斷層掃描是一種利用外來探測的能量來觀察目標物的反應進而對目標物進行成像的技術。目前已廣泛地應用在地球物理以及醫學領域上，然而在土木工程中鋼筋混凝土結構物上的應用仍在發展的階段；因此本論文回顧了基本斷層掃描與射線追蹤的理論，選擇較適用於鋼筋混凝土結構的級數展開法作為斷層掃描的理論依據，再利用邊界值問題的網格追蹤方法作為射線追蹤的理論選擇方法。 本論文延伸二維射線追蹤上的理論，提出一個可搜尋波於三維空間之行徑的三維線性走時內差法的數學運算模式。此一分析模型可在已知介質速度分布的條件之下正確模擬出波由波原傳播至接收點之最短路徑。 本論文希望提出之三維線性走時內差法能精確的運用於射線追蹤的正算模式，往後可再結合斷層掃描之反算理論而發展出可應用於土木工程非破壞檢測之顯像技術。 Tomography is an image technique, which generates a cross sectional picture of an object by utilizing the object’s response to the nondestructive, probing energy of an external source. Nowadays the theories and techniques of tomography have been well developed and applied to a number of fields such as Geophysics and Medicine. However, this technique is not well applied in civil engineering. In this thesis, reviews of some basic theories and methods of seismic tomography have conducted first. Then, the series expansion method of tomography has been selected to develop the nondestructive evaluation technique for civil infrastructures. A ray tracing technique for 3D computational tomography was developed based on the 2D linear traveltime interpolation (LTI) method. This model can correctly trace the curved ray path from a source point to a receiving point with the least travel-time in a three dimensional inhomogeneous medium. By combining this 3D linear traveltime interpolation (LTI) method with some backward inversion techniques, computational tomography (CT) schemes for civil infrastructures can be developed.
