震源時間函數是了解震源物理的重要參數之一。震源時間函數不僅記錄了震源破裂歷 時，也記錄了震源的破裂特徵。震源時間函數的歷時包含了兩個時間，一個是震源上揚時間， 另一個是破裂時間，這兩個時間反映出地震不同的破裂特性。一般評估震源時間函數的方法 主要是利用主震與其附近之小地震間進行解迴旋，此法稱為經驗格林函數法，一般可在時間 域或頻率域從事經驗格林函數法求解震源時間函數。在頻率域將主震頻譜與格林函數頻譜相 除，會因格林函數頻譜太小易造成在相除後有異常放大的現象，水準解迴旋經常被採用去抑 制這樣的現象。在時間域的解迴旋，基本上與逆推法有關，為使逆推穩定，可在逆推過程加 入阻尼或平滑化因子。無論何種方法，使解迴旋能夠穩定將是求解震源時間函數的首要條 件，因此，利用解迴旋穩定求出震源時間函數仍具挑戰性。本研究擬利用時間域解迴旋配合 逆推法求解震源時間函數，在此研究中以在主震位置產生不含震源時間函數的合成震波當成 是經驗格林函數，並採用阻尼平滑化逆推法求解震源時間函數。之後，將本研究所提的方法 應用在數個大地震的震源時間函數研究上。 Source time function (STF) is one of important source parameters to understand the physics of earthquakes. The STF records not only the source duration but also the features of ruptures. Generally, the source duration of an earthquake is composed of two times: one is the rise time and the other is the rupture time. The two times can account for different characteristics of faulting during an earthquake. Empirical Green’s function method (EGF method) is usually used to extract the STF from the main shock using the so-called deconvolution, which can be performed in frequency-domain or time-domain. In frequency-domain, the water-level deconvolution is a common method to obtain the STF because it can suppress the problem of spectral hole. Comparatively, to get the STF using time-domain deconvolution is basically related to the inversion technique. To make the inversion stable in the time-domain deconvolution, we can add damping values or smoothing factors to the inversion. In any case, to make the deconvolution stable is the most important condition in the use of EGF method. For this reason, it is worthy to challenge how to make the deconvolution stable in time-domain or frequency-domain. In this study, we develop a damped inversion method with smoothing constraint to catch the STF from the main shock. In addition, the theoretical waveform produced in the location of the main shock is regarded as the EGF, convenient to complete the deconvolution. The follow-up study will use the proposed method to investigate the STFs of large earthquakes.
