非均勻地震資料的統計分析

Abstract

本文主要在估計非均勻地震資料的intensity函數，一般來說，這種資料被視為一非均勻的卜瓦松過程。我們使用Cheng (2006)所提出的local maximum likelihood 方法來估計，經由模擬出的地震資料，我們比較了此方法與有母數的最大概似估計法的差別，此外，我們也使用Ogata (1984)所提出的殘差診斷方法來檢驗這兩個估計法。最後，我們利用此方法來觀察台灣在1999年發生的集集大地震所引發的餘震序列。

This article considers estimating the intensity of nonhomogeneous earthquake data, which can be modeled by a nonhomogeneous Poisson process. We use the local maximum likelihood method proposed by Cheng (2006) to estimate the intensity function. We compare our method with parametric MLE method through simulation. In addition, for examining each of the estimation method, we use a diagnosis tool of residual process proposed by Ogata (1984). With the local maximum likelihood estimator, we nvestigate the intensity of the aftershock sequence triggered by Chi-Chi earthquake, which occurred in Taiwan in 1999.