1887
Volume 37, Issue 1
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Array observations of the vertical component of microtremors are frequently conducted to estimate a subsurface layered-earth structure on the assumption that microtremors consist predominantly of the fundamental mode Rayleigh waves. As a useful tool in the data collection, processing and analysis, the spatial autocorrelation (SPAC) method is widely used, which in practice requires a circle array consisting of circumferential stations and one centre station (called “M-station circle array”, where is the number of stations). The present paper considers the minimum number of stations required for a circle array for efficient data collection in terms of analytical efficacy and field effort.

This study first rearranges the theoretical background of the SPAC algorithm, in which the SPAC coefficient for a circle array with infinite is solely expressed as the Bessel function, () ( is the radius and k the wavenumber). Secondly, the SPAC coefficient including error terms independent of the microtremor energy field for an -station circle array is analytically derived within a constraint for the wave direction across the array, and is numerically evaluated in respect of these error terms. The main results of the evaluation are: 1) that the 3-station circle array when compared with other 4-, 5-, and 9-station arrays is the most efficient and favourable for observation of microtremors if the SPAC coefficients are used up to a frequency at which the coefficient takes the first minimum value, and 2) that the Nyquist wavenumber is the most influential factor that determines the upper limit of the frequency range up to which the valid SPAC coefficient can be estimated.

© 2006 ASEG
Loading

Article metrics loading...

