如何能預測一個適合特定場址的地震動以進行構造物的耐震評估或特定區域的地震風險評估，乃成為近年工程地震學研究的主要課題。本研究首先將台北市指南宮測站規模大於5的地震動歷時，依據地震震央的位置分成四區，以離散傅立葉轉換，求得傅氏譜和群延遲時間，再以合適的機率密度函數來模擬，經由回歸分析求得所選取分布曲線的參數與地震規模間的關係，未來只要給定某一地區之地震規模就可經由離散傅立葉反轉換預測地震動。
就指南宮測站而言，研究結果顯示（1）傅氏譜可以利用對數常態分布的機率密度函數曲線來模擬。（2）將頻率分成十個區間後，每個區間的群延遲時間可以用常態分布的機率密度函數來模擬。（3）測站的地震歷時的震央來自某一個區域越多時，則可以越準確的預測由該區域所產生的地震動。（4）擁有相同數目的震央時，對於來自震央分布的範圍較大地震而言，地震動預測的結果將越不理想。

In recent years, a topic of considerable research interest in the engineering seismology is to predict a suitable ground motion for seismic evaluation of a structure or earthquake risk assessment of a designated site.
This study uses the discrete Fourier transform method to predict seismic ground motion of a recording site. The accelerograms at the recording site are divided into four sites according to which the location of epicenter, and for each site the suitable distributions of probability density function are selected to model Fourier spectrum and group delay time with the associated parameters being regressed as function of earthquake magnitude. Thus, with the given magnitude, predicted accelerograms can be generated using the inverse Fourier transform.
The earthquake records with magnitudes equal to or greater than 5.0 from the Jr-Nan Temple Station in Taipei are selected for this study. For the Jr-Nan Temple Station, the following conclusions can be drawn：（1）the Fourier spectrum of records can be modeled as a lognormal probability density function；（2）separated frequency range into ten intervals group delay time of records can be modeled as a normal probability density function in each interval；（3）if more records with the epicenters located within small region are available, the accuracy of the predicted motion originated from that region can be enhanced；（4）if two regions have the same numbers of epicenter, the accuracy of the predicted ground motion originated from the region with epicenters spread over a small area will be better.

[1] Papoulis, The Fourier Integral and Its Application, McGraw-Hill, New York (1962).
[2] P. C. Jennings, G. W. Housner and N. C. Tsai, “Simulated earthquake motions”. Earthquake Engineering Research Laboratory, California Institute of Technology (1968).
[3] Y. Ohsaki, “On the significance of phase content in earthquake ground motions”. Earthquake Engineering & Structural Dynamics 7, 427-439 (1979).
[4] T. Satoh, T. Sato, T. Uetake, and Y. Sugawara, “A Study on Envelop Characteristics of Strong Motions in a Period of 1 to 15 Seconds by Using Group Delay Time”. Proceedings of the 11th World Conference on Earthquake Engineering, Paper No. 149 (1996).
[5] H. Thráinsson, A. S. Kiremidjian, and S. R. Winterstein, “Modeling of earthquake ground motion in the frequency domain”. Technical Report 134, The John A. Blume Earthquake Engineering Center, Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA (2000).
[6] E. Oran Brigham, The fast Fourier transform and its applications, Englewood Cliffs, N.J Prentice Hall (2001).
[7] J. F. Chai, C. H. Loh, and T. Sato, “Modeling of phase spectrum to simulation design ground motions”. Journal of the Chinese Institute of Engineers, Vol. 25, No. 4, pp. 447-159 (2002).
[8] H. Thráinsson, and A. S. Kiremidjian, “Simulation of digital earthquake accelerograms using the inverse discrete Fourier transform”. Earthquake Engineering & Structural Dynamic, 31, 2023-2048 (2002).
[9] V. Montaldo, A. S. Kiremidjian, H. Thráinsson, and G. Zonno, “Simulation of the Fourier phase spectrum for the generation of synthetic accelerograms”, Journal of Earthquake Engineering, Vol. 7, No. 3, 427-445 (2003).
[10] 和泉正哲，勝昌裕，「地震動相位角之基本研究 」，日本建築學會論文報告集，第327號，昭和五十八年五月 (日文)。
[11] 理論地震動研究會，「地震動的合成與波形處理」，鹿島出版會，一九九四年二月二十八日。
[12] 黃炯憲、盧煉元、葉公贊、葉錦勳等，「宜蘭農工教學大樓之地震資料整理及初步分析」，國家地震工程研究中心，台北市，民國八十三年六月五日。
[13] 徐義人，「工程機率統計學」，國立編譯館，民國八十八年七月。