Third International Symposium on the Effects of Surface Geology on Seismic Motion Grenoble, France, 30 August - 1 September 2006 Paper Number: S04

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1 Third International Symposium on the Effects of Surface Geology on Seismic Motion Grenoble, France, 3 August - 1 September 26 Paper Number: S4 SPECTRAL ELEMENT MODELING OF 3D WAVE PROPAGATION IN THE ALPINE VALLEY OF GRENOBLE, FRANCE. Emmanuel CHALJUB Laboratoire de Géophysique Interne et Tectonophysique, CNRS-OSUG, Grenoble, France ABSTRACT - We present the results of the ESG26 numerical benchmark obtained with the Spectral Element Method. The benchmark consisted in computing the response of the Grenoble valley to two small local events (magnitude Ml<3) and two hypothetical events with magnitude Mw=6. Our computations include the effect of surface topography and are valid for frequencies up to about 2Hz. 1 Introduction Located in a Y-shaped valley filled with late quaternary deposits, the city of Grenoble is subject to strong site effects, typical of Alpine valleys 1. In order to understand the variability of those site effects as observed in weak motion data and to estimate strong ground motion for realistic scenarios, we have developped a numerical approach based upon the Spectral Element Method (SEM) (Chaljub et al., 24, 25, 26). The SEM is high-order finite element method built to retain the accuracy of spectral methods (see e.g. Komatitsch & Vilotte, 1998; Komatitsch & Tromp, 1999; Komatitsch et al., 25; Chaljub et al., 26, and references therein). The accurate implementation of the free-surface condition in the SEM is of particular interest in Alpine valleys since an important fraction of seismic energy is transported by Rayleigh and Love surface waves diffracted by valley edges (Cornou et al., 23). The SEM is also capable of handling complex surface and interface topographies, event though the natural brick in the SEM, the hexahedron, is not the most flexible element to capture geological features (see figure 2 and discussion in Chaljub et al. (26)). The paper is organized as follows: section 2 recalls the definition of the ESG26 benchmark (see also paper SB1), in section 3 we present details of the implemention of the SEM to handle the benchmark cases and we present our results in section 4 with a particular emphasis on the effect of surface topography. 1 For more information, visit the sismovalp website:

2 2 ESG26 Numerical Benchmark The ESG26 numerical benchmark (see paper SB1) consisted in computing the response of the Grenoble Valley to (i) two small local events which occured recently on the so-called Belledone Border Fault (BBF) (Thouvenot et al., 23) and (ii) two strong motion scenarios in which magnitude 6 events were defined as extensions to the two weak motion cases. The two weak (resp. strong) motion cases are referred to as W1 and W2 (resp. S1 and S2). Figure 1 shows the map of surface topography, the positions of sources and receivers and the map of sediment thickness obtained by Vallon (1999). The velocities used in the bedrock are taken from a simple 1D model used for event location in the Alps (Thouvenot et al., 23). In the basin, seismic velocities and density vary only with depth as described in paper SB1. Minimum S velocity at the surface is 3 m s ' W2 S2 W1 S1 R24 R9 R1 R23 R22 R5 R11 R1 R21 R2 R3 R12 R2 R17 R18 R14 R15 R16 R13 R4 R19 R25 R26 R27R28 R6 R7 R8 R29 R3 R31 R32 Figure 1: Left: Map of surface topography in the Grenoble area showing the 4 cases that were considered in the ESG 26 numerical benchmark. The Weak motion cases are indicated with red stars, and the strong motion scenarios with red lines. Yellow triangles denote the positions of the 4 receivers where a prediction was required. Right: Map of bedrock topography obtained by inverting gravimetric measurements in the Grenoble area (Vallon, 1999). The maximum sediment thickness exceeds 1 m in the western part of the Y -shaped valley. Note the stiff bedrock uplift in the center of the valley, with sediment thickness as small as 5m. R38 R37 R39 R4 R36 R34 R35 R33 Depth (m) Numerical Method The first step to apply the SEM to the ESG26 benchmark was to build a 3D spectral element mesh of the Grenoble area. Figure 2 shows the mesh used for the W1 and S1 cases (the W2 and S2 cases require extension of the mesh to the South to incorporate the sources). Free surface topography was smoothed with a 5m Gaussian window prior to be paved in order to avoid distorted elements. The mesh was coarsened with depth based upon the conforming technique detailed in (Komatitsch & Tromp, 1999). We use a polynomial order N=4 within each element.

