Ali Mikael -Philippe

Gueguen -Pierre-Yves Bard

Philippe Roux
email: philippe.gueguen@ujf-grenoble.fr

Mickael Langlais

Philippe Gueguen Isterre

The Analysis of Long-Term Frequency and Damping Wandering in Buildings Using the Random Decrement Technique

The characterization and monitoring of buildings is an issue that has attracted the interest of many sectors over the last two decades. With the increasing use of permanent, continuous and real-time networks, ambient vibrations can provide a simple tool for the identification of dynamic building parameters. This study is focused on the long-term variation of frequency and damping in several buildings, using the Random Decrement Technique (RDT). RDT provides a fast, robust and accurate long-term analysis and improves the reliability of frequency and damping measurements for structural health monitoring. This reveals particularly useful information in finding out precisely how far changes in modal parameters can be related to changes in physical properties. This paper highlights the reversible changes of the structure's dynamic parameters, correlated with external forces, such as temperature and exposure to the sun. Contrasting behaviors are observed, including correlation and anti-correlation with temperature variations.

INTRODUCTION

Over the last two decades, ambient vibrations methods for assessing the modal parameters of structures have received considerable attention. Since the design forces and displacements in structures are frequency and damping dependent (based on the seismic coefficient C(T,ξ) where T is the period of the building and ξ is the damping ratio), the use of ambient vibrations methods provides relevant information on the elastic characteristics of a building at relatively low cost. [START_REF] Carder | Observed vibrations of buildings[END_REF] established the first empirical relationships between the height and period of buildings in the US, and recent papers (e.g., [START_REF] Farsi | Estimation of natural periods of buildings and vulnerability of exist-ing frame structure in the urban area of grenoble[END_REF]Gallipolli et al., 2009;Michel et al., 2010) have

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provided other relationships based on experimental data for European buildings with different designs. In practice, semi-empirical formula are provided in earthquake-designed code or guidance documents, such as the ATC3-06 [START_REF] Atc | Tentative provisions for the development of seismic regulations for buildings[END_REF] in US or the EC8 in Europe (Eurocode 8, 2004), taking the form T=C t H b , T the period, H the height and C t and b depending on the building design and material. Frequency and damping are then key parameters for earthquake design and seismic vulnerability assessment since, as mentioned by Spence et al. (2003), the adjustment of structural models must assume a large set of unknown parameters influencing the response of existing buildings. Knowing frequency and damping can reduce the range of errors and epistemic uncertainties for representing the vulnerability as fragility curves [START_REF] Michel | Seismic vulnerability assessment to slight damage based on experimental modal parameters[END_REF].

Finally, ambient vibrations modal analysis methods provide an effective tool for shortand/or long-term monitoring of building health indicators, such as aging effects, or after extreme events. The basic idea is that any modification of the stiffness, mass or energy dissipation characteristics of a system may alter its dynamic response [START_REF] Doebling | Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review[END_REF][START_REF] Farrar | An introduction to structural health monitoring[END_REF]. Variations in these modal parameters can result from a change in the boundary conditions (e.g. fixed-or flexible-base structure), mechanical properties (e.g. reinforcement or retrofitting) or the elastic properties of the material (e.g. Young's modulus). The causes may also be related to non-linear responses of the buildings. For example, transient variations are observed during seismic excitation due to the non-linear response of the soil-structure boundary (e.g., [START_REF] Jennings | Vibration and soil-structure interaction tests of a nine-story reinforced concrete building[END_REF][START_REF] Crouse | Soil-structure interaction during the San Fernando earthquake[END_REF][START_REF] Ivanovic | Ambient vibration tests of a seven-story reinforced concrete building in Van Nuys, California, damaged by the 1994 Northridge earthquake[END_REF]Trifunac, 2008, Todorovska, 2009) or to the closing/opening process of pre-existing cracks within the elements of the reinforced concrete buildings (e.g., [START_REF] Luco | On the apparent change in dynamic behavior of a nine-story reinforced concrete building[END_REF][START_REF] Meli | A study of site effects and seismic response of an instrumented building in Mexico City[END_REF][START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF]Michel and Gueguen, 2010). Permanent variations may also appear due to structural damage due to strong seismic motion (e.g., [START_REF] Safak | Analyses of recorded responses of two high-rise buildings during the Loma Prieta earthquake of October 1989[END_REF][START_REF] Celebi | Dynamic characteristics of five tall buildings during strong and low-amplitude motions[END_REF][START_REF] Dunand | Comparison of the dynamic parameters extracted from weak, moderate and strong building motion[END_REF][START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF]. Finally, these variations can be long-term, reversible and 4/33 slight, as recently observed by [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF] and Todorovska and Al Rjoub (2006).

In most cases, the fluctuations of the fundamental frequency of buildings was correlated to the temporal variations of the atmospheric conditions (temperature, humidity, etc.) influencing the properties of the building and the soil, i.e. modifying the soil-structure interaction and the boundary conditions. Similarly, most previous studies conducted in civil engineering structures (e.g., [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF][START_REF] Deraemaker | Vibration-based structural health monitoring using output-only measurements under changing environment[END_REF][START_REF] Hua | Modeling of temperature-frequency correlation using combined principal component analysis and support vector regression technique[END_REF][START_REF] Nayeri | A novel approach for the structural identification and monitoring of a full-scale 17-story building based on ambient vibration measurements[END_REF] have shown that temperature is the most significant cause of variability of modal frequencies. [START_REF] Farrar | Vibration-based structural damage identification[END_REF] mentioned that frequencies are probably the modal parameters most sensitive to change, particularly because the loss of stiffness directly impacts the frequency values. Nevertheless, the apparent damping coefficient recorded in the building may also be directly sensitive to a local loss of stiffness (e.g., [START_REF] Jeary | Damping in structures[END_REF][START_REF] Modena | Damage localization in reinforced concrete structures by using damping measurements[END_REF] or to soil-structure interaction (e.g., [START_REF] Gueguen | Soil-structure and soil-structure-soil interaction: experimental evidence at the Volvi test site[END_REF]. Moreover, since the natural fluctuations of modal parameters has been reported by several authors, and since the variation in these parameters is used for structural health monitoring, two important points must be clarified: (1) what are the smallest variations in modal parameters that can be detected by ambient vibrations and related to structural health (in some cases, the amplitude of the variability of modal parameters caused by temperature may be such that it masks the changes due to physical damage); and (2) are variations in modal parameters always related to external conditions with the same trend regardless of the building typology?

