3D Imaging and Characterization of Fractures in Rock

岩石中裂隙和断层的几何和界面性质对采矿、地震、地震工程、环境保护、水文地质学和地热能利用等社会许多方面都具有至关重要的意义。体现骨折界面条件的一个特殊参数是所谓的比刚度，例如，量化其在剪切或压缩下的刚性。除了与岩体稳定性分析直接相关(例如在采矿过程中)，裂隙比刚度已被发现：i)与裂隙的水力特性密切相关(例如控制增强型地热系统的性能)，ii)作为岩石不连续面上剪切破坏的前兆，以及iii)帮助理解浅层地震的机制。然而，一般而言，骨折对给定激活的响应同样受其几何形状的驱动，这本质上并不限于平面条件。因此，揭示地下裂缝的几何和力学特征的整体特征是至关重要的。为了应对这一挑战，本研究旨在建立一个综合的分析、计算和实验平台，用于利用地震波对岩石中任意形状的不连续面进行几何重建和力学表征。重点是开发和验证用于骨折波形层析成像的健壮框架，该框架能够在不迭代的情况下解析其三维几何形状和特定刚度的空间分布。通常，由于裂缝特征和地震观测之间的高度非线性关系，波形层析成像方法需要递归。然而，近年来，应用数学的研究产生了一套非迭代的波形层析成像方法，如拓扑敏感度方法。通过在这些进展的基础上再接再厉，这项研究将迎合弯曲裂缝的成像和特征，同时允许在传感安排方面的巨大灵活性。这是由一种创新的三步法实现的，其中使用地震波形来顺序和非迭代地重建：i)裂缝几何形状，ii)裂缝张开位移分布，以及iii)非均匀比刚度。这些发展将在实验室环境中得到验证，利用最近获得的扫描激光多普勒测振仪，该测振仪能够以出色的分辨率和精度远程监测岩石样品表面的三轴波形。

Geometric and interfacial properties of the fractures and faults in rock are the subject of critical importance to many facets of our society including mining, seismology, earthquake engineering, environmental protection, hydrogeology, and utilization of geothermal energy. One particular parameter embodying the fracture's interfacial condition is the so-called specific stiffness, quantifying for instance its rigidity under shearing or compression. Beyond its immediate relevance to the stability analyses in rock masses (e.g. during mining operations), the fracture specific stiffness has been found to: i) bear an intimate connection to the fracture's hydraulic properties (governing for example the performance of enhanced geothermal systems), ii) serve as a precursor of shear failure along rock discontinuities, and iii) help understand the mechanism of shallow earthquakes. In general, however, the fracture's response to given activation is equally driven by its geometry, which is inherently not limited to the planar condition. Thus a holistic characterization of subterranean fractures, that unveils both their geometric and mechanical characteristics, is a paramount. To help meet the challenge, this research aims to establish a comprehensive analytical, computational, and experimental platform for the geometric reconstruction and mechanical characterization of arbitrarily-shaped discontinuities in rock by way of seismic waves. The focus is on developing and validating a robust framework for the waveform tomography of fractures that is capable of resolving their three-dimensional geometry and spatial distribution of specific stiffness without iterations. Typically, approaches to the waveform tomography entail recursions owing to a highly nonlinear relationship between the fracture characteristics and seismic observations. Recently, however, the research in applied mathematics has produced a suite of non-iterative approaches to the waveform tomography such as the method of Topological Sensitivity. By building on such advancements, this research will cater for the imaging and characterization of curved fractures while allowing for significant flexibility in terms of the sensing arrangement. This is made possible by an innovative 3-step approach where the seismic waveforms are used to sequentially - and non-iteratively - reconstruct: i) fracture geometry, ii) fracture opening displacement profile, and iii) heterogeneous specific stiffness. The developments will be verified in a laboratory setting, making use of the recently acquired Scanning Laser Doppler Vibrometer that is capable of remotely monitoring triaxial waveforms on the surface of rock specimens with exceptional resolution and accuracy.