本計畫中PI提出了一種相空間射線追踪算法，該算法跳脫了傳統地震學的射線追踪問題多僅著重到時的應用。研究中會牽涉到數位建模和圖像重建反演(層析成像)的演算法。高頻、高解析度的相空間波線模擬演算法在地震學問題中的應用具有同時解決所有可能的初始條件的優點。利用有效、實用的顯式尤拉解法在給定初值的條件下透過“因式分解”後的一級一階常微分Helmholtz方程採用Runge-Kutta-Fehlberg預估-校正算法求取對應的數值解，可達到該解具有高頻、高解析度特性解的目的。涉及的關鍵數值方法是AMR和RKF45。AMR建模是專為模型幾何構造而設計。RKF45是一種控制局部和累積誤差的計算方法，其精度為O(h4)，誤差估計可達O(h5)。透過自動確定步長的高階嵌入式(內嵌式)算法來估計和控制誤差。可自動地依據目前數位建模網格狀況進行偵測與分析,並重新規劃波線路徑。所涉及的震波屬性不僅僅涉及傳統運動學的走時，射線路徑，波前等的特性，而是強調振幅/相位/力矩/能量相關的動力學動態特性。相空間射線追踪法亦可模擬均向與非均向性物質的震波反應。透過相場法亦可針對動態裂隙/破裂傳遞的研究議題有其潛在應用價值。 ;PI proposed a phase space ray tracing algorithm which is beyond the conventional approach using kinematic seismic ray tracing algorithm for studying modeling and image reconstruction (tomography). Application of high frequency phase space optical ray for seismic problem has the advantage of simultaneously solving all possible initial conditions. The practical explicit Eulerian scheme which solve “factored” first order first degree differential Helmholtz equation with given initial value takes Runge-Kutta-Fehlberg predictor-corrector algorithm for numerical solution of ordinary differential equation. Key numerical methods involved are AMR and RKF45. AMR is designed for model geometry construction. RKF45 is a method of control computational local and cumulative errors with accuracy of order O(h4) and with an error estimator of order O(h5). The error can be estimated and controlled by using high-order embedded method that allow for an adaptive stepsize to be determined automatically. The seismic properties involved will not simply focus on kinetic issues covering travel-time, ray path, wave front but rather emphasis on its dynamic properties related to amplitude/phase/moment/energy tracking. Simulation not only cover isotropic but also anisotropic material responses. Potential application on dynamic crack/rupture propagation study through phase field approach.