The main purpose of this paper is to analyse the long-term variations in the frequency and damping coefficient of existing buildings using the Random Decrement Technique (RDT). We applied RDT to three existing buildings equipped with temporary or permanent instrumentation. After presenting the method in section Damping and frequency using random decrement technique, the variations in frequency and damping 5/33 are discussed in section One-year observation of modal parameters, as well as the link between frequency and damping fluctuations and the effect of temperature. Concluding remarks are presented in section Discussion. (1997) focuses on the fundamental frequency fluctuations to detect changes in buildings. This parameter is very sensitive and it can be easily tracked for structural health monitoring or for the long-term analysis of buildings. For instance, under the singledegree-of-freedom system (SDOF) assumption, the fundamental frequency is related to stiffness K and mass M, through the equation:

DAMPING AND FREQUENCY USING THE RANDOM DECREMENT TECHNIQUE

Salawu

(1) where ω=2π.f is the resonant circular frequency of the building. To first order, we assume that the mass M remains constant. The frequency variations are then related to the variation of stiffness K, K depending on the properties of the building (e.g., Young's modulus, height, design of the building, etc.), but also on the cracks opening and the boundary conditions (e.g., fixed-or flexible-base building). Frequency analysis is currently included in building tests since the simple fast Fourier transform of ambient vibrations recorded at the top of the building provides relevant information on the modal frequencies, above all for very tall buildings exhibiting a good signal-to-noise ratio and a low damping.

Many papers have discussed the fundamental frequency sensitivity in the case of damage after an extreme event (e.g. [START_REF] Luco | On the apparent change in dynamic behavior of a nine-story reinforced concrete building[END_REF]Celebi et al., 1996;[START_REF] Ivanovic | Ambient vibration tests of a seven-story reinforced concrete building in Van Nuys, California, damaged by the 1994 Northridge earthquake[END_REF] 6/33 Todorovska, 2009;Michel and Gueguen, 2010), on the long-term analysis of buildings (e.g., [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF][START_REF] Nayeri | A novel approach for the structural identification and monitoring of a full-scale 17-story building based on ambient vibration measurements[END_REF] or on the damage localisation (e.g., [START_REF] Kim | Crack detection in beam-type structures using frequency data[END_REF]Xu et al., 2007), most studies being based on the Fourier analysis or the time-frequency analysis of the recorded data.

Even though the damping coefficient is a critical parameter for assessment design, it is not usually easy to determine the damping coefficient in experimental conditions and its physical origin in most practical systems are seldom fully understood. [START_REF] Jacobsen | Steady forced vibration as influenced by damping[END_REF] provided an early formulation for damping, corresponding for the sake of simplicity to an equivalent coefficient including viscous damping (proportional to velocity), constant Coulomb's damping and material damping. [START_REF] Crandall | The role of damping in vibration theory[END_REF] mentioned that damping is amplitude dependent, i.e. non-linear effects may be observed that increase the damping value as shaking amplitude increases. Moreover, and whatever the excitation amplitude, damping is frequency dependent and becomes significant at the highest resonant frequencies [START_REF] Crandall | The role of damping in vibration theory[END_REF]. The shape of the frequency-response curve at each mode is controlled by the system's damping coefficient and can be estimated using the half-power bandwidth method [START_REF] Clough | Dynamics of Structures[END_REF]. The free-oscillating response of the SDOF, as controlled by the e -ξωt function, is thus proportional to the frequency ω and the critical damping coefficient ξ. The critical damping coefficient ξ is expressed as follows:

(2) where c represents the energy-loss mechanism, and K and M the stiffness and mass of the SDOF respectively. In buildings, radiative damping must be included in the "apparent" c, according to the soil-structure interaction since it affects the seismic energy radiated back into the ground (e.g., [START_REF] Gueguen | Soil-structure and soil-structure-soil interaction: experimental evidence at the Volvi test site[END_REF][START_REF] Gueguen | Experimental and numerical analysis of soil motions caused by free vibrations of a building model[END_REF][START_REF] Gueguen | Site-City interaction in Mexico City-like environments: An analytical study[END_REF]. In very

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tall buildings, aerodynamic effects may also contribute to damping (Solari, 1996;Tamura and Suganuma, 1996). [START_REF] Jeary | Damping in tall buildings, a mechanism and a predictor[END_REF], [START_REF] Lagomarsino | Forecast models for damping and vibration periods of buildings[END_REF], [START_REF] Farsi | Estimation of natural periods of buildings and vulnerability of exist-ing frame structure in the urban area of grenoble[END_REF] and Satake et al. (2003) proposed empirical relationships for estimating damping as a function of height, frequency and shaking amplitude. These equations can be used to offer a rough estimate when designing new buildings. Several authors have analysed the variation of damping with shaking amplitude and frequency [START_REF] Hart | Earthquake design of buildings: damping[END_REF][START_REF] Jeary | Damping in tall buildings, a mechanism and a predictor[END_REF]Tamura and Suganuma,1996;[START_REF] Li | Damping in buildings : its neural network model and AR model[END_REF]Satake et al., 2003). All observed that damping increases with shaking amplitude and increases with the fundamental frequency of the building (Satake et al., 2003). Finally, as previously mentioned for frequency, the variation of stiffness K may also cause the damping coefficient to vary.

An effective solution to track frequency and damping variations over time is to apply the RDT. This method was first proposed by Cole in 1973 and is based on the fact that, at any given time, ambient vibrations contain a random and impulse element. By stacking a large number of windows with identical initial conditions, ambient vibrations remain stationary and the impulse response of the structure is revealed. Vandiver et al. (1982) and [START_REF] Asmussen | Statistical theory of the vector random decrement technique[END_REF] provide details on the theory of RDT and its mathematical formulation that can be simplified by:

(3)

where N is the number of windows with fixed initial conditions, s is the ambient vibration window of duration τ, and t i is the time verifying the initial conditions (Fig. 1). The choice of initial conditions is a key point in ensuring the stability of the Random Decrement signature. The null displacement and positive velocity conditions proposed by [START_REF] Cole | On-line failure detection and damping measurement of aerospace structures by random decrement signatures[END_REF] and verified by [START_REF] Asmussen | Statistical theory of the vector random decrement technique[END_REF] were used in the present work. The number of 8/33

windows N is also critical to obtain a stable and relevant damping estimation. [START_REF] Jeary | Damping in structures[END_REF] recommended at least 500 windows, i.e. one hour of recording, as sufficient for almost buildings having fundamental frequencies between 0.5 and 2Hz. In our study, the duration of each recording was one hour, corresponding to more than 1000 periods T of the fundamental mode (around 1Hz for the buildings tested herein), keeping the same criteria whatever the building. We considered a sampling of one hour, i.e. one value of frequency and damping per hour. No overlap was considered between two successive one hour windows.  is the length of the windows selected (and stacked) in one hour. In our case, since the RDT amplitude gets smaller towards the end of the signature, we limited its length to 20 seconds to avoid the average being biased by the reducing amplitude. The number of windows N selected for one hour depends on the number of times the initial conditions are found on the one hour window. The minimal value is 3600/20, i.e. 180 windows without overlap. In practice, considerable overlap exists between each window of 20 seconds, the initial conditions t i ending up almost in every period, i.e. about 1 second. N is then greater than 500 windows.

