Ambient Vibrations

Various types of vibration sources are always producing so-called Ambient Vibrations on the Earth ground (also called ambient noise). These vibrations are mostly surface waves (Rayleigh waves, Love waves) propagating on the surface. Low frequency waves (below 1 Hz) are generally called microseisms and high frequency waves (above 1 Hz) are called microtremors. These ambient vibrations are used in practice to derive the elastic properties of the ground and the low-strain dynamic properties of civil-engineering structures (bridges, buildings, dams...). This information is useful for different purposes : fundamental seismology, engineering seismology, Earthquake engineering, Seismic microzonation, Structural health monitoring, but also Hydrology, Geotechnical Engineering, etc.

Contents

Physical origin of the ambient vibrations

Bonnefoy-Claudet et al.[1] reviewed the scientific work studying the origin of the noise wavefield. At low frequency (below 1 Hz), the noise sources are natural and mostly due to ocean waves. In particular the peak between 0.1 and 0.3 Hz is clearly associated with the interaction of water waves of nearly equal frequencies but opposite directions[2][3][4][5]. At high frequency (above 1 Hz), the wavefield is mainly produced by human activities (road traffic, industrial work...) but there are also natural sources like rivers. Around 1 Hz, the local atmospheric conditions (wind...) are also a major source of ground vibrations. The amplitude of ground ambient vibrations is typically in the range of 1e-6 m, i.e. in the order of the tenth of micrometers to tens of micrometers. Peterson [6] provided high and low noise models as a function of frequency. The ambient wave field is made of a small amount of body waves (P- and S-waves), and a most generally predominant part of surface waves, i.e. Love and Rayleigh waves. Theses waves are dispersive, i.e. their phase velocity varies with frequency (most generally, it decreases with increasing frequency). The dispersion curve (phase velocity or slowness as a function of frequency) is tightly related to the variations of the shear-wave velocity with depth in the different ground layers: it can thus be used as a non-invasive tool to investigate the underground structure.

History of their use

Ground ambient vibrations have very low amplitudes and cannot be felt by humans. Their amplitude was also too low to be recorded by the first seismometers at the end of 19th century. However, at that time, the famous Japanese seismologist Fusakichi Omori could already record ambient vibrations in buildings, where the amplitudes are magnified. He found their resonance frequencies and studied their evolution as a function of damage [7]. After the 1933 Long Beach earthquake in California, a large experiment campaign led by Carder [8] in 1935 allowed to record and analyze ambient vibrations in more than 200 buildings. These data were used in the design codes to estimate resonance frequencies of buildings but the interest of the method went down until the 1950s. The interest on ambient vibrations in structures rose again thanks to famous earthquake engineers, especially in California and Japan (G. Housner, D. Hudson, K. Kanai and T. Tanaka [9]...). Ambient vibrations were however supplanted - at least for some time - by forced vibration techniques that allow to increase the amplitudes and control the shaking source and their system identification methods. Even if Trifunac [10] showed as early as 1972 that ambient and forced vibrations led to the same results, the interest in ambient vibration techniques rose again only in the late 1990s. The relatively low-cost and easiness of implementation, the improvement of the recording material and of the computation opportunities make these techniques very popular nowadays, especially as the low-strain dynamic characteristics they provide were shown to be close enough to the measured dynamic characteristics under strong shaking, at least as long as the buildings are not severely damages [11].

The use of noise recordings on the ground started in the 1950s with the enhancement of seismometers to monitor nuclear tests and the development of seismic arrays. The main contributions at that time for the analysis of these recordings came from the Japanese seismologist K. Aki [12] in 1957 who first proposed the methods used nowadays (Spatial Autocorrelation method -SPAC-, Frequency-wavenumber -FK- method, correlation method...). However, the practical implementation of these methods was not possible at that time because of the low precision of clocks in seismic stations. Again, the opportunities of computations and the enhancements in the recording material led to a rise of interest in the 1990s. The first widely implemented method, rediscovered by Nakamura [13] in 1989 is the Horizontal to Vertical Spectral Ratio (H/V) method to derive the resonance frequency of sites. Assuming that the shear wave dominates the microtremor, Nakamura indicated that the H/V spectral ratio of ambient vibrations were roughly equals the S-wave transfer function between the ground surface and the bedrock at a site. This assumption is however now criticized in the literature (e.g. SESAME project). In the late 1990s ([14],[15],[16],[17], among many others), the array methods on ambient vibration data started to allow deriving the ground properties in terms of shear waves velocity profiles. The European Research project SESAME [1] (2004–2006) was one of the first structured attempts to standardize the use of ambient vibrations to retrieve the properties of the ground, in the aim of estimating site amplifications in case of earthquake (site effects).