/content/journals/10.1071/EG06073
2006-03-01
2026-01-14

  • From This Site

    /content/journals/10.1071/EG06073
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Aki, K., 1957, Space and time spectra of stationary stochastic waves, with special reference to microtremors: Bulletin of the Earthquake Research Institute, 35, 415–456.
  2. Aki, K., 1965, A note on the use of microseisms in determining the shallow structures of the earth’s crust: Geophysics, 30, 665–666.
  3. Aki, K., Tsujiura, M., Hori, M., and Goto, K., 1958, Spectral study of near earthquake waves (1): Bulletin of the Earthquake Research Institute, 36, 71–98.
  4. Arfken, G.B., and Weber, H.J., 2001, Mathematical Methods for Physicists (5th edition): Academic Press.
  5. Apostolidis, P., Raptakis, D., Roumelioti, Z., and Pitilakis, K., 2004, Determination of S-wave velocity structure using microtremors and spac method applied in Thessaloniki (Greece): Soil Dynamics and Earthquake Engineering, 24, 49–67.
  6. Asten, M.W., 2003, Lessons from alternative array design used for high-frequency microtremor array studies: in Earthquake Risk Mitigation, Wilson, J.L., Lam, N.K., Gibson, G.M., and Butler, B., Proceedings of a Conference of the Australian Earthquake Engineering Society, Melbourne, Paper No. 14.
  7. Asten, M.W., 2004, Passive seismic methods using the microtremor wave field: 17th Geophysical Conference and Exhibition, Australian Society of Exploration Geophysicists, Extended Abstracts.
  8. Asten, M.W., 2005, On bias and noise in passive seismic data from finite circular array data processed using SPAC methods: (preprint).
  9. Asten, M.W., and Henstridge, J.D., 1984, Array estimators and the use of microseisms for reconnaissance of sedimentary basins: Geophysics, 49, 1828–1837.
  10. Asten, M.W., Dhu, T., and Lam, N., 2004, Optimised array design for microtremor array studies applied to site classification; observations, results and future use: Conference Proceedings of the 13th World Conference of Earthquake Engineering, Paper 2903.
  11. Capon, J., 1969, High-resolution frequency-wavenumber spectrum analysis: Proceedings of the Institute of Electrical and Electronics Engineers, 57, 1408–1418.
  12. Chatfield, C., 1989, The Analysis of Time Series, an Introduction, 4th edition: Chapman and Hall.
  13. Cho, I., Tada, T., and Shinozaki, Y., 2004, A new method to determine phase velocities of Rayleigh waves from microseisms: Geophysics, 69, 1535–1551.
  14. Chouet, B., De Luca, G., Milana, G., Dawson, P., Martini, M., and Scarpa, R., 1998, Shallow velocity structure of Stromboli Volcano, Italy, derived from smallaperture array measurements of Strombolian tremor: Bulletin of the Seismological Society of America, 88, 653–666.
  15. Henstridge, J.D., 1979, A signal processing method for circular arrays: Geophysics, 44, 179–184.
  16. Hidaka, E., 1985, Phase velocity of Rayleigh waves and S-wave velocity distribution estimated from long-period microtremors: M.Sc. thesis (unpublished), Hokkaido University.
  17. Horike, M., 1985, Inversion of phase velocity of long-period microtremors to the S-wave-velocity structure down to the basement in urbanized areas: Journal of Physics of the Earth, 33, 59–96.
  18. Hough, S.E., Seeber, L., Rovelli, A., Malagnini, L., DeCesare, A., Selveggi, G., and Lerner-Lam, A., 1992, Ambient noise and weak-motion excitation of sediment resonances: results from the Tiber Valley, Italy: Bulletin of the Seismological Society of America, 82, 1186–1205.
  19. Kudo, K., Kanno, T., Okada, H., Özel, O., Erdik, M., Sasatani, T., Higashi, S., Takahashi, M., and Yoshida, K., 2002, Site specific issues for strong ground motions during the Kocaeli, Turkey Earthquake of August 17, 1999, as inferred from array observations of microtremors and aftershocks: Bulletin of the Seismological Society of America, 92, 448–465.
  20. Lacoss, R.T., Kelly, E.J., and Toksöz, M.N., 1969, Estimation of seismic noise structure using arrays: Geophysics, 34, 21–38.
  21. Malagnini, L., Rovelli, A., Hough, S.E., and Seeber, L., 1993, Site amplification estimates in the Garigliano Valley, central Italy, based on dense array measurements of ambient noise: Bulletin of the Seismological Society of America, 83, 1744–1755.
  22. Matsuoka, T., Umezawa, N., and Makishima, H., 1996, Experimental studies on the applicability of the spatial autocorrelation method for estimation of geological structures using microtremors: Butsuri Tansa, 49, 26–41.
  23. Matsuoka, T., and Shiraishi, H., 2002, Application of an exploration method using microtremor array observations for high resolution surveys of deep geological structures in the Kanto plains – Estimation of 3-D S-wave velocity structure in the southern part of Saitama prefecture : Butsuri Tansa, 55, 127–143.
  24. Matsushima, T. and Okada, H., 1989, A few remarks of the scheme of observation and analysis in estimating deep geological structures by using long-period microtremors: Geophysical Bulletin of Hokkaido University, 52, 1–10.