Before the RDT processing, a fourth-order band pass filter was applied to the raw data, centred on the expected fundamental frequency with a 10% frequency band. The RDT signature of the mode is exponentially damped and corresponds to the so-called logarithmic decrement of damping [START_REF] Clough | Dynamics of Structures[END_REF]. Its period is computed by averaging the time lapse between two upward zero crossing points. Simultaneously, we estimate the damping value  from the logarithmic decrement of the RDT signal by adjusting an e -ξωt function.

To demonstrate the RDT for the long-term monitoring of buildings, this method was first applied to the Mont-Blanc (MB) and Belledonne (BD) buildings (Fig. 2a), two of the three Ile Verte towers located in Grenoble (France). These stand-alone towers are 30storey reinforced concrete buildings. They were built between 1963 and 1967 and were 9/33 not designed to be earthquake resistant. Their shape is a rhombus of (LxT) 40x20m. The structural strength system is provided by two main continuous walls throughout the height of the structures (100m), completed by small RC walls in the horizontal directions. They have the same orientation, N10°. For sake of simplicity, their L and T directions are considered as North-South and East-West, respectively, throughout the paper. Soil conditions are soft, with a mixture of clay deposits and sand and gravel in thin layers, resulting from the glacio-lacustrine deposits and later fluviatile processes that are characteristic of Alpine valley deposits such as the Grenoble basin [START_REF] Gueguen | On the limitation of the H/V spectral ratio using seismic noise as an exploration tool: application to the grenoble valley, a small apex ratio basin[END_REF]. Ambient vibrations were recorded simultaneously at the top of the two towers during one month using a 24 bit Analog/Digital CityShark TM acquisition system [START_REF] Chatelain | Cityshark: A user-friendly instrument dedicated to ambient noise (microtremor) recording for site and building response studies[END_REF] connected to a 5-s Lennartz 3C velocimeter. Continuous recording was performed and recording files were divided into one-hour long time windows sampled at 50Hz. This sample rate was selected in order to optimize the acquisition for detecting the building frequencies (estimated using empirical relationships close to 1Hz) and to use the memory storage of the temporary experiment. The acquisition systems in the two buildings were completely independent.

Examples of fast Fourier transforms are shown in Fig. 2a (right). The behavior of the two buildings is quite similar, their fundamental mode being at 0.67Hz (T) and 0.89Hz (L), and 0.65Hz (T) and 0.84Hz (L) for the BD and MB buildings, respectively. Overtones of bending modes close to 3Hz and 5Hz were also observed, as well as a torsion mode close to 1Hz. All these values were also observed by [START_REF] Michel | Seismic vulnerability assessment to slight damage based on experimental modal parameters[END_REF] using extensive modal analysis, with multi-channels recordings. Herein, only the fundamental mode was used to test the RDT. The long-term variations of frequency and damping were then computed hourly from the RDT, i.e. for time-windows greater than 1000 periods. Frequency fluctuations are shown in Fig. 3 for one month and for the two buildings and the two horizontal directions. Near-perfect synchronization was observed in the frequency 10/33 variations between the two buildings (Fig. 3a), RDT being able to detect very small fluctuations (less than 0.1%). Stronger transient variations, such as between the 10th and 11th of August, were also observed for the two buildings. Since the buildings are completely independent, the origin of these variations must be physical and directly related to different building stiffness or boundary conditions. The trend roughly follows the regional temperature curves provided by a meteorological station 20km from the buildings.

Correlations with the daily variations are clear and longer period of variations are also observed, such as during the second week of August. The same trend was previously observed by [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF], i.e. frequency increases with temperature. The scientific explanation for frequency variations has not yet been completely understood but it may result from the expansion of concrete or cladding in relation to sun exposure. For example, Fig. 3b shows the differences between behavior in the NS (L) and EW (T) directions.

Frequency variations are less correlated between T and L for either building (correlation coefficient C BD =0.75 and C MB =0.65), and more correlated between the buildings when the same direction is considered (C T =0.89 and C L =0.85). This can be explained by the effects of sun exposure, the same faces being exposed in the same manner for both structures.

Unlike with [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF] and [START_REF] Herak | Continuous monitoring of dynamic parameters of the DGFSM building (Zagreb, Croatia)[END_REF], no clear effects of rain and wind were observed (Fig. 3a). In our case, their effects may not have been strong enough to influence frequency, even though the building is founded on soft soil. Todorovska and Al Rjoub (2006) explained the frequency variations of the Millikan Library during rainfall by modification of the soil-structure interaction. For the wind, the data are not enough for doing the link between wind and frequency variation, further analysis are needed for definitively conclude, especially since the temperature is the dominant (at the first order) factor controlling the wandering. Some regional effects may also introduce a bias between the temperature at the meteorological station and at the building. Nevertheless, strong correlation are observed with temperature, let us assume a moderate regional effect.

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RDT is also used for long-term monitoring of the damping value (Fig. 4). No clear variations are observed in Fig. 4a, although the stability of the measurement may reflect the efficiency of RDT for damping estimation. One conclusion could be that damping is less sensitive to external conditions. In contrast to results obtained with stronger motion (e.g., [START_REF] Hart | Earthquake design of buildings: damping[END_REF][START_REF] Jeary | Damping in tall buildings, a mechanism and a predictor[END_REF]Tamura and Suganuma,1996;[START_REF] Li | Damping in buildings : its neural network model and AR model[END_REF]Satake et al., 2003), the frequency and damping are not clearly correlated at these levels of excitation (Fig. 4b), regardless of the building and the direction. Finally, the relationship between the modal parameters (frequency and damping) and the temperature is displayed in Fig. 4c. We observe an overall positive trend between frequency and temperature. The highest correlation parameter was observed for the T direction (C BD/T =0.56 -C MB/T =0.48 -C BD/L =0.36 -C MB/L =0.09), i.e. the direction of the longest facade, confirming the effects of exposure to sunlight. No clear correlation was observed for damping.

