Experiments on the stability of the spatial autocorrelation method (SPAC) and linear array methods and on the imaginary part of the SPAC coefficients as an indicator of data quality

Sos Margaryan; Toshiaki Yokoi; Koichi Hayashi

doi:10.1071/EG08101

RESEARCH ARTICLE

Previous Next Contents Vol 40(1)

Experiments on the stability of the spatial autocorrelation method (SPAC) and linear array methods and on the imaginary part of the SPAC coefficients as an indicator of data quality

Sos Margaryan ¹ ³ Toshiaki Yokoi ¹ Koichi Hayashi ²

+ Author Affiliations

- Author Affiliations

¹ International Institute of Seismology and Earthquake Engineering, Building Research Institute, 1 Tachihara, Tsukuba, Ibaraki 305-0802, Japan.

² OYO Corporation, 43 Miyukigaoka, Tsukuba, Ibaraki 305-0802, Japan.

³ Corresponding author. Email: msos78@hotmail.com

Exploration Geophysics 40(1) 121-131 https://doi.org/10.1071/EG08101
Submitted: 2 November 2007 Published: 27 February 2009

Abstract

In recent years, microtremor array observations have been used for estimation of shear-wave velocity structures. One of the methods is the conventional spatial autocorrelation (SPAC) method, which requires simultaneous recording at least with three or four sensors. Modified SPAC methods such as 2sSPAC, and linear array methods, allow estimating shear-wave structures by using only two sensors, but suffer from instability of the spatial autocorrelation coefficient for frequency ranges higher than 1.0 Hz.

Based on microtremor measurements from four different size triangular arrays and four same-size triangular and linear arrays, we have demonstrated the stability of SPAC coefficient for the frequency range from 2 to 4 or 5 Hz. The phase velocities, obtained by fitting the SPAC coefficients to the Bessel function, are also consistent up to the frequency 5 Hz. All data were processed by the SPAC method, with the exception of the spatial averaging for the linear array cases. The arrays were deployed sequentially at different times, near a site having existing Parallel Seismic (PS) borehole logging data.

We also used the imaginary part of the SPAC coefficients as a data-quality indicator. Based on perturbations of the autocorrelation spectrum (and in some cases on visual examination of the record waveforms) we divided data into so-called ‘reliable’ and ‘unreliable’ categories. We then calculated the imaginary part of the SPAC spectrum for ‘reliable’, ‘unreliable’, and complete (i.e. ‘reliable’ and ‘unreliable’ datasets combined) datasets for each array, and compared the results. In the case of insufficient azimuthal distribution of the stations (the linear array) the imaginary curve shows some instability and can therefore be regarded as an indicator of insufficient spatial averaging. However, in the case of low coherency of the wavefield the imaginary curve does not show any significant instability.

Key words: imaginary spatial autocorrelation coefficient, linear array, microtremor, spatial autocorrelation, stability.

Acknowledgments

We are grateful to Professor Michael Asten for valuable comments and suggestions. The comments of the Associate Editor, Dr Binzhong Zhou and reviewer Professor Anderson helped us to improve the manuscript. We thank Mr. Chisato Konishi and Mr. Toru Suzuki who helped us for conducting array observation. The authors also express their gratitude to the Japan Society for the Promotion of Science for financial support during the period of this study.

References

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.
Ling S. , and Okada H. , 1993, An extended use of the spatial autocorrelation method for the estimation of geological structure using microtremors: Proceedings of the 89th SEGJ Conference, 44–48 (in Japanese).

Margaryan S. , 2006, Determination of S-wave velocity structure using array microtremor measurements: conventional and two-site spatial autocorrelation method: Proceedings of the First European Conference on Earthquake Engineering and Seismology, Paper No. 478.

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.
| Crossref | GoogleScholarGoogle Scholar | Okada H. , 1998, Microtremors as an exploration method: Geo-exploration Handbook, vol. 2, Society of Exploration Geophysicists of Japan.

Okada H. , 2003, The microtremor survey method (translated by Koya Sato): Geophysical monograph series, No. 12, Society of Exploration Geophysicists.

Okada, H., 2006, Theory of efficient array observations of microtremors with special reference to the SPAC method: Exploration Geophysics 37, 73–85.
| Crossref | GoogleScholarGoogle Scholar | Suzuki H. , and Takahashi T. , 1999, S-wave Velocity Survey in Tsukuba City by Array Microtremor Measurements – Comparison with deep borehole data: Proceedings of the 101st SEGJ Conference, 50–53.

Tsuno S. , and Kudo K. , 2004, On the efficiency and precision of array analysis of microtremors by the SPAC method in practical engineering use: The 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, Paper No. 345.

Yamanaka H. , 2004, Application of heuristic search methods to phase velocity inversion in microtremor array exploration: Conference Proceedings of the 13th World Conference of Earthquake Engineering, Paper No. 1161.

Yamanaka, H., and Ishida, H., 1996, Application of genetic algorithms to an inversion of surface-wave dispersion data: Bulletin of the Seismological Society of America 86, 436–444.
Yokoi T. , 2005, Combination of Down Hill Simplex Algorithm with Very Fast Simulated Annealing Method – An effective cooling schedule for inversion of surface wave’s dispersion curve: Proceedings of the Fall Meeting of Seismological Society of Japan. B049.