Application of the spatial auto-correlation method for site effect evaluation using ambient noise

Michael Asten, Koichi Hayashi

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Natural vibrations on the surface of the Earth are termed ambient noise or microtremors. Such energy is generated by the various sources, such as wind, ocean waves at the seashore, traffic noise, heavy machinery, factories and household appliances. Because microtremors are generated by sources on the ground surface, the energy propagates mainly as surface waves. The vertical component of the microtremor energy is associated with Rayleigh waves which are primarily sensitive to the S-wave velocity-depth profile of the locality, and the phase velocity of such energy allows construction of a dispersion curve. Microtremors used in Spatial Auto-Correlation (SPAC) methods consist of a wide frequency range of surface waves from the frequency of about 0.1 Hz to several tens of Hz. The wavelengths (and hence depth sensitivity of such surface waves) allows determination of the site S-wave velocity model from a depth of one or two meters down to a maximum of several kilometers; it is a passive seismic method using only ambient noise as the energy source.
Ambient noise methods use a 2D seismic array with a small number of seismometers (generally between two and fifteen) to estimate the phase velocity dispersion curve and hence the S-wave depth profile for the site. A large number of methods have been proposed and used to estimate the dispersion curve; SPAC is the one of the oldest and the most commonly used methods due to its versatility and minimal instrumentation requirements. We show that direct fitting of observed and model SPAC spectra gives a superior bandwidth of useable data than does the more common inversión after the intermédiate step of constructing an observed dispersión curve.
Current case histories demonstrate the method with a range of array types including two-station arrays, L-shaped multi-station arrays, triangular and circular arrays. Array sizes from a few meters to several-km diameters have been successfully deployed in sites ranging from downtown urban settings to rural and remote desert sites.
A fundamental requirement of the method is the ability to average wave propagation over a range of azimuths; this can be achieved with either or both of the wave sources being widely distributed in azimuth, and the 2D array sampling the wave-field over a range of azimuths. Several variants of the method extend its applicability to under-sampled data from sparse arrays, the complexity of multiple-mode propagation of energy, and the problem of precise estimation where array geometry departs from an ideal regular array. We find that sparse nested triangular arrays are generally sufficient, and the use of high-density circular arrays is unlikely to be cost-effective in routine applications.
Passive seismic arrays should be the method of first choice when characterizing Vs30 and deeper, with active seismic methods being a complementary method for use if and when condition so require.
The use of computer inversion methodology allows estimation of not only the S-wave velocity profile but parameter uncertainties in terms of layer thickness and velocity. The coupling of SPAC methods with horizontal:vertical particle motion spectral ratio analysis generally allows use of lower frequency data with consequent resolution of deeper layers, than is possible with SPAC alone.
Considering its non-invasive methodology, logistical flexibility, simplicity, applicability, and stability, the SPAC method and its various modified extensions will play an increasingly important role in site effect evaluation. The paper summarizes the fundamental theory of the SPAC method, reviews recent developments, and offers recommendations for future blind studies.
Original languageEnglish
Title of host publication16th World Conference on Earthquake Engineering
Subtitle of host publication16WCEE 2017
Number of pages12
Publication statusPublished - 2017
EventWorld Conference on Earthquake 2017 - Santiago, Chile
Duration: 9 Jan 201713 Jan 2017
Conference number: 16th


ConferenceWorld Conference on Earthquake 2017
Abbreviated titleWCEE 2017


  • Passive seismic
  • active seismic
  • micrtremor
  • ambient noise
  • surface wave
  • Rayleigh wave
  • Vs30
  • seismic array
  • HVSR
  • SPAC
  • Vobs
  • Vmodel

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