In conclusion, one clear observation is the accuracy of RDT that enables the monitoring of very small variations (~0.1 %) in modal frequencies. RDT provides the effective assessment of the building's frequency and damping, the accuracy of the measurement having coefficient of variation (σ/μ f ) close to 0.3% (Tab 1). These variations are of physical origin, related to the natural variations in building stiffness.

In these examples, temperature is the main parameter controlling the fluctuations. Using RDT, structural health monitoring can be achieved by distinguishing the natural (weatherrelated) frequency fluctuations from variations caused by natural aging or damage. Greater scattering are observed for damping than for frequency, but remain less than 10%, with σ/μ ξ between 9 and 14%, assuming effective and stable assessment of the damping value by RDT (Tab. 1).

ONE-YEAR OBSERVATION OF MODAL PARAMETERS

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In order to confirm the relevancy of RDT for long-term monitoring, two other buildings were tested (Fig. 2b): Grenoble city hall (CHB) and the Ophite tower (OT) in Lourdes (southwestern France). These two RC buildings are permanently monitored by accelerometric stations as part of the National Building Array program of the French Accelerometric Network (RAP, [START_REF] Pequegnat | The French accelerometric network (RAP) and national data centre (RAP-NDC)[END_REF]. Accelerometric sensors (EST-FBA) at the top of the building perform continuous recordings at 125Hz and transmit them in real time to the RAP National Data Centre hosted at the Institute of Earth Science (ISTerre, Grenoble). These structures were not designed to resist earthquakes and the original design report was not available to the authors.

The city hall building (CHB), fully described in Michel et al. (2010[START_REF] Michel | Seismic vulnerability assessment to slight damage based on experimental modal parameters[END_REF], is a 13storey RC building (Fig. 2b), built in 1967 (LxTxH=44x13x52m). The inter-storey height is regular between the 3rd and 12th floors (3.2m) and larger on the 1st (4.68m) and 2nd stories (8m), above which there is a pre-stressed slab with a 23m span, supported by two inner cores. These cores, consisting of RC shear walls, enclose the stairwells and lift shafts at the two opposite sides of the building and provide the lateral resistance system (Michel et al. 2010). This building is founded on soft sediment, composed of mud and soft clay; its foundations are deep piles anchored on a stiff sandy layer at a depth of around -15m. The orientation of the building is close to N°45, i.e. the two faces of the building are exposed to the sun for the same period every day. Michel et al. (2010) performed a modal analysis of the building: the fundamental modes in the L and T directions are 1.16Hz and 1.22Hz respectively, with a torsion mode at 1.45Hz. Overtones were also observed, confirmed by a 3D Finite-Element model of the building (Michel et al., 2010), but they are not energetic enough to be analyzed here. Glass cladding is present, attached to a steel frame on the external perimeter of the structure.

The Ophite tower (OT) is an 18-storey dwelling building built in 1972 (Fig. 2c). The inter-storey height is regular (3.3m) throughout the height, with a regular lateral resistance 13/33 system in the two horizontal directions, provided by RC shear walls. Its dimensions are 19m width (T), and 24m long (L). This building is founded on a rocky site, composed by Ophite rock, and we therefore assume a shallow foundation system. In addition, a temperature sensor is installed at the top of the OT which provides hourly temperature measurements. These values are influenced by the heat radiated by the building, thus reducing the amplitude of the temperature variations over the year. The orientation of the building is N°15, i.e. the L direction (close to the North-South direction) is more exposed to the sun. The fundamental frequencies of the building are 1.74Hz and 1.73Hz for the L and T directions respectively. Second bending modes were also observed, corresponding to 5.28Hz and 6.13Hz in the L and T directions respectively. An additional torsion mode was observed close to 2.2Hz, but this is not considered in this paper. Two different responses were observed for the two buildings (Fig. 5). Frequency wanderings are clearly related to temperature, variations (see Tab. 1) being less significant for the CHB building (σ/μ f close to 0.4%) than for the OT building (σ/μ f close to 1.0%). The behavior of the CHB building seems to be the opposite of that observed in the BD and MB buildings, i.e. the frequency decreases when the temperature increases. This is also clear during the winter season (end of the time series) during which strong and fast temperature variations were observed at the OT and CHB building. During the winter, the frequency increases with the decrease of the temperature for the CHB and with the increase of the temperature for the OT for several clearly observed cycles of temperature variations.

Moreover, a sudden response of the structure behavior was observed (as during december 2009 for the CHB) and we assume that the cladding effects must dominate in this case because of a slower diffusive effect of the temperature into the building. While for the CHB building, the L and T directions have similar variation amplitudes, the L direction of the OT building is more sensitive to heat than the T direction, which can be explained by the orientation, i.e. N°45 and N°15 for the CHB and OT buildings respectively. Moreover, 14/33 the different trends observed between both buildings could be explained by the cladding effects and/or by the soil-structure interaction, since the two buildings have different cladding and different foundations, in spite of having the same resistance design (RC shear walls).

For damping, no clear correlation was observed for the CHB, with mean values around 1.027% (σ/μ ξ =11.88%) and 1.034% (σ/μ ξ =13.93%) in the L and T directions respectively (Tab. 1). This was not the case for the OT building, for which the trend in damping variations was opposite to those of frequency and temperature, as also observed by [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF] and [START_REF] Herak | Continuous monitoring of dynamic parameters of the DGFSM building (Zagreb, Croatia)[END_REF]. The mean values of damping were 0.880% (σ/μ ξ =24.55%) and 0.827% (σ/μ ξ =15.96%) in the L and T directions respectively (Tab. 1).

This observation is also confirmed by Fig. 6 where frequency and damping are displayed for the CHB (Fig. 6a) and OT (Fig. 6b) buildings. For the latter building, the analysis of the second modes in the T and L directions are also shown, since the frequency modes were clearly detected using ambient vibrations. For the CHB, we observe a decrease in frequency as temperature increased (C L = -0.6 -C T = -0.6), the two faces of the building having the same exposure effect. This trend is opposite to that observed by [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF] and [START_REF] Herak | Continuous monitoring of dynamic parameters of the DGFSM building (Zagreb, Croatia)[END_REF], and for the two BD and MB twin towers too. No correlations are clearly put in evidence for the damping value (C L =0.02 -C T =0.12). On the contrary, the OT building showed a clear correlation between frequency and temperature, and also between damping and temperature, for the first and second modes (Fig. 6b). A change in trend was observed between the coldest (November to April) and warmest (May to October) months: the correlation parameter was C L1 = 0.69 and C T1 =0.84 (coldest) and C L1 = -0.32 and C T1 =0.51 (warmest). The same difference but opposite direction was observed for damping between the coldest and warmest months, i.e. damping decreased when temperature increased: C L1 = -0.74 and C T1 =-0.56 for the coldest months, and C L1 = 15/33 0.04 and C T1 =-0.06 for the warmest months. Frequency and damping must therefore be strongly correlated. The cladding effect could explain the first trend, i.e. an increase in stiffness related to the external windows exposed to the sun, also confirmed by the building orientation (N°15), while the second trend could be directly related to the effects of the concrete being exposed to the sun, reducing its Young's modulus. Similar trends were observed for the second mode of the OT building (Fig. 6b All these observations are consistent with the theory that the variations are physical in origin, apparently related to the temperature's effects on the cladding. Moreover, the Fourier transforms of temperature, frequency and damping are displayed in Fig. 7. A clear peak is observed for the CHB and OT buildings, corresponding to a period of about 24 hours, confirming a direct correlation with the daily variation of temperature.

