Figures (For the Appendix)
Appendix
We extend the study of Douglas et al. (2007) to the case of an anelastic medium so as to study how the anelastic attenuation influences the decay of ground motions in different 1D stratified models. First, we consider variations of the source mechanism. For all four simulations, we use the Rhine crustal structure, the source magnitude is Mw 5.0 and the source depth is 10 km. Figure S1 shows the results of each mechanism as well as those in an elastic medium for reference. As the source parameters are the same for the elastic and the anelastic case, the PGV values are generally smaller in the anelastic case. Up to a source-to-site distance of about 50 km, the conclusions we can draw from the results of the simulations are similar to the conclusions made by Douglas et al. (2007) in their study of the decay for the Alpine structure. The dip-slip mechanisms show nearly the same decay of the ground motions. For a distance lower than about 20 km, the effects of diminution are more noticeable for the strike-slip mechanism than for the dip-slip mechanisms because the horizontal S-waves are dominant in the PGV. However, for a distance higher than about 20 km, the decay of the ground motion for the strike-slip mechanism is similar to those observed for the dip-slip mechanisms. We can conclude that the decay of ground motions is not strongly affected by the fault mechanism. A similar pattern is observed for the anelastic case, the PGV values being lower in the anelastic case than in the elastic case.
Next, we consider variations of the source magnitude (Figure S2). In addition to the differences in source magnitude, there are differences in the source frequency, because the use of the Wells and Coppersmith (1994)’s relationship between magnitude and subsurface fault length gives different durations of the source time history. For all five simulations, we use the Rhine crustal structure, the source mechanism is dip-slip with 45° dip and the source depth is 10 km. The magnitude strongly affects the PGV values, but the decays stay similar for the lower magnitudes (Mw 4.5 and Mw 5.0). For the larger magnitudes (Mw 5.5, Mw 6.0 and Mw 6.5) and for the smaller distances (up to about 20 km), the decay is similar to the decay for the lower values of the magnitude. However, for the larger distances, the decay is smaller than for the lower values of the magnitude and decreases with the magnitude. Additionally, for the larger magnitudes, the amplitude increase appears for a larger distance (about 70 km for Mw 5.5 instead of about 50 km for the lower magnitudes) or disappears (Mw 6.0 and Mw 6.5). These are because large earthquakes contain much lower frequencies, which play a significant role in PGV map. A similar pattern is observed for the anelastic case, the PGV values being lower in the anelastic case than in the elastic case. However, for the larger magnitudes (Mw 6.0 and Mw 6.5), the effects of the attenuation are much smaller than for the lower magnitudes and the decay is similar in the elastic and the anelastic case. As the frequency content of the source is different for each magnitude, the variations of the decay may be due to the variations of the frequency content, and not to the variations of the magnitude itself. We apply a Butterworth filter with critical frequencies equal to 0.25 and 0.75 Hz, 0.75 and 1.25 Hz and 1.25 and 1.75 Hz respectively, before computing the average PGV at each source-to-site distance. Figure S3 shows for each value of the magnitude, the decay of the PGV for each band of frequencies. For the larger magnitudes, the amplitude of the PGV is significantly different for each band of frequencies. However, the decay seems only a little stronger at the larger distances for magnitudes Mw 6.0 and 6.5. Therefore, the variations of the decay with the magnitude do not seem to be due to the different frequency content of the source.
Finally, we consider variations of the focal depth for the three crustal structures (Figure S4). For all three simulations, the source mechanism is dip-slip with 45° dip and the source magnitude is Mw 5.0. The decays of the curves are noticeably different from one source depth to another. In the case of the Rhine crustal structure, while the PGV value decreases with the distance even for short distances in the case of the 5 and 10 km deep sources, we can note the maximum of PGV appear at a distance of about 10 km for the 15 km deeper source. Moreover, whereas the PGV is higher for the shallower sources up to a distance of about 20 km, this pattern changes for the farther distances, for which the PGV value is lower for the 10 km deep source. The PGV value increase for the distances larger than about 50 km is much more pronounced for the 10 km deep source than for the other focal depths, and nearly disappears in the case of the 5 km deep source. A similar pattern is observed for the anelastic case, the PGV values being lower in the anelastic case than in the elastic case. Figure S5 shows for the Rhine crustal structure and for each value of the focal depth, the decay of the PGV for each band of frequencies. For the lower frequencies (0.25 to 0.75 Hz), the decay rate seems a little weaker than for the higher frequencies, especially for the deeper sources (10 and 15 km). The same pattern is observed in the anelastic case. The frequency does not appear to have a significant effect on the decay. This may be due to the fact that the frequency content of the sources used in this study is very simple; a different pattern may be observed with sources with a more complex frequency content. In the case of the Pyrenean and the Alpine crustal structures (Figure S4), up to a distance of about 20 km, we find the same pattern as for the case of the Rhine crustal structure: the PGV value decreases with the distance in the case of the 5 and 10 km deep sources, while it increases up to a distance of about 10 km for the 15 km deep source, and the PGV value is higher for the shallower sources than for the deeper sources. For distances higher than about 20 km, the variations of the PGV value with the distance differ from the Rhine case: the PGV values of the 10 km deep source are close to the PGV values of the 15 km deep source. Moreover, the increase in the PGV value for the distances larger than about 50 km is much attenuated in the case of the Alpine crustal structure and totally disappear in the case of the Pyrenean crustal structure. A similar pattern is observed for the anelastic case, the PGV values being lower in the anelastic case than in the elastic case.
