Real-Time Estimation of Spatial Distribution of Natural-Period-Dependent Seismic Intensity on Engineering Bedrock Using Limited Number of Seismometers

This study proposes a method for estimating the spatial distribution of FSI (Natural- Period-Dependent Fourier Spectrum Intensity) on engineering bedrock by utilizing ground motion FSIs recorded at a limited number of seismometers, along with FSIs inferred from surface observations. Employing universal Kriging, the method enables accurate estimation of FSI at arbitrary locations immediately following an earthquake. Validation was conducted using seismic waves computed at each 250-meter mesh, based on three Nankai Trough megaquake scenarios that incorporated the latest geological models. Six representative waves—comprising two orthogonal components per scenario—were analyzed. Kriging analysis based on the Akaike Information Criterion indicated that a lognormal random field best represents the FSI distribution: FSI at a site can be expressed as the product of the trend and the stochastic component. Key findings include: 1) the trend component is strongly influenced by source characteristics and varies across scenarios and directions, yet can be modeled using simple polynomials; 2) the statistical properties of the stochastic component, referred to as “compensation ratio” in this study, remain stable at each site. By constructing the compensation ratio database, the spatial distribution of FSI can be estimated as follows: (1) calculate trend values using observed FSIs and compensation ratios; (2) fit a polynomial to estimate the spatial trend; and (3) multiply the compensation ratios by the trend to derive the spatial distribution of FSI. Reproduction tests conducted over a 5,200 km² target area using FSIs from 20 seismometers demonstrated that the reproduced FSI distributions closely matched the original FSI.