重要結構物基於極端水準的耐震需求，進入非線彈性狀態，需要進行動態歷時分析，此時外力輸入即為基底的加速度歷時。設計震譜為結構物耐震設計的依據，其形狀往往是諸多實測地表加速度紀錄的綜合結果，與之相符的地表加速度歷時只能人為產生。目前不論是時域或頻域演算法產生人工地表加速度歷時，其收斂條件以滿足與目標反應譜相符的容許誤差為主，較少考慮PGA的擬合、地動歷時波形的維持，以及基線偏移與否。本文首先理論推導新演算法產生人工地震，包含：(1)以高階高斯小波為基底函數；(2)直接調整反應位移歷時，再微分得地表加速度歷時；(3)加入低階高斯小波以滿足某些因地動延時有限的需求；以及(4)建議最佳需求之設定。接著以各種實例產生人工地震，進行比較，包含：(1)採用平滑或曲折的目標反應譜，一般或近斷層設計震譜；(2)選用等差或等比數列的反應譜擬合週期點，週期點數由23個至1000個不等；(3)針對不同的基底函數和修正對象；以及(4)降低反應譜擬合的容許誤差。經由理論推導與實例驗證，本文利用複合高斯小波逐次直接調整最大偏差的反應位移歷時，皆可在設定的反應譜擬合容許誤差和各項限制條件下，達致收斂，因此本文的人工地震新演算法極具實務應用價值。

Important structures will vibrate inelastically on the seismic demand of extreme level, and then their dynamic time history analyses should be performed under specified base excitation. For the purpose of seismic design, design spectra are usually proposed, where their forms are constituted based on many free-field records. Hence, ground accelerograms compatible with design spectra are generated only artificially. No matter what artificial accelerograms are generated in the time or the frequency domain, the results of convergence is reached as long as the maximum error compared with a target response spectrum is less than a tolerance, without the consideration of PGA matching, wave form maintenance, and baseline drift prevention. At first, this study develops a new algorithm theoretically to generate artificial earthquakes. The algorithm contains: (1) the use of a high-order Gaussian wavelet as the base function, (2) adjusting the response displacement time history corresponding to a single period directly, then obtaining the ground accelerogram by differential, (3) adding several low-order Gaussian wavelets to satisfy some demands due to the finite duration of ground accelerograms, and (4) suggesting the optimal demand setting. Then, the new algorithm are compared and verified through various simulation study and practical cases on generating artificial earthquakes. Those comparisons include: (1) using smooth or piecewise-defined target response spectra, general or near-fault site design spectra, (2) covering 23 to 1000 various matching periods from an arithmetic or a geometric sequence, (3) selecting different base functions and time histories under modification, and (4) reducing tolerance of matching. On the basis of theoretical formulation and practical verification, the new algorithm, which uses compound Gaussian wavelets to directly adjust the response deformation at one period at a time, can achieve convergence in all cases. Therefore, our new algorithm of generating artificial earthquakes is worthy of practical application.

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