3 For calculations accurate for frequencies up to 2 Hz, the mesh contains 332,16 elements and 22,62,624 gridpoints. To account properly for elastic parameters discontinuities in a finite or spectral element method, the elements should not intersect the physical interfaces. However, as stated in the introduction it is not straightforward to satisfy this constraint everywhere in a hexahedra-based SEM, especially close to the valley edges. Here we follow the same strategy as Komatitsch et al. (24), i.e. we do not honor the sediment-bedrock contrast at shallow depths (see right part of figure 2). The velocity contrasts near valley edges are thus approximated by continuous variations using the polynomial basis within each element. The error made by this approximation should not be too large however since the element size close to valley edges is that of the smallest wavelength of the simulation (i.e. 15 m for 2 Hz calculation). To model the strong motion cases S1 and S2, we considered a set of 125 point sources regularly distributed on the fault planes. Each point source was assigned a moment magnitude M w 2.9 and an onset time consistent with the imposed rupture kinematics (circular growth with constant rupture velocity V R = 2.8 km s 1 ). Time extrapolation was handled by a secondorder explicit Newmark scheme, an additional Runge-Kutta scheme being used to march in time the memory variables needed to model anelasticity (see e.g. Komatitsch & Tromp, 1999). Stability condition imposed a time step of t = s. It took about 7 hours to run 6, time steps (3 s of seismic signal) on 8 sun v4z (quadriprocessors of 64-bits amd opteron). Figure 2: Left: Surface view of the spectral-element mesh used to compute synthetic waveforms accurate up to approximately 1 Hz in the Grenoble valley. Note that the mesh used for the computations presented in this paper is twice finer: it contains surface elements. The color scale indicates surface elevation above sea level, which ranges from 2 m (blue) to approximately 25 m (red). The vertical exaggeration factor is 5 and a spatial Gaussian filter has been applied to smooth sharp topographic variations. Right: View from the south-east of a cross section through the spectral-element mesh. Brown indicates elements that intersect the bedrock, whereas green represents elements located entirely within the sediments. The mesh is coarsened twice in depth to adapt it to the variations of seismic wavelengths. The sediment/bedrock interface is honored exactly for depths greater than 22 m. At shallower depths (in particular near valley edges) the contrast between bedrock and sediments is interpolated by the local polynomial basis within each element.

4 4 Results 4.1 Comparison to data Figure 3 shows the comparison of SEM predictions to data for the Lancey event of 24/4/26 (W1 case) at two stations of the french accelerometric network located within the Montbonnot borehole (Nicoud et al., 22). All traces have been band-pass filtered between.2hz and 2Hz, then aligned and scaled to fit the first arrival on the vertical component at the deep borehole receiver. The need for scaling the amplitudes stems from the uncertainty in the event magnitude. The correction applied here suggest an actual magnitude of M L = 2.8. The agreement on the vertical component is satisfying both at depth and at the surface. This confirms the validity of the P velocity model at the borehole. Note however that some late phases are absent in the synthetics. The misfit is larger on the horizontal components: the amplitude of the first arrivals do not compare well and the overall duration is not well reproduced by the synthetics. This could be partly improved by tuning the source location and mechanism, but the lack of duration in the synthetics is probably due to incorrect S velocities in shallow layers. Same observations can be drawn from the comparison to data for the W2 case (not shown here). Improving the fit to data for the Grenoble valley is an ongoing project that goes beyond the scope of this paper. For the benchmark purpose, we conclude that the present agreement is a first order validation of our approach and gives credit to our estimations of strong ground motion presented hereafter. RR East-West North-South Up-Down R R Figure 3: Comparison between data (solid black lines) and SEM predictions (dashed red lines) at the borehole receivers R8 (535 m deep borehole) and R6 (surface). Note the amplification of the surface ground velocity compared to the input motion. Traces have been band-pass filtered between.2hz and 2Hz. At those frequencies, the velocity model is accurate enough to explain amplitude and duration reasonably especially on the vertical component (see text). 4.2 Peak ground velocity maps Figure 4 shows the maps of peak ground velocity obtained for the four benchmark cases. In order to obtain the PGV maps for the weak motion cases, we had to low-pass filter the original source