DISCUSSION

The natural fluctuations of the two main parameters that classically control the seismic response of a building during an earthquake (i.e., frequency and damping) have been analysed under ambient noise solicitation. While frequency variations had already been studied [START_REF] Clinton | The observed wander of the natural frequencies in a structure[END_REF]Hezak 2010), few works had focused on damping. The use of RDT has shown its effectiveness in measuring damping and frequency variations for the long-term monitoring of buildings. In our study, the main parameter controlling the fluctuations is the outside temperature. This was confirmed by the analysis of the Ile Verte towers, two stand-alone buildings (BD and MB) with the same design, that showed the same frequency versus temperature trend, based on independent measurements and for 16/33 independent buildings. Conclusion is that these variations are of physical origin. By comparing horizontal direction behavior with respect to the building orientation, exposure to the sun seems to have a direct effect, influencing the overall stiffness of the building by acting on the cladding or external windows. No direct correlation with rain and wind was observed here due to a lack of strong atmospheric events.

While almost all previous studies showed a positive correlation between frequency and temperature (i.e., Clinton et al., 2006, Herak and[START_REF] Herak | Continuous monitoring of dynamic parameters of the DGFSM building (Zagreb, Croatia)[END_REF], no definitive conclusions can be drawn from this analysis. As a matter of fact, the frequency-vstemperature trend seems to depend on the building. The responses of the MB and BD buildings exhibit a positive correlation with temperature, CHB an anti-correlation and finally the OT building showed two different mechanisms, with a trend that changed between the coldest and warmest months. Additional data will be needed to draw definitive conclusions on the physical parameters explaining these trends. We can suggest some explanations.

All the buildings have different foundations, OT being on a rocky site while the MB, BD and CHB buildings rest on soft sediments. The soil-structure interaction affects the sensitivity of the building's response to external conditions. Todorovska and Al Rjoub (2006) have put forward such an explanation in the case of exceptional rainfall influencing soil properties. Cladding also differs from one building to another and the slight variations in frequency and damping could be directly related to this difference.

Nevertheless, RDT is an effective and robust tool that enables an accurate monitoring of the building response to ambient noise. The small variations observed are not related to the integrity of the building, assuming that less than 0.5% variation of the building fundamental frequency cannot be related to structural health but only to the natural fluctuations. This information is thus relevant for building monitoring, especially after extreme events when building tests using ambient vibrations are performed and compared with pre-event characteristics. Moreover, the modal parameters estimation

  ): for frequency, correlation coefficients were C 2L =0.78 and C 2T =0.83 for the coldest months and C 2L =-0.07 and C 2T =0.62 for the warmest; for damping, C 2L =-0.5 and C 2T =-0.23 for the coldest months and C 2L =-0.09 and C 2T =0.43 for the warmest.

Figure 1 :

 1 Figure 1: Schematic view of the Random Decrement Technique (RDT) used in this paper.

Figure 2 :

 2 Figure 2: Spectral analysis of the buildings of this study, using ambient vibrations recorded

Figure 3 :

 3 Figure 3: a. Frequency variations (normalized) of the Mont-Blanc (MB) and Belledonne

Figure 4 :

 4 Figure 4: a. Damping variations of the Mont-Blanc (MB) and Belledonne (BD) buildings in

Figure 5 :

 5 Figure 5: Frequency (a) and damping (b) variations for the City-Hall CHB (left) and Ophite

Figure 6 :

 6 Figure 6: Correlation between frequency and damping variations with temperature in the

Figure 7 :

 7 Figure 7: Fourier transform of the one-year temperature (upper row), building frequency

Figure 8 :

 8 Figure 8: Lognormal (L, black line) and normal (N, dashed grey line) distribution adjusted

Table 1 .

 1 Mean value, standard deviation and coefficient of variation of the frequency and damping obtained in the buildings using the Random Decrement Technique.

				L direction					T direction
	Bldg.	Frequency Hz		Damping %	Frequency Hz	Damping %
		μ f	σ	σ/μ f μ ξ	σ	σ/μ ξ	μ f	σ	σ/μ f μ ξ	σ	σ/μ ξ
	BD	0.890 0.003 0.33	1.094 0.099 9.05	0.672 0.002 0.29	0.666 0.073 10.96
	MB	0.837 0.003 0.36	0.855 0.099 11.57 0.648 0.002 0.31	0.586 0.081 13.82
	CHB	1.162 0.005 0.43	1.027 0.122 11.88 1.224 0.004 0.33	1.034 0.144 13.93
	OT	1.747 0.013 0.74	0.880 0.216 24.55 1.741 0.022 1.26	0.827 0.132 15.96

Note: μ: mean value; σ: standard deviation; σ/μ: coefficient of variation; BD: Belledonne building; MB: Mont-Blanc building; CHB: City-Hall of Grenoble; OT: Ophite tower; index f: frequency; index ξ: damping; L: longitudinal direction; T: transverse direction. 26/33

ACKNOWLEDGMENTS

This work was supported by the French Research National Agency (ANR) under the RiskNat program (project URBASIS n°ANR-09-RISK-009). Data were prepared with the help of Catherine Pequegnat, in the framework of the RESIF datacenter (http://www.resif.fr).

DATA AND RESOURCES

Accelerometric data used in this study were collected as part of the National Data Center of the French Accelerometric Network (RAP-NDC). Data can be obtained from the RAP-NDC at http://www␣rap.obs.ujf␣grenoble.fr/ (last accessed January 2011), part of the French Seismological and Geodetic Network (RESIF, http://www.resif.fr).

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using ambient vibration methods may be useful for reducing the model's uncertainties which are included in the fragility curves for seismic vulnerability (e.g. [START_REF] Michel | Seismic vulnerability assessment to slight damage based on experimental modal parameters[END_REF].

