地震時序之多重碎形分析

Multifractal Analysis of Earthquakes Inter-arrival Time

湯高文(Gao-Wen Tang)

指導教授 ： 伍次寅

國立臺灣大學/工學院/機械工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.10328

摘要

台灣位處於環太平洋地震帶，地震活動發生頻繁，也經常伴隨著大規模的地震。尤其在921集集大地震後，台灣人民更見識到了大規模地震所帶來的毀滅性災害，因此，地震的預防和減低地震災害之相關研究是刻不容緩的。
隨著過去二十年來碎形的發展漸趨成熟，相關的研究成果也指出許多自然界的時間歷程資料存在著多重碎形的表現，而地震所展現出來的各種特性也符合多重碎形之特質。故本研究嘗試利用碎形方法來觀察地震發生頻率在時間序列上的表現，並輔以多重碎形方法來分析於大地震發生前地震活動是否有所徵兆可循。
研究中，我們以1990年1月至2003年12月期間所發生之規模4級以上地震為分析目標。我們首先將地震資料轉換為時間序列，並利用Hölder指數的連續分布來觀察地震活動之變化。研究成果顯示，在大規模地震發生前，Hölder指數皆會有一段震盪區域，而這段震盪區域的多重碎形特性也會有所變化，此變化可用來做為大地震發生前的依據，並供日後研究者更進一步進行地震預測研究時之參考。

關鍵字

地震 ； 碎形 ； 多重碎形 ； 時間序列

並列摘要

Taiwan is located on the Circum-Pacific Ocean Seismic Zone, where earthquakes happen frequently, and sometimes accompany drastic earthquakes. After 921-earthquake, Taiwanese people experienced the destructive consequences caused by a drastic earthquake. Therefore, the researches of prevention and reduction of the damages of earthquakes are so urgent that there is no time for waiting.
In the past twenty years, the development of fractal theory has become mature, and many research reports have indicated that time-series in nature exhibits multifractal behaviors. Earthquakes also possess these properties. The purpose of this study aims at using the fractal method to analyze the time-series of seismic activities, with attention focused on the finding of any precursor before the major earthquake arrives.
In this study, we analyzed the interarrival-time between seismic events with size over 4 in the period from Jan. 1990 to Dec. 2003 in Taiwan area. We first transformed the data into a time-sequence, and then calculated the Hölder exponent of the sequence to study the changes in the frequency of seismic activities. Our results showed that the Hölder exponents will display a drastic fluctuation before the major earthquake arrives. There are also some significant changes in the multifarctal spectra of the sequence in this time span. These changes can serve as precursors of the oncoming of major earthquakes; they also provide important information to the future improvement of earthquake forecast.

並列關鍵字

earthquake ； fractal ； multifractal ； time-sequence

參考文獻

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