5 time function below 2Hz with a non-causal butterworth filter. This step was not necessary for the strong motion cases since the source contains no energy above 2 Hz (see paper SB1). As shown on figure 4, most of the amplification occurs in the eastern part of the valley. The distribution of PGV is in general similar for weak and strong motion cases, except in the S1 case where source directivity amplifies considerably the S wave impinging the southeastern part of the valley. Movies of the ground velocity (not shown here) reveal that the peak value in this case is obtained at quite late time (t 8s) and is related to very localized constructive interferences of surface waves generated off the valley edges. In the S2 case, directivity does not affect the valley because of the fault s orientation. The PGV values are then a factor of two smaller than in the S1 case. The PGV values obtained in the strong motion cases may seem quite large (more than 1.7 m s 1 in the S1 case). These high values are due to (i) the choice of Haskell s model to define the kinematics of the source, which favors very energetic stopping phases and (ii) the fact that the source is quite shallow. Changing the source depth in the S1 case (i.e. setting the nucleation point at 6 km depth instead of 3km) resulted in a reduction of the PGV values of a factor of two.

6 W1 S1 m/s m/s ' 6 ' 45 ' 6 ' W2 S2 m/s m/s ' 6 ' 45 ' 6 ' Figure 4: Maps of peak ground velocity computed for the four benchmark cases: weak motion cases W1 (top left) and W2 (bottom left); strong motion cases S1 (top right) and S2 (bottom right). The Y -shaped footprint of the sedimentary filling is indicated by the thick external line. Note that all simulations show little amplification in the western branch of the valley and close to the bedrock uplift in the center of the valley (see also figure 1). The high values obtained in the S1 case are caused by a directivity effect (see text). 4.3 Effect of surface topography The ESG26 benchmark offered the possibility to test the influence of surface topography on ground motion. Figure 5 shows the ratios of PGV computed with and without surface topography in the S1 and S2 cases. Most of the differences occur on rock sites where steep topography is present. Amplifications up to a factor of 2.5 are obtained in the S1 case. Within the valley, the effect of surface topography on the PGV values does not exceed 4 %. For both strong motion cases, maximal amplification (resp. deamplification) is seen on crests (resp. valleys), consistent with reported observations (see e.g. Géli et al., 1988). The effect of slopes on seismic motion is not so systematic. As it is seen on figure 5 for the S1

7 case, the two sides of the Romanche valley (southeast of the computing box) behave in the opposite way: the northern side (right-bank) is amplified whereas the southern side (left-bank) is deamplified. S1 Amplification S2 Deamplification Figure 5: Left: Ratio of peak ground velocity computed with and without topography for the strong motion cases 1 (top) and 2 (bottom). Right: Maps of surface topography in the Grenoble area with color lines indicating the regions where PGV ratio exceeds 1.5 (top) or is less than 2/3 (bottom). Red and blue colors stand for the S1 case, whereas yellow and cyan are related to the S2 case. Systematic amplification is seen on mountains crests, whereas on the slopes, the motion can be either amplified or deamplified (see the southern part of the Belledonne massif in the S1 case). 5 Conclusions We have presented the results of the ESG26 numerical benchmark obtained with the SEM. Our computations include the effect of surface topography and are accurate for frequencies up to 2Hz. The comparison of the SEM synthetics to data shows a reasonnable agreement which is very encouraging for future studies. Given the earthquake scenarios considered in the benchmark, our results indicate that the largest shaking should occur in the eastern part of the Grenoble area. At the frequencies considered here and given the simplicity of the velocity

