Fourier Amplitude Spectrum at Arbitrary Points Estimated by Kriging Method

This paper reports a method for estimating an acceleration Fourier amplitude spectrum (FS) on ground surface at arbitrary points using the transfer functions of the surface strata and the observation records of limited number of seismometers. The transfer functions at arbitrary points in Owari-asahi City are estimated by using a modified Kriging method based on the results of the seismic response analysis of the surface strata at 748 boring points using seismic waves on engineering bedrock caused by six earthquake scenarios. The acceleration FS on the surface at 642 boring points inside the city are estimated by using the proposed method based on only 20 observation records on the surface (estimated value). The result is compared to the acceleration FS estimated by the transfer functions and seismic waves on the engineering bedrock from earthquake scenarios at the same boring points (tentative observed value). It is found that the correlation coefficients per frequency between the estimated and tentative observed value at 642 points are no less than 0.5 any earthquake scenario. To date, earthquake ground motion intensities (GMIs) have been estimated for predefined meshes with fixed sides of lengths of 50 m, 250 m, or 500 m using hypothetical ground models created on the basis of boring investigation data. However, to employ effective measures for seismic damage mitigation and contribute to a resilient society, the GMI should be estimated in greater detail, such as at each construction site. In order to do so, Sugai et al. (2015) proposed a modified Kriging method that can take into account for non-negligible errors in the estimations of the spatial distributions of the GMIs at boring points. The method has already been applied to the estimations of seismic hazards and risks using earthquake scenarios in Owari-asahi City, Aichi prefecture, Japan. Expanding the above method, it should be possible to estimate the GMI at an arbitrary point using observation records of limited number of seismometers. However, it is practically impossible to estimate the spatial distribution of the GMI on the surface directly from the observation records on the surface. For example, in Owari-asahi City, it is necessary approximately one seismometer for every 100 m to estimate the GMI at an arbitrary point on the surface, considering that the auto-correlation distances for the GMI (PGA, PGV and instrumental seismic intensity) on the surface are approximately 150–700 m in the city (Sugai et al. 2016). In contrast, the auto-correlation distances for the GMI on engineering bedrock are much longer approximately 1.5–2 km in the city (Mizutani et al. 2017). Accordingly, the GMI on the surface at an arbitrary point could be estimated by an amplification factor and the spatial distribution of the seismic wave on the engineering bedrock at the same point, which is 13 International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP13 Seoul, South Korea, May 26-30, 2019 2 estimated by using the modified Kriging method based on seismic waves on the engineering bedrock at seismometer points by using seismic response analysis of surface strata based on the observation records, requiring approximately one seismometer for every 1 km on the surface. However, the amplification factor of the GMI depends not only on the characteristics of the surface strata, but also on the frequency characteristics of earthquake ground motion. This paper demonstrates estimating an acceleration Fourier amplitude spectrum (FS) on ground surface at an arbitrary point using a transfer function of surface strata and observation records of limited number of seismometers in Owari-asahi City. Using the acceleration FS, it is possible to calculate an acceleration response spectrum (AIJ 2015) to estimate seismic damage. At first, the authors calculated the transfer function at an arbitrary point by using the modified Kriging method based on the transfer function at boring points and earthquake scenarios. The transfer function at a boring point is calculated by using seismic response analysis of surface strata based on input seismic wave on the engineering bedrock from earthquake scenarios. Also, the authors compare the acceleration FS by the proposed method at the boring points with those estimated by the transfer functions and seismic waves on the engineering bedrock for earthquake scenarios at the same boring points.