Application of Kriging method into practical estimations of earthquake ground motion hazards

Abstract

The aim of the present paper is to propose a system that provides spatial distribution of strong ground motions based on Kriging analysis along with a simple one dimensional earthquake response analysis using ordinary boring investigation data. Hazard maps of cities have been created by covering their areas with numbers of meshes of which sizes are such as 250meters square less or more, and the strong ground motion intensities are indicated for each mesh. Strong ground motions are, however, more desired to be estimated at each construction site than for those large size meshes. Large meshes cannot provide information detail enough to plan earthquake countermeasures. On the other hand, when the meshes are reduced in size, it requires a large amount of time and costs, because the ground layered systems must be modeled for all the meshes. It also should be noted that the amount of information about ground conditions and soils in the city is not increased by reducing the size. Simple adoption of small size meshes would lead us to create an expensive but not adequately accurate hazard map. Recently, some advanced numerical analysis methods, such as based on three dimensional finite element methods (FEM), are developed to estimate soil behaviors highly accurately. The methods, however, need very accurate soil parameters and detail boundary conditions; yet, either of them is hardly available in a whole city. Such advanced numerical methods can be effectively utilized for only particular places, but not for all over a city On the contrary, a number of boring investigations have been performed in wide areas of cities; they are easily and commonly used in one dimensional earthquake response analysis. Especially the densities of boring investigations are high around houses, buildings and important infrastructures etc., where accurate estimation is highly expected in the hazard maps. Kriging analysis is one of the most suitable methods to estimate and interpolate the strong ground motion at each construction site. A number of theoretical results of studies on the Kriging analyses have been published to apply them to estimate the special statistics of the strong ground motions. However, those results have not been able to be practically utilized to create the hazard map, when boring data and the one dimensional methods are used. One dimensional analysis using ordinary boring investigation data would provide estimates accompanied with unignorable errors. In this paper the authors propose the Kriging method, which can take account the errors into the stochastic analysis. Applying the method, the authors develop a system that can objectively compute spatial distributions of strong ground motions very accurately. The cost of the estimation can be minimized because the system does not require expensive ground layered system models. The Kriging method can show not only the ground motion estimators but also its errors quantitatively. Accordingly, the proposed method prospects the areas where ground motions can be estimated with higher accuracies and where with lower accuracies. The suitable countermeasure, which would depend on the accuracies, can be well selected based on the information provided by the proposed system. Some samples of seismic hazard maps of instrumental seismic intensity and its accuracy at each site of buildings and houses in the all target area of a whole city are presented in this paper. These sample maps suggest that various measures for earthquake disasters mitigation can be compared with one another considering the necessity, purposes, cost-performances, etc. Accordingly, the decision-makings can be supported toward the best countermeasures.