Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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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

공간자기상관법 (SPAC)의 안정성과 선형 배열법과 자료 품질 지시자로 활용되는 SPAC 계수의 허수 성분에 대한 실험

  • Margaryan, Sos (International Institute of Seismology and Earthquake Engineering, Building Research Institute) ;
  • Yokoi, Toshiaki (International Institute of Seismology and Earthquake Engineering, Building Research Institute) ;
  • Hayashi, Koichi (OYO Corporation)
  • Published : 2009.02.28
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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.

최근 상시 진동 탐사법은 횡파 속도 구조의 규명을 위하며 이용되고 있다 상시 진동 탐사법 중 공간자기상관(SPAC)법은 적어도 3 혹은 4개의 수신기에서 동시에 기록된 자료를 이용한다. 2sSPAC과 선형 배열 상시 진동법과 같은 수정된 SPAC법은 2개의 수신기 자료만 이용하여 횡파 속도를 추정할 수 있지만, 1.0 Hz 이상의 주파수 대역에 대한 공간 자기상판 계수가 불안정해지는 문제점을 가지고 있다. 4개의 서로 다른 크기의 삼각형 배열과 4개의 같은 크기의 삼각형 및 선형 배열을 이용한 상시 진동 측정치에 근거하여, 2 Hz 에서 4 Hz 혹은 5 Hz주파수 대역에 대한 SPAC 계수의 안정성을 증명하였다. SPAC 계수를 Bessel 함수로 회귀하는 방식으로 획득되는 위상속도는 5 Hz까지 일관성을 보여주었다. 공간평균법을 이용한 선형배열의 경우를 제외하고, 모든 자료는 SPAC법으로 처리되었다. 평행탄성파법 자료가 있는 시추공 주변에서 상시 진동 배열을 순차적으로 다른 시간에 적용하였다. 자료의 품질을 나타내는 지시자로 SPAC 계수의 허수 성분을 이용하였다. 자기상관 스펙트럼의 변화량 (어떠한 경우에는 기록된 파동장에 대한 육안 검사)에 근거하여, 측정된 자료를 '신뢰성있는(reliable)'과 '신뢰성이 없는(unreliable)'로 구분하였다. 그 후, 'reliable'과 'unreliable'로 구분된 자료와 모든 자료에 대하여 SPAC 스펙트럼의 허수 성분을 계산하고 비교하였다. 측점의 방위각 분포가 불충분한 경우 (선형 배열), 허수 성분 곡선은 불안정한 형태를 나타내었고, 이러한 결과는 불충분한 공간평균의 지시자로 간주할 수 있음을 의미한다. 하지만, 측정된 파동장이 낮은 일관성을 나타낼 경우에도 허수성분 곡선은 주목할 만한 불안정성을 나타내지 않았다.

Keywords

References

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