Spatial Interpolation of Ground Motion Intensity Measures Based on Two-Step Gaussian Process Regression

Abstract

The spatial distribution of ground motion intensity measures estimated through spatial interpolation is utilized for various purposes in the field of earthquake disaster prevention. While methods such as Simple Kriging and Inverse distance weighting are commonly used for spatial interpolation, we propose a new method based on Gaussian process regression to improve estimation accuracy. In the proposed method, spatial interpolation of ground motion intensity measures is performed in two steps. In the first step, spatial interpolation is conducted on the ground motion intensity measures after introducing virtual noise. In the second step, spatial interpolation is applied to the errors between the observed values and the first-step estimated values, which are caused by the virtual noise. By summing the results of the first and second steps, the spatial distribution of ground motion intensity measures is obtained. Through analyses of various past earthquakes, we confirmed that the proposed method achieves higher estimation accuracy compared to conventional approaches, such as direct Gaussian process regression without virtual noise and methods based on Simple Kriging and site amplification factors.