Current use of ambient vibrations

Characterization of the ground properties

The analysis of the ambient vibrations leads to different products used to characterize the ground properties. From the easiest to the most complicated, these products are: power spectra, H/V peak, dispersion curves and autocorrelation functions.

Single-station methods:

Array methods: Using an array of seismic sensors recording simultaneously the ambient vibrations allow to understand more deeply the wavefield and therefore to derive more properties of the ground. Due to the limitation of the available number of sensors, several arrays of different sizes may be realized and the results merged. The information of the Vertical components is only linked to the Rayleigh waves, and therefore easier to interpret, but method using the 3 space components are also developed, providing informations about Rayleigh and Love wavefield.

Characterization of the vibration properties of civil engineering structures

Like earthquakes, ambient vibrations force into vibrations the civil engineering structures like bridges, buildings or dams. This vibration source is supposed by the greatest part of the used methods to be a white noise, i.e. with a flat noise spectrum so that the recorded system response is actually characteristic of the system itself. The vibrations are perceptible by humans only in rare cases (bridges, high buildings). Ambient vibrations of buildings are also caused by wind and internal sources (machines, pedestrians...) but these sources are generally not used to characterize structures. The branch that studies the modal properties of systems under ambient vibrations is called Operational modal analysis or Output-only modal analysis and provides many useful methods for civil engineering. The observed vibration properties of structures integrate all the complexity of these structures including the load-bearing system, heavy and stiff non-structural elements (infill masonry panels...), light non-structural elements (windows...) and the interaction with the soil (the building foundation may not be perfectly fixed on the ground and differential motions may happen). This is emphasized because it is difficult to produce models able to be comparable with these measurements.

Single-station methods: The power spectrum computation of ambient vibration recordings in a structure (e.g. at the top floor of a building for larger amplitudes) gives an estimation of its resonance frequencies and eventually its damping ratio.

Transfer function method: Assuming ground ambient vibrations is the excitation source of a structure, for instance a building, the Transfer Function between the bottom and the top allows to remove the effects of a non-white input. This may particularly be useful for low signal-to-noise ratio signals (small building/high level of ground vibrations). However this method is not able to remove the effect of soil-structure interaction.

Arrays: They consist in the simultaneous recording in several points of a structure. The objective is to obtain the modal parameters of structures: resonance frequencies, damping ratios and modal shapes for the whole structure. Notice than without knowing the input loading, the participation factors of these modes cannot a priori be retrieved. Using a common reference sensor, results for different arrays can be merged.

Several methods use the power spectral density matrices of simultaneous recordings, i.e. the cross-correlation matrices of these recordings in the Fourier domain. They allow to extract the operational modal parameters (Peak Picking method) that can be the results of modes coupling or the system modal parameters (Frequency Domain Decomposition method).

Numerous system identification methods exist in the literature to extract the system properties and can be applied to ambient vibrations in structures

Inversion/Model updating/multi-model approach

The obtained results cannot directly give information on the physical parameters (S-wave velocity, structural stiffness...) of the ground structures or civil engineering structures. Therefore models are needed to compute these products (dispersion curve, modal shapes...) that could be compared with the experimental data. Computing a lot of models to find which agree with the data is solving the Inverse problem. The main issue of inversion is to well explore the parameter space with a limited number of computations of the model. However, the model fitting best the data is not the most interesting because parameter compensation, uncertainties on both models and data make many models with different input parameters as good compared to the data. The sensitivity of the parameters may also be very different depending on the model used. The inversion process is generally the weak point of these ambient vibration methods.

Material needed

The acquisition chain is mainly made of a seismic sensor and a digitizer. The number of seismic stations depends on the method, from single point (spectrum, HVSR) to arrays (3 sensors and more). Three components (3C) sensors are used except in particular applications. The sensor sensitivity and corner frequency depend also on the application. For ground measurements, velocimeters are necessary since the amplitudes are generally lower than the accelerometers sensitivity, especially at low frequency. Their corner frequency depends on the frequency range of interest but corner frequencies lower than 0.2 Hz are generally used. Geophones (generally 4.5 Hz corner frequency or greater) are generally not suited. For measurements in civil engineering structures, the amplitude is generally higher as well as the frequencies of interest, allowing the use of accelerometers or velocimeters with a higher corner frequency. However, since recording points on the ground may also be of interest in such experiments, sensitive instruments may be needed. Except for single station measurements, a common time stamping is necessary for all the stations. This can be achieved by GPS clock, common start signal using a remote control or the use of a single digitizer allowing the recording of several sensors. The relative location of the recording points is needed more or less precisely for the different techniques, requiring either manual distance measurements or differential GPS location.