Figure 8 shows the normal and lognormal distribution of frequency and damping for the CHB and OT buildings. In both cases, σ was less than 0.01Hz and 0.2% for the frequency and damping values respectively. [START_REF] Nayeri | A novel approach for the structural identification and monitoring of a full-scale 17-story building based on ambient vibration measurements[END_REF] studied the variations of modal frequencies and damping in the Factor Building, a 17-storey steel frame structure located on the UCLA campus in California. They used a sophisticated method for modal analysis applied to ambient vibrations recordings over 50 days. The order of magnitude of the coefficient of variation σ/μ computed for the first mode was 1% with σ = 0.005, and close to 60% for damping with σ = 2.0. In the present work, RDT provided lower frequency variations (less than 0.3%) with σ =0.02 and of the damping coefficient (less than 15%) with σ = 0.2. These lower variations may be due to the type of building (steel frame for the Factor Building and RC shear walls for the buildings in our study) but may also be due to a more accurate assessment using RDT. Thanks to the fast operability of the RDT approach, long-term analysis can be envisaged for the permanent monitoring of buildings.

Moreover, the effect of the frequency and damping variation must be introducing into models for seismic vulnerability assessment. The RDT provides an accurate estimate of these parameters, reducing then the epistemic uncertainties to the model (Spence et al., 2003). This method opens new perspectives for engineering seismology, well adapted to continuous and real-time data that start to be more and more available.

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Vandiver, J. K., A. B. Dunwoody, R. B. Campbell, and M. F. Cook (1982). A mathematical basis for the random decrement vibration signature analysis technique, Journal of Mechanical Design 104, 307-313. Xu, G. Y., W. D. Zhu, and B. H. Emory (2007). Experimental and numerical investigation of structural damage detection using changes in natural frequencies, Journal of Vibration and Acoustics 129,no. 6,[686][687][688][689][690][691][692][693][694][695][696][697][698][699][700]


Jean-Luc Chatelain

Bertrand Guillier

Philippe Guéguen

Julien Fréchet

Jacques Sarrault

Ambient vibration recording for single-station, array and building studies made simple: CityShark II

This article describes an improved data acquisition system from a previous system dedicated to one-sensor site studies, aimed at recording ambient vibrations (microtremors). A multi-channel and/or remote triggering system is proposed. The system was conceived by IRD-Leas, France, and used at ISTerre, France, for research activities. The size, weight of this high quality system and its autonomy (no need to be connected to a laptop) make it a real portable device. The system acquires data with 24-bit delta-sigma ADCs in the 10 -1000 sps range at 10 -20 bit resolution on up to 18 channels in the multi-channel version. The input stage dynamics is available at ±2.5V or ±5V. The dynamic range varies, for example, from 108 dB at 100 sps to 90 dB at 250 sps. Gain is selectable from 1 (0 dB) to 8192 (78 dB) by powers of two (6 dB). Its very low level of internal noise allows recording of very low tension signals without missing code. Continuous recording and GPS may also be implemented in the system, and continuous recording is available. While primarily dedicated to ambient vibration recordings, this system can be connected to any type of instrument delivering an output tension in the ±5V range.

INTRODUCTION

CityShark II (Figure 1) is an enhanced version of the CityShark station [START_REF] Chatelain | CityShark: A user-friendly instrument dedicated to ambient noise (microtremor) recording for site and building response studies[END_REF], aimed at single-station, array and building studies using ambient vibration, or any low voltage signal, recordings. It has been developed at ISTerre by IRD, the French Institute for Research for Development, and LEAS, a French company dedicated to geophysical data acquisition.

Although CityShark has been very well rated for use in ambient vibration experiments, and ranked second among 12 tested stations in the SESAME equipment evaluation [START_REF] Guillier | the SESAME Project WP02-Team[END_REF][START_REF] Guillier | Influence of instruments on the H/V spectral ratios of ambient vibrations[END_REF]4], the need for such enhancement appeared because CityShark was originally designed to record data from only one sensor, without any time base, aimed at ambient vibration H/V and simple building studies. While it rapidly appeared that CityShark proved very adapted and reliable for H/V ambient vibration studies [4], the fact that no time reference was used in the data acquisition, as it is not necessary in H/V experiments or simple fundamental building frequency determination, turned out to be a burden when considering ambient vibration array experiments and/or determining buildings parameters such as modal deformation, for example. In other words, while possible with a bit of imagination, CityShark was complicated to use in getting synchronous ambient vibration recordings from several places/sites, and a multi-channels option appeared to be essential for array and building applications.

It has therefore been decided to develop an instrument, keeping the simple operating philosophy of CityShark, with new capabilities aimed at getting synchronous recordings.

CITYSHARK II

CityShark II follows the operating philosophy of CityShark, i.e. (1) all field operations are performed without a computer connected to the station, (2) push-buttons to set up recording parameters, as well as to manage the recording procedure, and (3) the station communicates with the operator through a 20-character 4line LCD built-in screen [START_REF] Chatelain | CityShark: A user-friendly instrument dedicated to ambient noise (microtremor) recording for site and building response studies[END_REF]. As for CityShark, the operating instruction manual simply fits in a single doublesided sheet.

CityShark users will have no surprise: CityShark II is lodged in the same type of case, i.e. it is not more voluminous (420 x 335 x 180 mm), although somewhat heavier (7 kg) in its 6-sensor configuration mainly because of the use of a more powerful internal battery (12V/7Ah). Also, the same sensor connectors are used (Souriau 851, i.e. Lennartz sensor compatibility). Active sensor(s) is/are powered through the station internal battery, although for longer studies it is possible to connect the station to an external battery or to power it with the battery charger. When used with six active sensors the power consumption is 200 mA, with an auto power-off mode in case of low battery voltage.

Main new features

The three main capabilities added to CityShark II are: (1) CityShark II is available in any configuration to synchronously record one (CityShark II-1) to six (CityShark II-6) 3C sensors, i.e. 3 to 18 channels, by step of 3, a CityShark II-1 being equivalent to the former CityShark; (2) an option for continuous recording, with data storage into files, which size is chosen by the operator, which allows applications such as short or/and long-term monitoring of structures (Mikael et al., 2012), for example for structural health monitoring. Thanks to the new features (2) and (3), it is now also possible to use CityShark II as an earthquake recording device; (3) CityShark II may be equipped with an embedded GPS receiver providing the time at start and at end of recording, as well as the site geographical coordinates; (4) CityShark II may be equipped with a remote triggering device. This option proves very useful to get synchronous records in large array experiment or on large structures such as bridges (over 100-200 m) for which the use of cables might be a constraint. The remote start is triggered using a 0.5 or 5-watt radio transmitter; (5) when interrupting a recording before its programmed end, the operator has the choice to either save the recorded data or to delete them, a convenient option to operate CityShark II for short experiments of unknown duration.

