論文提要：
大地震發生時除了引起地表強烈振動外，從許多災害性地震的案例分析發現，地震所伴隨的地動變對於建築構造物也會帶來巨大的破壞力，因此有必要針對近斷層之地變動空間分布及其位移衰減趨勢進行分析研究，作為近震位移估算之參考依據。近年來近震資料由於測站密集佈設，資料量已逐漸增加，但仍不足夠作為分析樣本，本研究透過數值理論分析計算，產生理論位移資料來進行地變動特性分析，再以實際觀測資料進行比對及修飾，得到最佳之近震位移衰減公式。本研究提出由強震資料經由基線修正及二次積分處理標準化流程，可以得到測站所在地的同震位移紀錄及最大地表位移。標準化流程應用於儀器振動台測試紀錄，透過本文提出的方法，可以回復輸入位移量到97﹪；由實測地震資料處理及GPS觀測結果比較，兩者平均比值為1.05，大部分的資料落在0.78到1.41之間，數公分到數公尺的同震變形均能夠透過強震紀錄，經由標準化的基線修正得到，顯示本研究提出的標準化基線修正方法可以應用在同震變形資料的處理上。應用上述標準化處理流程，本文完成921集集地震及1210成功地震最大地表位移及同震變形的資料處理，得到之數值可作為位移衰減公式調整及修飾的參考。
為計算理論位移，本研究以ABAQUS有限單元軟體，利用接觸元素概念，修改模型網格資料，增加一組虛擬節點用以模擬斷層錯動，計算之應力及位移結果與解析解及前人研究比對結果一致，可以將ABAQUS有限單元軟體延伸應用於斷層錯動模擬之研究工具。應用此一網格修正，對於具不同滑移量之斷層上下盤錯動所致之地變動模擬，經由921集集地震的實測資料，驗證以本文所提出之增加虛擬節點之ABAQUS有限單元法具有良好模擬的結果。利用增加虛擬節點之ABAQUS有限單元法，給予不同斷層參數，透過理論計算得到模擬之近震位移資料，分析各個斷層參數對於所引起之地變動空間分布及衰減趨勢影響權重，本文認為斷層長度為主要影響參數。本研究建立位移衰減通式為：log（Y）= C1 + C2 ×log（sqrt(A)）–C3 ×log（R+sqrt(A)）- C4 ×R，其中Y為觀測地動值或理論地動值，單位為公尺，A 為斷層破裂面積，單位為KmXKm ，R為測站至斷層的最短距離，單位為公里，C1 、C2 、C3 及C4 為欲迴歸的係數。依據理論計算所得之走向滑移斷層及傾角30度之逆衝斷層理論值，本研究回歸得到得到以下的位移衰減迴歸公式：
（1）走向滑移斷層
log（Y）= -1.393+ 2.216×log（sqrt(A)）– 3.049×log（R+sqrt(A)）-0.003×R
（2）傾角30度之逆衝斷層
上盤位移衰減公式
log（Y）= -1.479+ 1.665×log（sqrt(A)）–1.945×log（R+sqrt(A)）-0.004×R
下盤位移衰減公式
log（Y）= -1.437+ 1.138×log（sqrt(A)）–0.872×log（R+sqrt(A)）-0.036×R
上述三個衰減公式使用單位滑移量廻歸，只要加乘滑移量倍律，即可計算得到該滑移量之位移衰減估算值。

A study on the estimation of earthquake ground deformation and its attenuation
Chien-Fu Wu
Abstract
Strong ground shaking caused by a major earthquake may induce great damage. However, large fault rupture and ground deformation and failure may also have big destructive power to structures. In order to realize the effects of rupture process of shallow fault to the distribution of ground deformation, the following works were done in this study. (1) Modify the existing finite element program and design some appropriate shallow crustal structures to calculate the ground deformation induced by different fault ruptures with various geometry, source mechanism, and slip distribution. The computed ground deformation data were then used to analyze the attenuation relations of ground deformation with respective to source distance for different magnitude. (2) Integrate the acceleration data of the Chi Chi earthquake, collected by TSMIP (Taiwan Strong Motion Instrumental Program conducted by Taiwan Central Weather Bureau), to the corresponding displacement records and then some analyses are made to their peak values.
Since 1990 digital strong-motion accelerographs and Globe Position System (GPS) instruments have been widely deployed in the Taiwan region (Shin et al., 2003; Yu et al., 2001). The 1999 Chi-Chi, Mw 7.6 earthquake and the 2003 Chengkung, Mw 6.8 earthquake were well recorded by both digital accelerographs and GPS instruments. These data offer a good opportunity to determine permanent displacements from the strong-motion records and to compare the results with those derived from the GPS measurements. As noted by Boore (2001), a double integration of the acceleration data often leads to ridiculous results, and baseline corrections are therefore required in most cases before the integration step. Based on the pioneering work of Iwan et al. (1985) and Boore (2001), this study developed an improved method for baseline correction and validated it using an extensive set of data from shaking table test of a known displacement on 249 accelerographs. Our baseline correction method recovered about 97% of the actual displacement from the shaking table data. We then applied this baseline correction method to compute permanent displacements from the strong-motion data of the Chi-Chi and Chengkung earthquakes. Our results agree favorably with the coseismic displacements determined by the GPS measurements at nearby sites. The ratio of seismic to geodetic displacement varies from 0.78 to 1.41, with an average ratio of about 1.05.
Near field peak ground displacement(or permanent displacement) attenuation relationships are deduced with data from improvement finite element method. They are
（1） strike slip fault
log（Y）= -1.393+ 2.216×log（sqrt(A)）–3.049×log（R+sqrt(A)）-0.003×R
（2） thrust fault （dip angle 30 degree）
Hanging wall
log（Y）= -1.479+ 1.665×log（sqrt(A)）–1.945×log（R+sqrt(A)）-0.004×R
Foot wall
log（Y）= -1.437+ 1.138×log（sqrt(A)）–0.872×log（R+sqrt(A)）-0.036×R
Where Y is the amplitude of displacement in meter, A is fault rupture area in square kilometers, R is rupture distance in km.

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