Advantages and limitations

The advantages of ambient vibration techniques compared to active techniques commonly used in exploration geophysics or earthquake recordings used in Seismic tomography.

Limitations of these methods are linked to the noise wavefield but especially to common assumptions made in seismic:

See also

  1. Seismology

References

  1. ^ S. Bonnefoy-Claudet, F. Cotton, and P.-Y. Bard. The nature of noise wavefield and its applications for site effects studies. A literature review. Earth Science Review, 79:205–227, 2006.
  2. ^ M. S. Longuet-Higgins. A theory of the origin of microseisms. Phil. Trans. Roy. Soc. London A, 243:1–35, 1950.
  3. ^ K. Hasselmann. A statistical analysis of the generation of micro- seisms. Rev. of Geophys., 1(2):177–210, 1963.
  4. ^ S. Kedar, M. Longuet-Higgins, F. W. N. Graham, R. Clayton, and C. Jones. The origin of deep ocean microseisms in the north Atlantic ocean. Proc. Roy. Soc. Lond. A, 1–35, 2008.
  5. ^ F. Ardhuin, E. Stutzmann, M. Schimmel, and A. Mangeney. Ocean wave sources of seismic noise. J. Geophys. Res., 115, 2011 (in press).
  6. ^ Peterson (1993). Observation and modeling of seismic background noise, U.S. Geol. Surv. Tech. Rept. 93-322, 1–95.
  7. ^ C. Davison. Fusakichi Omori and his work on earthquakes. Bulletin of the Seismological Society of America, 14(4):240–255, 1924.
  8. ^ D. S. Carder. Earthquake investigations in California, 1934-1935, chapter 5 Vibration observations, pages 49–106. Number Spec. Publ. n201. U.S. Coast and Geodetic Survey, 1936.
  9. ^ Kanai, K., Tanaka, T., 1961. On microtremors VIII. Bulletin of the Earthquake Research Institute 39, 97–114
  10. ^ M. Trifunac. Comparison between ambient and forced vibration experiments. Earthquake Engineering and Structural Dynamics, 1:133–150, 1972.
  11. ^ Dunand, F., P. Gueguen, P.–Y. Bard, J. Rodgers and M. Celebi, 2006. Comparison Of The Dynamic Parameters Extracted From Weak, Moderate And Strong Motion Recorded In Buildings. First European Conference on Earthquake Engineering and Seismology (a joint event of the 13th ECEE & 30th General Assembly of the ESC) Geneva, Switzerland, 3–8 September 2006, Paper #1021
  12. ^ Aki, K. (1957). Space and time spectra of stationary stochastic waves, with special reference to microtremors, Bull. Earthquake Res. Inst. 35, 415–457.
  13. ^ Nakamura Y. A Method for Dynamic Characteristic Estimation of SubSurface using Microtremor on the Ground Surface. Q Rep Railway Tech Res Inst 1989;30(1):25–33.
  14. ^ Matshushima, T., and H. Okada, 1990. Determination of deep geological structures under urban areas using long-period microtremors, BUTSURI-TANSA, 43-1, p. 21-33.
  15. ^ Milana, G., S. Barba, E. Del Pezzo, and E. Zambonelli, 1996. Site response from ambient noise measurements: new perspectives from an array study in Central Italy, Bull. seism. Soc. Am., 86-2, 320-328.
  16. ^ Tokimatsu, K. , H. Arai, and Y. Asaka, 1996. Three-dimensional soil profiling in Kobé area using miccrotremors, Xth World Conf. Earthq. Engng., Acapulco, # 1486, Elsevier Science Ltd.
  17. ^ Chouet, B., G. De Luca, G. Milana, P. Dawson, M. Martini and R. Scarpa, 1998. Shallow velocity structure of Stromboli Volcano, Italy, derived from small-aperture array measurements of strombolian tremor, Bull. seism. Soc. Am., 88-3, 653-666.
  18. ^ Bonnefoy-Claudet, S., C. Cornou, P.-Y. Bard, F. Cotton, P. Moczo, J. Kristek and D. Fäh, 2006. H/V ratio: a tool for site effects evaluation. Results from 1D noise simulations. Geophys. J. Int, 167, 827-837.
  19. ^ Haghshenas, E., P.-Y. Bard, N. Theodulidis and SESAME WP04 Team, 2008. Empirical evaluation of microtremor H/V spectral ratio, Bulletin of Earthquake Engineering, 6-1, pp. 75-108, Feb. 2008.

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