Other new features

Several convenient features have been added or changed from the original CityShark configuration: (1) the sample frequency range has been extended to 18 selectable rates in the 10 -1000 sps range, (2) display of actual battery voltage and choice of low-battery voltage cut-off, (3) automatic detection of faulty or unusable flash card, (4) programmable recording start, and (5) programmed repeating recording time in minutes during the first hour. Data download software has been developed for other systems than MS-Windows (see section below).

Future station software updates will be directly available on the LEAS website, and transferred to the station through the station flashcard reader.

CityShark II performances

CityShark II timing is based on a 1.5 ppm TCXO crystal, working in the -20°C +70°C range. The acquisition board comprises up to six modules of three 24-bit delta-sigma ADCs (one module per 3C-sensor), with input stage dynamics available at ±2.5V or ±5V. The dynamic range varies from 108 dB at 100sps to 90 dB at 250 sps. 14 selectable amplifier gains are available, from 1 (0 dB) to 8192 (78 dB), by powers of two (6dB).

Gain values

A test performed on gains shows that up to 512 gain values are within 0.001 -0.3 % from their nominal values, and from -5 to -6 % in the 1024 -8192 gain range, while variations throughout the 18 channels are less than 0.3 % in the entire 1 -8192 gain range. Voltage saturation does not produce any perturbation in the following recorded signal.

Internal noise, missing code, offsets and anti-aliasing filter

The first three parameters were evaluated trough statistical tests, performed using histogram techniques (distributions of the number of count values, i.e. the number of times a count value is reached, versus count values). The tests were first performed by recording the signal obtained without any sensor connected to any of the 18 channels, the entries being not short-circuited. In a second series of tests a 1-kΩ resistor has been connected between the two signal pins (+ and -) of the 18 input channels. Recordings were performed at 100 sps in both cases, on a CityShark II-6 and a CityShark II-1 respectively.

The average internal noise level reaches a value of ±1/131072 counts (± 19 µV) at gain 1 (Figure 2) and ±15/131072 counts (± 0.035 µV) at gain 8192. This high signal-to-noise ratio permits CityShark II to record very low amplitude signals, allowing, for example, to get a 0.4 Hz H/V peak from a 4.5-Hz seismometer (Figure 3).

These results also show that there is no missing code, as there is no "hole" in the number of count values, i.e. count values that are not reached within the distribution range, to the contrary of what is encountered with some other types of data acquisition systems [START_REF] Pillet | Missing Code et filtre anti-aliasing de deux acquisitions numériques[END_REF]. Offsets are within ±15 counts (± 275 µV) at gain 1 and ± 13600 counts (± 32 µV) at gain 8192.

The anti-aliasing filter has been tested by recording, at 125 sps, 2.5-Volt sine waveforms with frequencies varying from 12.5 Hz up to 375 Hz. To the contrary of what is observed for other recording devices, the CityShark II anti-aliasing filter works fine (Figure 4).

Synchronism in-between channels

A simultaneous recording of the same 1 Hz triangle-shape signal by all of the 18 CityShark II channels has been completed at 100 sps, using various gains. Then, in order to check their synchronism, the signal differences have been performed, after removing the trace offsets. As in the precedent test, results are shown as the distributions of the number of count values versus count values, which in this case should be Gaussian curves centered on zero, the deviations from zero being due to the combined effect of internal noise and the slight variations in gain value in-between channels. The results show a perfect synchronism between channels, as we indeed do obtain Gaussian curves centered on 0, without missing values (Figure 5). These curves also confirm that the combined effect of internal noise and variations in gain in-between channels is negligible.

Synchronism in-between stations using remote triggering

The synchronism of recording start-up in-between several stations when using the remote triggering has been evaluated by recording the logical level of 7 station receivers on an oscilloscope in two series of 4, with a reference station. The average delay is about 60 µs, with a maximum of about 125 µs (Figure 6).

OPERATING CITYSHARK II 3.1. Recording data

CityShark II works in a similar way to CityShark. Parameters and internal time settings are completed on the station itself, without connecting an external computer, with the help of two press-buttons labeled "gain up" and "gain down", with basically only three recording parameters to set up: gain, sample rate, and recording duration. Optional parameters can be set-up: the maximum percentage of clipped samples allowed during a record, a period of repeated recording, overwriting the default file index used in the data file. The signal level is indicated by a bar-graph on the built-in screen. For a more detailed description of operating CityShark, and on the way it works, see [START_REF] Chatelain | CityShark: A user-friendly instrument dedicated to ambient noise (microtremor) recording for site and building response studies[END_REF].

Retrieving data

CityShark II stores recorded data on a removable flash memory card, with storage capacity ranging from 32 MB to 4 GB. The flash card must be formatted and prepared on an external computer before its first operation. Once the data have been recorded, the flash card is read on a PC using ReadCity, software developed specifically to handle the CityShark data format for MS-Windows (Figure 7), Linux and Mac OSX systems. In the CityShark II station, data records are written on the flash card into a single large binary file, each record including a small header containing all relevant parameters. ReadCity allows to select some of or all these records, and to download them to the PC as ASCII files in a spreadsheet-ready format (Figure 8) or as binary files, at the operator convenience. After downloading in ASCII format it is possible to include any commentaries in the header, as long as they are added in-between the first and last line of the actual header. After saving the data, ReadCity can prepare the flash card for a new recording session by erasing all records and initializing the flash card header. Data are however not physically erased from the card, and a ReadCity option allows to retrieve them in the case of a mistakenly erasure, as long as no new record has been performed. Data analysis can be performed with standard scientific software or ambient vibration processing dedicated software. Alternatively, data files can be directly downloaded into the seismic SAC format, allowing using the large library of seismic software based on this format.

Results

CityShark II has been successfully used in various types of ambient vibration studies: buildings (Figure 9, and [6 -11]), ground arrays (Figure 10, and [12 -15]), landslides [START_REF] Lacroix | Caracterización de los procesos sismicos y gravitacionales sobre el deslizamiento de Maca (Colca, Peru)[END_REF] and single-station (H/V) [Figure 3, and [16 -22].

