Studies on real-time estimation method of earthquake ground motions under imperfect information

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This study presents a theoretical procedure for efficiently estimating the spatial distribution of earthquake ground motion indices when observed data at some discrete points are available.1. The spatial estimation method of the average of the process over a block whose location and geometry are known was proposed. A theoretical formulation is presented to estimate conditional lognormal stochastic field when observation is made at some discrete points. The optimum estimator and minimized mean-squared estimation error of a block average value are then compared with the results obtained by point kriging when an unknown value at a known location is estimated. Numerical examples were carried out to examine the influence of block size on the optimum estimator and estimated error variance. Except for very small block sizes, the results indicate that the block kriging is critical method.2. The approximate algorithm for stochastic interpolation and extrapolation of conditional non-Gaussian fie … More lds produces a nonlinear unbiased estimator with the characteristic minimum variance of errors. The extended Kalman filtering procedure is then used for solving the conditional estimation problem transformed into the Gaussian stochastic field. A lognormal stochastic field is taken up as an example. The accuracy and efficiency of the proposed method is discussed compared with the theoretical solutions of simple kriging. It is found that the proposed method does not suffer from the difficulties associated with computing the optimum estimator and estimated error variance.3. A theory for evaluating the maximum entropy estimators and their associated entropy indices for conditional non-Gaussian translation stochastic fields was proposed when observation is made at some discrete points. Through analytical development and numerical examples of stochastic fields with the six types of distribution, kriging and maximum entropy techniques for spatial estimation are also compared. It was found that : 1) the maximum entropy estimate and conditional entropy are dependent on the values of observed data ; and 2) the average conditional entropy has an independence on the observations, and is not larger than the average unconditional entropy. Less