To emphasize the variations of the attenuation effect due to the crustal structure, we compare in Figure S6 the decay of ground motion for the three structures in the case of the focal depth of 5 km, 10 km and 15 km. Up to a distance of about 20 km, the PGV values are higher for the Rhine case and lower for the Pyrenean case. This is in agreement with the values of the P- and S-wave velocities which are lower for the Rhine case and larger for the Pyrenean case, at least for the shallower layers. For the larger distances, the PGV values stay generally higher for the Rhine case than for the two other cases, and the anelastic attenuation is clearly observed as a decrease in the amplitude. For the Alpine and the Pyrenean cases, the pattern changes depending on the source focal depth: the PGV values are very close for the 5 km deep source while for the 15 km deep source, the PGV values for the Alpine case become lower than the PGV values for the Pyrenean case. Summarily, the PGVs show noticeable inter-region differences for the same focal depth and intra-region differences for different focal depths. However the effect of anelastic attenuation does not change the general PGV pattern for all the sets and appears in the decrease of PGV values according to the distance.
Figures (for the Appendix)
Figure S1. Decay of the ground motion for a dip-slip mechanism with 30° dip (red line), 45° dip (blue line), 60° dip (green line) and a strike-slip mechanism (cyan line). Abscissa is the distance from the source to the station and ordinate is the average horizontal PGV. The dashed lines correspond to the case of an anelastic medium, and the full lines to the case of an elastic medium.
Figure S2. Decay of the ground motion for magnitude Mw 4.5 (red line), 5.0 (blue line), 5.5 (green line), 6.0 (cyan line) and 6.5 (pink line). Abscissa is the distance from the source to the station and ordinate is the average horizontal PGV. The dashed lines correspond to the case of an anelastic medium, and the full lines to the case of an elastic medium.
Figure S3. Decay of the ground motion for magnitude Mw 4.5 (top left), 5.0 (top middle), 5.5 (top right), 6.0 (bottom left) and 6.5 (bottom middle), and for frequencies 0.25 to 0.75 Hz (red line), 0.75 to 1.25 Hz (blue line) and 1.25 to 1.75 Hz (green line). Abscissa is the distance from the source to the station and ordinate is the average horizontal PGV. The dashed lines correspond to the case of an anelastic medium, and the full lines to the case of an elastic medium.
Figure S4. Decay of the ground motion for the Rhine crustal structure (left), the Pyrenean crustal structure (middle) and the Alpine crustal structure (right), and for source depth 5 km (red line), 10 km (blue line) and 15 km (green line). Abscissa is the distance from the source to the station and ordinate is the average horizontal PGV. The dashed lines correspond to the case of an anelastic medium, and the full lines to the case of an elastic medium.
Figure S5. Decay of the ground motion for the Rhine crustal structure for source depth 5 km (left), 10 km (middle) and 15 km (right), and for frequencies 0.25 to 0.75 Hz (red line), 0.75 to 1.25 Hz (blue line) and 1.25 to 1.75 Hz (green line). Abscissa is the distance from the source to the station and ordinate is the average horizontal PGV. The dashed lines correspond to the case of an anelastic medium, and the full lines to the case of an elastic medium.
Figure S6. Decay of the ground motion for source depth 5 km (left), 10 km (middle) and 15 km (right), and for the Rhine crustal structure (red line), the Pyrenean crustal structure (blue line) and the Alpine crustal structure (green line). Abscissa is the distance from the source to the station and ordinate is the average horizontal PGV. The dashed lines correspond to the case of an anelastic medium, and the full lines to the case of an elastic medium.
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