使用震源機制和GNSS位移場發展最終岩石應力模型 −以台灣中部為例

Abstract

現地應力為地球資源探勘及地下工程設計的重要資訊，精細化現地應力調查成果兼具科學防災以及提高地質工程設計水平的效益。利用震源機制反演現地應力為地球科學界常見探求區域尺度現地應力方向的途徑，配合設定的地層強度可以估計現地應力張量；而水力破裂、套鑽法等現地試驗量測所得現地應力常受到地層變異性、地質構造，甚至是試驗位置不連續面的影響，相較於區域尺度現地應力張量，不僅量值常有偏差，主應力方向也常不一致，以致工程尺度的現地應力評估，迄今仍是一大挑戰。

本研究以車籠埔斷層鄰近區域為例，以集集地震、2000年至2002年、2002年至2004年，作為分析時間序。按國際岩石力學會建議流程，分為最佳估算模式(Best Estimate Stress Model，BESM)、補充現地應力調查方法/補充應力資料(Stress Measurement Methods，SMM)、整合測定模式(Integrated Stress Determination，ISD)及最終岩石應力模型(Final Rock Stress Method，FRSM)。最佳估算模式採用震源機制應力反演，結合自助抽樣法(Bootstrap Method)嘗試提供區域尺度主應力方向及量值不確定性;現地應力量測方法使用位移勢函數(Displacement Potential Function)嘗試建立地表位移與地殼內部應力關係，並透過二維有限差分軟體提供補充現地應力資料;整合測定模式使用三維有限差分法軟體建立數值模型，考慮地形、地質與構造的影響，並參GNSS觀測所得速度給定邊界相對運動速率，透過正算分析反覆迭代，至地表變位速度逐漸接近GNSS觀測值，藉此計算地殼中現地應力;最終岩石應力模型整合上述三種不同尺度應力資料，標示不確定性，此模型亦可新增地真應力資料來交互驗證及修正前述的BESM、SMM、ISD模型，增強模型的準確性和可靠性。

In-situ stress is essential for Earth resource exploration and underground engineering design, offering benefits for scientific disaster prevention and improved geological engineering. The commonly used method in geosciences to determine regional-scale in-situ stress orientations involves seismic source mechanism inversions, combined with established rock strength parameters to estimate the in-situ stress tensor. However, measurements obtained from hydraulic fracturing or overcoring are often affected by heterogeneities in rock layers and geological structures, leading to discrepancies in stress magnitudes and principal directions, which complicates the engineering-scale evaluation of in-situ stress.

This study examines the area around the Chelungpu Fault, analyzing data spanning from the Chi-Chi earthquake through 2000 to 2004. Following the International Society for Rock Mechanics guidelines, the methodology is divided into four main models: Best Estimate Stress Model (BESM), Stress Measurement Methods (SMM), Integrated Stress Determination (ISD), and Final Rock Stress Method (FRSM).

The BESM uses stress inversion from seismic sources along with the Bootstrap Method to estimate regional-scale principal stress directions and magnitudes with associated uncertainties. The SMM utilizes the Displacement Potential Function to relate surface displacement to internal crustal stresses, supported by two-dimensional finite difference software to provide supplementary in-situ stress data. The ISD employs three-dimensional finite difference software to develop numerical models, taking into account the influence of topography, geology, and structural configurations. It integrates velocities from GNSS observations to define boundary relative motion rates, using forward modeling and iterative adjustments until surface displacement velocities closely match those observed by GNSS, thereby calculating in-situ stresses within the crust. Finally, the FRSM integrates these diverse scales of stress data, marks uncertainties, and incorporates true stress data for mutual verification and adjustments of the previous models.