Bulletin of the Seismological Society of America, Vol. 100, No. 5A, pp. 2322–2328, October 2010, doi: 10.1785/0120090285 Ⓔ Short Note Impulse Response of Civil Structures from Ambient Noise Analysis by German A. Prieto, Jesse F. Lawrence, Angela I. Chung, and Monica D. Kohler Abstract Increased monitoring of civil structures for response to earthquake motions is fundamental to reducing seismic risk. Seismic monitoring is difficult because typically only a few useful, intermediate to large earthquakes occur per decade near instrumented structures. Here, we demonstrate that the impulse response function (IRF) of a multistory building can be generated from ambient noise. Estimated shear- wave velocity, attenuation values, and resonance frequencies from the IRF agree with previous estimates for the instrumented University of California, Los Angeles, Factor building. The accuracy of the approach is demonstrated by predicting the Factor build- ing’s response to an M 4.2 earthquake. The methodology described here allows for rapid, noninvasive determination of structural parameters from the IRFs within days and could be used for state-of-health monitoring of civil structures (buildings, bridges, etc.) before and/or after major earthquakes. Online Material: Movies of IRF and earthquake shaking. Introduction Determining a building’s response to earthquake an elastic medium from one point to another; traditionally, it motions for risk assessment is a primary goal of seismolo- is the response recorded at a receiver when a unit impulse is gists and structural engineers alike (e.g., Cader, 1936a,b; applied at a source location at time 0. Çelebi et al., 1993; Clinton et al., 2006; Snieder and Safak, In many studies using ambient vibrations from engineer- 2006; Chopra, 2007; Kohler et al., 2007). Unfortunately, this ing structures (see Ivanovic et al., 2000 and references method of risk assessment is limited by the amount of therein), frequency domain analysis is performed to determine available data. A preciously small number of instrumented modal frequencies and mode shapes, sometimes including buildings exist that have recorded actual earthquake motions damping ratios. Usually, one would like to see if there are (Dunand et al., 2004), which can be used to verify building variations in modal parameters before and after major earth- response. Wavefield-based seismic analysis of full-scale quakes (Snieder et al., 2007) or before and after retrofitting instrumented structures can yield important information (Celebi and Liu, 1998). for earthquake engineering: seismic velocity, frequency- Traveling wave phase properties may also be useful for dependent attenuation, resonant frequencies, and mode identifying damage by providing additional information shapes (Snieder and Safak, 2006; Kohler et al., 2007). about changes in elastic parameters that result in variations With increases in data quantity, computer power, and in wave speeds, travel times for specific phases (e.g., the initial disk storage, seismologists recently began analyzing large direct shear wave), and reflection coefficients (e.g., Brenguier, volumes of ambient noise field data to determine the struc- Campillo, et al., 2008). For example, Muto et al. (2007) ture of the Sun (Rickett and Claerbout, 1999) and the Earth showed numerically how the introduction of fractured welds (e.g., Sabra et al., 2005; Shapiro et al., 2005; Yao et al., on three floors of one wall of a finite-element model of a high 2006; Villaseñor et al., 2007; Zheng et al., 2008, Prieto et al., rise subjected to small-amplitude earthquake excitation gave 2009). Aki (1957) first proposed a method to study subsur- rise to a new propagating torsional wave. For elastic struc- face phase velocity beneath a seismic array using spatial tures, traveling wave techniques to determine the location autocorrelations. Later, Claerbout (1968) suggested that and time of occurrence of a high-frequency damage event that temporal averaging of these spatial correlations could yield has been recorded on a seismic network (Kohler et al., 2009; impulse response functions (IRF). This technique requires Heckman et al., 2010) is not very common in the literature, as analysis of large data volumes, which was computationally opposed to passive damage detection methods that do not rely cumbersome until recently. Fundamentally, an IRF is an em- on active sources (e.g., Sabra et al., 2007; Nayeri et al., 2008; pirical function describing the propagation of waves through Duroux et al., 2010). 