Sites response estimates at the city of Lourdes, Pyrenees, France, using the spectral ratio method
Authors: Dubos Noalwenn , Souriau Annie , Ponsolles Christian , Fels Jean-François , Sénéchal Guy 
Published: June 2005

Abstract
The city of Lourdes, in the central part of the French Pyrenees, has been damaged several times by earthquakes, in particular in 1660 and 1750, two events which partly destroyed the city [Lambert et Levret-Albaret, 1996]. The Pyrenees is the most seismically active area in France. Historical seismicity indicates the possible occurrence of a magnitude 6 event in the Lourdes area. As Lourdes is an important place of pilgrimage with more than five millions of visitors each year, the evaluation of the seismic risk is of major importance. To this purpose, it is necessary first to correctly identify the active faults near the city, second to determine the ground motion response to local events, also called site effects. The active faults are rather well known thanks to the permanent network of the Observatoire Midi-Pyrénées [Souriau et Pauchet, 1998], and complementary studies [Dubos, 2000] (fig. 1). In the present paper, we present the results of an experiment devoted to the determination of the site effects in the city of Lourdes, using a classical spectral ratio method based on the record of small local events. Although the extrapolation from weak motion to strong motion is often non linear [Darragh et Shakal, 1991 ; Seekins et Boatwright, 1994], this approach gives crucial information for the evaluation of the ground response in case of a magnitude 6 event.
The Pyrenees are an intraplate collision range [Choukroune, 1992]. A major tectonic feature is the North Pyre-nean Fault (FNP, fig. 1), which separates the Paleozoic Axial Zone to the south from the North Pyrenean Zone, made of Mesozoic sediments, to the north. Lourdes is located inside this latter unit (fig. 1). Quaternary glaciations have added various superficial structures [Alimen, 1964]. The city, at an altitude of about 400 m, is at the junction of five glacial beds (fig. 2), two of them corresponding to the Gave de Pau river. Two heights, the Beout (719 m) and the Pic du Jer (1948 m), are located south of the city.
The experiment has been conducted during seven months using ten digital three-component instruments with broadband sensors. They have been set up with interstation spacing of 200 m to 1200 m. The station locations (fig. 2 and table I) were chosen by taking into account the importance of some sites for the population, but also the geological nature of the ground. It is well known that site effects are strongly influenced by the lithological features of the superficial structures, which may induce resonance phenomena, and by the topography of the surface and layer interfaces, which may induce focusing effects [Gao et al., 1996]. In our experiment, all the stations are at about the same altitude (400 m ± 40 m), except CIT located on the slope of the Beout at an altitude of 535 m. ROC, CIT, HOP and CHA are on the bedrock, EDF is at the foot of an ophite cliff. CHA is located half-way up the 40 meter-heigh hill of the castle. The other stations are on the sediments. GEN and PMP are at the base of buildings of 5 levels and 7 levels respectively, these structures may possibly modify the site effects [Wirgin and Bard, 1996]. 19 local events with magnitude 1.4 to 3.2 at epicentral distance 5 to 62 km have been analysed (fig. 3), as well as two regional events (table II). The local events are well representative of the local seismicity, they have been recorded at many stations (table II) with a very good signal to noise ratio. As shown by Riepl et al. [1998], eight to ten events per station are sufficient to define correctly the site effects. Only GEN does not fulfil this criterion because of its later installation. The records show that the amplitudes and frequency contents of the signals are very different from one station to another (fig. 4). For instance, PMP and ROC are distant of 300 m, but the signal at PMP is about four times larger than at ROC. Also, the signal at CHA appears depleted in high frequencies compared to the others stations.
The method used is a classical spectral ratio method with a reference station [Borcherdt, 1970]. It consists in determining the site amplification at each site with respect to a reference site located on the bedrock, thus poorly affected by site effects. This method is applied to the signal of local events, whose distance to the stations must be large compared to the interstation distance. The site response is computed by dividing the amplitude spectrum of a record at a station by the amplitude spectrum of the similar record at the reference station (see fig. 5, which describes the main steps of the method). The spectra are computed for the S-wave, which is more sensitive than the P-wave to sediment amplification. An important step is the smoothing of the spectra : it removes instabilities, but it may also remove resonance peaks which could have some physical significance (fig. 8). Spectral ratios are computed for both the vertical (V) and horizontal (H) components. H is a combination of the N-S and E-W components. We present logarithmic average ratios for each station, plus or minus one standard deviation. The reference station must be close to the other stations, it must be located on a rock outcrop of the same nature as the substratum beneath the other stations, and it must be free of site effect. An empirical way to check this last point is to analyse the H/V spectral ratio between the H and V components at a single station [Nakamura, 1989 ; Lermo and Chavez-Garcia, 1993] : this ratio is close to 1 in the absence of site effect [Le Brun, 1997]. It has been determined for stations CHA and ROC (fig.6). The choice of ROC as reference site is more appropriate, as the H/V ratio remains close to 1 at any frequency.
The spectral ratios for the nine stations other than ROC (fig. 7) exhibit a great geographic variability of the amplifications : for example, at 20 Hz, the amplitude of the H-ratio is ten times greater at AUZ than at CHA, which is distant by less than 500 m. The results show that amplification and frequency variations are nearly similar for the H and V components : site effects affect both vertical and horizontal components. EDF and HOP, located on rock, do not show any amplification in the frequency range considered. CHA and CIT, also located on rock but with possible topographic effects, exhibit more complex spectral ratios. In particular, at CHA, the amplification decreases drastically for frequencies higher than 5 Hz. The other stations, which are on Quaternary structures, show peaks on the two components at frequencies between 6 and 10 Hz. However, on the horizontal component, the peak is generally at a lower frequency than on the vertical one (see PMP and AUZ, fig. 7). SAN is characterized by a high amplification over a large frequency band : on the horizontal component, the ratio is higher than 5 between 1.6 and 20 Hz and reaches 10 at 3 Hz. The results discussed here concern smoothed spectra, but the amplification at some particular frequencies may exceed the smoothed value by a factor 2 to 5. For instance, the PMP spectra show systematically a peak near 5.5 Hz (fig. 8), twice larger than the smoothed value. For this particular station located at the basement of a building, a soil-structure interaction may possibly explain the observed prominent peak. A similar effect is observed at GEN, which is also located at the bottom of a building.
In order to know if some parameters, like the phase used, the magnitude, the epicentral distance or the back-azimuth, may influence the spectral ratios, we have performed various tests with the ratios obtained at PMP (fig. 9). It turns out that none of these parameters has an important influence on the spectral ratios obtained.
If the structure is known, the site effects can be modelled with synthetic seismograms. The structure of the subsurface beneath the station SAN is known thanks to a seismic refraction experiment made on a 100 m-long profile. With a simple 1D-model, synthetic spectral ratios have been calculated with the reflectivity method [Müller, 1985] for a structure with sediment layers (SAN) compared to a structure without sediment layer (ROC). For the H-component, the resonance frequencies obtained with the model are quite similar to the observed ones, but the amplifications are about three times too low (fig. 10). This is also the case at station PMP, where the subsurface structure used in the model has been derived from empirical relationship between peak frequency and sediment layer thickness. On the other hand, the agreement is poor for the V-component. 2D and 3D effects, which are not taken into account here, may possibly explain this difference.