8 model (no lateral variations), the peak values of ground velocity are caused by interferences of surface waves diffracted off valley edges. We found that the effect of surface topography is less important within the valley (4% variations in the peak ground velocity values were obtained) than at rock sites outside the valley where aggravation factors of 2.5 are measured. Amplification on mountains crests and deamplification in ridges seems to be systematic, whereas seismic motion on slopes is less predictable. The SEM provides a very useful tool to get deeper understanding of the seismic response of Alpine valleys. Future work will aim at explaining the duration of shaking observed in data, as well as predicting ground motion for more realistic scenarios than those considered in the benchmark. 6 Acknowledgments We thank D. Komatitsch and J. Tromp for providing the original version of their 3D spectral element code specfem3d basin. The calculations presented here were performed at the Service Commun de Calcul Intensif de l Observatoire de Grenoble (scci) in Grenoble. This work has been supported by the European InterReg III-B Alpine space program sismovalp. References Chaljub, E., Cornou, C., Guéguen, P., Causse, M., & Komatitsch, D., 24, Spectral element modeling of 3D site effects in the alpine valley of Grenoble, France., in Fall Meet. Suppl., Abstract S41C-7, vol. 85(47), Eos Trans. AGU. Chaljub, E., Cornou, C., Guéguen, P., Causse, M., & Komatitsch, D., 25, Spectral-element modeling of 3D wave propagation in the alpine valley of Grenoble, France, in Geophysical Research Abstracts, vol. 7, 5225, EGU 2nd general assembly, Wien, Austria. Chaljub, E., Komatitsch, D., Vilotte, J.-P., Capdeville, Y., Valette, B., & Festa, G., 26, Spectral element analysis in seismology, in Advances in Wave Propagation in Heterogeneous Media, edited by R.-S. Wu & V. Maupin, Advances in Geophysics, pp , Elsevier. Cornou, C., Bard, P.-Y., & Dietrich, M., 23, Contribution of dense array analysis to the identification and quantification of basin-edge-induced waves, Part II: Application to the Grenoble basin (French Alps), Bull. Seismol. Soc. Am., 93(6), Géli, L., Bard, P. Y., & Julien, B., 1988, The effect of topography on earthquake ground motion: a review and new results, Bull. Seismol. Soc. Am., 78, Komatitsch, D. & Tromp, J., 1999, Introduction to the spectral-element method for 3-D seismic wave propagation, Geophys. J. Int., 139, Komatitsch, D. & Vilotte, J. P., 1998, The spectral-element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures, Bull. Seismol. Soc. Am., 88(2),

9 Komatitsch, D., Liu, Q., Tromp, J., Süss, P., Stidham, C., & Shaw, J. H., 24, Simulations of ground motion in the Los Angeles basin based upon the spectral-element method, Bull. Seismol. Soc. Am., 94, Komatitsch, D., Tsuboi, S., & Tromp, J., 25, The spectral-element method in seismology, in AGU Geophysical Monograph on Seismic Data Analysis and Imaging with Local Arrays, edited by A. Levander & G. Nolet, AGU, Washington DC, USA. Nicoud, G., Royer, G., Corbin, J.-C., Lemeille, F., & Paillet, A., 22, Creusement et remplissage de la vallée de l Isère au Quaternaire récent: apports nouveaux du forage GMB1 (1999) dans la région de Grenoble (France), Géologie de la France, 4, 39 49, in French. Thouvenot, F., Fréchet, J., Jenatton, L., & Gamond, J.-F., 23, The Belledonne border fault: identification of an active seismic strike-slip fault in the western Alps, Geophys. J. Int., 155(1), Vallon, M., 1999, Estimation de l épaisseur d alluvions et sédiments quaternaires dans la région grenobloise par inversion des anomalies gravimétriques (Estimation of the thickness of alluvial and quaternary deposits in the Grenoble area by inverting gravimetric anomalies), Tech. rep., LGGE, IPSN/CNRS, Université Joseph Fourier, in French.