2322 Short Note 2323 Snieder and Safak (2006) calculated IRFs by using inter- 17 east–west channels along the southern wall of the Factor ferometry on earthquake data from each floor in an instrumen- building. The sensor locations are shown in Figure 1. Factor ted building (the Millikan Library in Pasadena, California). array data have previously been analyzed for mode identifica- Phase information allowed them to obtain the time domain tion using ambient vibrations and earthquakes (Kohler et al., IRF of the building and observe propagating waves inside 2005; Skolnik et al., 2006; Nayeri et al., 2008). Twenty small- 2:5 <M < 6:0 it. More recently, Michel et al. (2008) compared building to-medium ( L ) earthquakes were recorded motions with predictions obtained through ambient vibra- between 2004 and 2005, enabling calculation of impulse tions. They used a frequency domain decomposition method response functions with interferometric methods (Kohler for modal parameter analysis and were able to simulate the et al., 2007). Different sources (such as wind and mechanical motion of the building due to a weak-to-moderate earthquake. devices) also excite the building, enabling further estimation Their study illustrates the limitations, however, of working of dynamic characteristics (Nayeri et al., 2008). The Factor solely in the spectral domain because of difficulties that often building array provides an excellent set of data with which arise in trying to identify true spectral peak and spectral ratios, we compare results from the new ambient noise technique especially when the data are not broadband in nature. with those of previous earthquake-based techniques. Previous studies (Snieder and Safak, 2006; Kohler et al., 2007; Snieder, 2009) have obtained IRFs from recorded Transfer Function and Impulse Response motions excited by an earthquake using interferometric methods. In this study, we demonstrate for the first time that The transfer function describing a linear medium’s out- IRFs for multistory buildings can also be retrieved using put response to an input force excitation provides an empiri- ambient noise only. cal impulse response function, I t, for the medium between These IRFs can then be used to study (1) modal param- the input, f t, and output, u t, locations (utIt × ft eters of the building, (2) wave propagation inside the build- or Iωuω=fω in the frequency response domain, e.g., ing, (3) estimates of the quality factor (Q) associated with the Meirovitch, 1997). The IRF results from the constructive normal modes, and (4) predictions of building response to interference of signals from stationary source locations and scenario ground motions of moderately sized earthquakes. destructive interference from nonstationary source locations. Given the presence of continuous background noise gener- Time averaging over a longer duration for numerous random ated by man-made and natural sources, only a short duration sources ensures a sufficiently uniform source distribution of time series data may be needed to obtain stable results. (e.g., Campillo, 2006; Bensen et al., 2007). This leads to the possibility of rapid structural monitor- Snieder (2009) discussed the advantages of analyzing ing through ambient vibrations without the need to wait for the transfer function in the time domain rather than in the subsequent earthquakes as proposed in Snieder et al. (2007). frequency domain. In Figure 2, for example, it is pretty clear As discussed by Ivanovic et al. (2000), monitoring using that the waveforms represent the interference of upgoing and ambient vibrations has been used since the 1970s, mostly downgoing waves arriving from opposite arrival times. From studying the modal shape variations. For example, Nayeri the amplitude spectrum, this interpretation would not be et al. (2008) determined modal parameters using ambient trivial. Clearly, both domains provide complementary infor- vibrations and observed a strong correlation of the parameter mation about the impulse response of the building. variations with temperature. Noise-correlation (interfero- For each station and for each 10-min ambient noise data metric) methods without active sources have also been tested series, we compute impulse response functions with respect to in laboratory-scale mechanical systems. The impulse re- the lowest floor along the south wall (sub-basement level). sponse of a metal hydrofoil due to changes in mounting con- The results were averaged for 1-, 14-, 30-, and 50-day dura- ditions before and after large-amplitude load fluctuations tions. In order to compensate for each source having varying was computed from high-frequency (>400 Hz) ambient amplitudes at each frequency, the 10-min subsets of the vibration cross correlations (Sabra et al., 2007). ambient noise field are normalized (i.e., whitened) per fre- quency using a multitaper technique (Prieto et al., 2009). Data Processing To avoid the effects of transients, windows with large ampli- tudes are not used in calculating