CONCLUSION

CityShark II is a very user-friendly instrument specially designed to meet a wide range of ambient vibration recording applications such as array or building dynamics studies, or any kind of low voltage signal, avoiding all unnecessary recording parameters that are part of operating a station devoted to earthquake recording. Portability of the station is assured through the station lightweight and its independence from external devices, i.e. external battery and computer. It is very easy to use by a non-specialist. Synchronous data acquisition for large size array or structure ambient vibration studies is made easy by using remote triggering, or postsynchronization during data processing when using GPS time.

With the continuous recording and GPS options CityShark II can also be used for earthquake recording operations.

Statistical tests, performed using histogram techniques, used to evaluate gain variations, offsets, absence of missing code, internal noise level, remote triggering and in-between channels synchronism proved CityShark II to be a very reliable data acquisition system.

The data software package, provided with the station, allows to format the flash card and retrieve data in ASCII spreadsheet-ready format, in an easy and time-effective way producing very easy to handle data files, or directly in Sac format. The software runs under the most common systems (MS-Windows, Linux, Mac OSX).

Finally, while mostly used in the framework of ambient vibration studies, CityShark II can handle any kind of low voltage signal. 8. Example of a CityShark II 3-channels data file retrieved using ReadCity. The original file name is transformed by adding the year, obtained from the internal date of the computer with which the data is retrieved, and hour minute are separated from the rest of the name by an underscore. File name may also include sensor number (1 to 6) when recording several sensors (e.g. Capt_1_050430_1612.001, and/or the station serial number (e.g. 050430_1612.001_001.001, Capt_1_050430_1612.001_001.001); the latter should be used when recording from several stations with the same time set. The conversion factor is the value by which following data, in counts, should be divided to get data in Volts at gain 1. This value should be divided by the gain for gain values over 1. Dynamic range is the full dynamic range (e.g. 5 Volts for ± 2.5 Volts). Maximum amplitude is the maximum absolute count value reached by the data. Other header parameters are self-explanatory. Commentaries may be included in the header in-between the first and last line, which must not be changed. Data are listed as a sample per line, in counts, in the Z, N-E, E-W order, i.e. signal from the A-B, C-D, and E-F input connector pins respectively.

Figure 1 .

 1 Figure 1. View of a CityShark II-6 station.

Figure 2 .

 2 Figure 2. Examples of histograms of count values from recordings obtained without any sensor connected toCityShark II for channels 1-3 (top, A) and channels 10-12 (bottom, B). Recordings were made at 100 sps and gain 1. The internal noise obtained from the half width of the Gaussian curves has a value of 1. The curves are centered on the channel offset value, which reached a maximum of 15. No "missing code" is evidenced, as within each curve all count values are reached.

Figure 3 .

 3 Figure3. Comparison of H/V curves from ambient vibration recordings, with a 0.4 Hz peak, obtained with a 5-second Lennartz seismometer (left) and a Mark Products 4.5-Hz seismometer (right) on the same ground site. The very low level of internal noise of CityShark II results in a very high signal/noise ratio, which allows obtaining the same peak frequency value (0.4 Hz) with both the 4.5-Hz and the 5-second seismometer, even though it is way below the 4.5-Hz seismometer frequency cut-off. Understandably, though, the H/V amplitude of the peak is lower when using the 4.5-Hz seismometer.

Figure 4 .

 4 Figure 4. Maximal count values from 2.5 Volts sine waveforms with frequencies in the 12.5 -375 Hz range recorded at 125 sps at gain 1 using a 10 V dynamic range CityShark II, showing the behavior of the antialiasing filter.

Figure 5 .

 5 Figure5. Examples of test of the synchronism in-between the 18 CityShark II channels. The same 1 Hz triangle is sent simultaneously on the 18 channels at 100 sps. The top of the figure (A and B) show002 s the differences in-between channels of the same acquisition board (channels 2 to 3), at gain 1 (A) and 8192 (B). The bottom of the figure (C and D) shows the differences in-between channels of different acquisition boards (channels 1, 7 and 18), at gain 1 (C) and 8192 (D). The only differences come from the slight gain variations from one channel to another, evidenced by the differences of the top values of the Gaussian curves.

Figure 6 .

 6 Figure 6. Example of starting time delays from 7 CityShark II-1 when using the remote triggering. Starting time is indicated by a downward step.

Figure 7 .

 7 Figure 7. ReadCity screen under MS-Windows system. ReadCity shall be used to download CityShark data from a flash card, and to erase data.

Figure

  Figure 8. Example of a CityShark II 3-channels data file retrieved using ReadCity. The original file name is transformed by adding the year, obtained from the internal date of the computer with which the data is retrieved, and hour minute are separated from the rest of the name by an underscore. File name may also include sensor number (1 to 6) when recording several sensors (e.g. Capt_1_050430_1612.001, and/or the station serial number (e.g. 050430_1612.001_001.001, Capt_1_050430_1612.001_001.001); the latter should be used when recording from several stations with the same time set. The conversion factor is the value by which following data, in counts, should be divided to get data in Volts at gain 1. This value should be divided by the gain for gain values over 1. Dynamic range is the full dynamic range (e.g. 5 Volts for ± 2.5 Volts). Maximum amplitude is the maximum absolute count value reached by the data. Other header parameters are self-explanatory. Commentaries may be included in the header in-between the first and last line, which must not be changed. Data are listed as a sample per line, in counts, in the Z, N-E, E-W order, i.e. signal from the A-B, C-D, and E-F input connector pins respectively.

Figure 9 .

 9 Figure 9. Example of determination of the transversal and longitudinal vibration modes of a 28-storey building from ambient vibrations simultaneously recorded with a CityShark II-6 station using five 4.5-Hz sensors (left). The fundamental frequency and the 1 st harmonic are clearly showing up. Higher modes need a zoom of the figure to show up. The first three modes of longitudinal deformations (right) are obtained from the amplitudes of the figure on the left.

Figure 10 .

 10 Figure 10. Example of result from a 8-sensor array ambient vibration recordings. Two 1-channel and one 6channel CityShark II were used, with remote triggering. The seismic shear-wave velocity model (right) is obtained from the Rayleigh wave dispersion curve (left).

Figure 1 Figure 2

 12 Figure 1

Figure 3

 3 Figure 3

Figure 4 - 11 -

 411 Figure 4

Figure 5

 5 Figure 5

Figure 6 - 12 -

 612 Figure 6

Figure 7 Figure 8

 78 Figure 7

Figure 10

 10 Figure 10

ACKNOWLEDGEMENTS

We had fruitful discussions with P.-Y. Bard, F. Dunand, and S. Bonnefoy-Claudet, who also helped to test Cityshark II through its validation process. This project has been funded by IRD (Institut de Recherche pour le Développement), a French public research institute, and LEAS company. Save public research.