-DRP approximations. We compare accuracy of the numerical wavenumbers and numerical frequencies of the basic TE, DRP and TE-DRP approximations. Based on the developed approximations, we construct and numerically investigate 14 basic TE, DRP and TE-DRP finite-difference schemes on SG and CG. We find that (1) the TE second-order in time, TE fourth-order in space, 2-point in time, 4-point in space SG scheme (that is the standard (2,4) VS SG scheme, say TE-2-4-2-4-SG) is the best scheme (of the 14 investigated) for large fractions of the maximum possible time step, or, in other words, in a homogeneous medium; (2) the TE second-order in time, combined TE-DRP second-order in space, 2-point in time, 4-point in space SG scheme (say TE-DRP-2-2-2-4-SG) is the best scheme for small fractions of the maximum possible time step, or, in other words, in models with large velocity contrasts if uniform spatial grid spacing and time step are used. The practical conclusion is that in computer codes based on standard TE-2-4-2-4-SG, it is enough to redefine the values of the approximation coefficients by those of TE-DRP-2-2-2-4-SG for increasing accuracy of modelling in models with large velocity contrast between rock and sediments.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 7
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    International Benchmark on Numerical Simulations for 1D, Nonlinear Site Response (PRENOLIN): Verification Phase Based on Canonical Cases (2016)
    Seismological Society of America (SSA)
    Details
    Publication Date: 2016-10-08
    Description: PREdiction of NOn-LINear soil behavior (PRENOLIN) is an international benchmark aiming to test multiple numerical simulation codes that are capable of predicting nonlinear seismic site response with various constitutive models. One of the objectives of this project is the assessment of the uncertainties associated with nonlinear simulation of 1D site effects. A first verification phase (i.e., comparison between numerical codes on simple idealistic cases) will be followed by a validation phase, comparing the predictions of such numerical estimations with actual strong-motion recordings obtained at well-known sites. The benchmark presently involves 21 teams and 23 different computational codes. We present here the main results of the verification phase dealing with simple cases. Three different idealized soil profiles were tested over a wide range of shear strains with different input motions and different boundary conditions at the sediment/bedrock interface. A first iteration focusing on the elastic and viscoelastic cases was proved to be useful to ensure a common understanding and to identify numerical issues before pursuing the nonlinear modeling. Besides minor mistakes in the implementation of input parameters and output units, the initial discrepancies between the numerical results can be attributed to (1) different understanding of the expression "input motion" in different communities, and (2) different implementations of material damping and possible numerical energy dissipation. The second round of computations thus allowed a convergence of all teams to the Haskell–Thomson analytical solution in elastic and viscoelastic cases. For nonlinear computations, we investigate the epistemic uncertainties related only to wave propagation modeling using different nonlinear constitutive models. Such epistemic uncertainties are shown to increase with the strain level and to reach values around 0.2 (log 10 scale) for a peak ground acceleration of 5 m/s 2 at the base of the soil column, which may be reduced by almost 50% when the various constitutive models used the same shear strength and damping implementation.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
    Published by Seismological Society of America (SSA)
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  • 8
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    An orthorhombic representation of a heterogeneous medium for the finite-difference modelling of seismic wave propagation (2017)
    Oxford University Press
    Details
    Publication Date: 2017-01-07
    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.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 9
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    On the initiation of sustained slip-weakening ruptures by localized stresses (2014)
    Oxford University Press
    Details
    Publication Date: 2014-12-19
    Description: Numerical simulations of dynamic earthquake rupture require an artificial initiation procedure, if they are not integrated in long-term earthquake cycle simulations. A widely applied procedure involves an ‘overstressed asperity’, a localized region stressed beyond the static frictional strength. The physical properties of the asperity (size, shape and overstress) may significantly impact rupture propagation. In particular, to induce a sustained rupture the asperity size needs to exceed a critical value. Although criteria for estimating the critical nucleation size under linear slip-weakening friction have been proposed for 2-D and 3-D problems based on simplifying assumptions, they do not provide general rules for designing 3-D numerical simulations. We conduct a parametric study to estimate parameters of the asperity that minimize numerical artefacts (e.g. changes of rupture shape and speed, artificial supershear transition, higher slip-rate amplitudes). We examine the critical size of square, circular and elliptical asperities as a function of asperity overstress and background (off-asperity) stress. For a given overstress, we find that asperity area controls rupture initiation while asperity shape is of lesser importance. The critical area obtained from our numerical results contrasts with published theoretical estimates when background stress is low. Therefore, we derive two new theoretical estimates of the critical size under low background stress while also accounting for overstress. Our numerical results suggest that setting the asperity overstress and area close to their critical values eliminates strong numerical artefacts even when the overstress is large. We also find that properly chosen asperity size or overstress may significantly shorten the duration of the initiation. Overall, our results provide guidelines for determining the size of the asperity and overstress to minimize the effects of the forced initiation on the subsequent spontaneous rupture propagation.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 10
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    3D Fourth-Order Staggered-Grid Finite-Difference Schemes: Stability and Grid Dispersion (2000)
    Seismological Society of America
    Details
    Publication Date: 2000-06-01
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
    Published by Seismological Society of America
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