  25. Matsushima, T. and Ohshima, H., 1989, Estimation of underground structures using long-period microtremors – Kuromatsunai Depression, Hokkaido: Butsuri Tansa, 42, 97–105.
  26. Matsushima, T. and Okada, H., 1990, Determination of deep geological structures under urban areas: Butsuri Tansa, 43, 21–33.
  27. Miyakoshi, K., Okada, H., Sasatani, T., Moriya, T., Ling, S., and Saito, S., 1994, Estimation of geological structure under ESG blind prediction test sites in Odawara city by using microtremors: Journal of the Seismological Society of Japan, 47, 273–285.
  28. Miyakoshi, K., Okada, H., and Ling, S., 1996, Maximum wavelength possible to estimate phase velocities of surface waves in microtremors: Proceedings of the 94th SEGJ Conference, 178–182.
  29. Morikawa, H., Sawada, S., and Akamatsu, J., 2004, A method to estimate phase velocities of Rayleigh waves using microseisms simultaneously observed at two sites: Bulletin of the Seismological Society of America, 94, 961–976.
  30. Nguyen, F., Rompaey, V., Teerlynck, H., Van Camp, M., Jongmans, D., and Camelbeeck, T., 2004, Use of microtremor measurement for assessing site effects in Northern Belgium –interpretation of the observed intensity during the Ms = 5.0 June 11 1938 earthquake: Journal of Seismology, 8, 41–56.
  31. Okada, H., 1998, Microtremors as an exploration method: Geo-exploration Handbook, vol.2, Society of Exploration Geophysicists of Japan.
  32. Okada, H., 2003, The Microtremor Survey Method (translated by Koya Suto): Geophysical Monograph Series, No.12, Society of Exploration Geophysicists.
  33. Okada, H., and Sakajiri, N., 1983, Estimates of an S-wave velocity distribution using long-period microtremors: Geophysical Bulletin of Hokkaido University, 42, 119–143.
  34. Okada, H., Matsushima, T., and Hidaka, E., 1987, Comparison of spatial autocorrelation method and frequency-wavenumber spectral method of estimating the phase velocity of Rayleigh waves in long-period microtremors: Geophysical Bulletin of Hokkaido University, 49, 53–62.
  35. Okada, H., Matsushima, T., Moriya, T., and Sasatani, T., 1990, An exploration technique using long-period microtremors for determination of deep geological structures under urbanized areas: Butsuri Tansa, 43, 402–417.
  36. Okada, H., Matsuoka, T., Shiraishi, H., and Hachinohe, S., 2003, Spatial autocorrelation algorithm for the microtremor survey method using semicircular arrays: Proceedings of the 109th SEGJ Conference, 183–186.
  37. Priestley, M.B., 1981, Spectral Analysis and Time Series: Academic Press.
  38. Roberts, J.C., and Asten, M.W., 2004, Resolving a velocity inversion at the geotechnical scale using the microtremor (passive seismic) survey method: Exploration Geophysics, 35, 14–18.
  39. Roberts, J.C., and Asten, M.W., 2005, Estimating the shear velocity profile of Quaternary silts using microtremor array (SPAC) measurements: Exploration Geophysics, 36, 34–40.
  40. Sasatani, T. (Head Investigator), 2000, Earthquake disaster evaluation based on estimation of deep underground structure and observation of strong ground motion in deep sedimentary basins: A Report of the Study on Fundamental Science with Grant-in-Aid for Scientific Research (B)(2) by the Ministry of Education, No. 10480090, 164pp.
  41. Sasatani, T., Yoshida, K., Okada, H., Nakano, O., Kobayashi, T., and Ling, S., 2001, Estimation of deep subsurface structures and observation of strong ground motions in Sapporo urban districts: J. JSNDS, 20, 325–342.
  42. Sheriff, R.E., and Geldart, L.P., 1983, Exploration Seismology, vol. 2: Cambridge University Press.
  43. Watson, G.N., 1952, A Treatise on the Theory of Bessel Functions (2nd edition): Cambridge University Press.
  44. Yaglom, A.M., 1962, An introduction to the theory of stationary random functions (translated and edited by R.A. Silverman): Dover Publications Inc.
  45. Yamamoto, H., Iwamoto, K., Saito, T., and Yoshida, A., 1997, Discussion on sensor location in circular array for spatial autocorrelation method: Proceedings of the 96th SEGJ Conference, 444–447.
  46. Yamanaka, H., Takemura, M., Ishida, H., Ikeura, T., Nozawa, T., Sasaki, T., and Niwa, M., 1994, Array measurements of long-period microtremors and estimation of S-wave velocity structure in the western part of the Tokyo metropolitan area: Journal of the Seismological Society of Japan, 47, 163–172.
  47. Yamanaka, H., Sato, H., Kurita, K., and Seo, K., 1999, Array measurements of longperiod microtremors in southwestern Kanto plain, Japan, – Estimation of S-wave profiles in Kawasaki and Yokohama cities: Journal of the Seismological Society of Japan, 51, 355–365.
/content/journals/10.1071/EG06073
Loading
  • Article Type: Research Article
Keyword(s): Bessel functions; efficient circular array; microtremor method; Rayleigh waves; SPAC coefficient

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error