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、地震学、地震工程、环境保护、水文地质学和地热能利用等许多方面都是至关重要的课题。体现裂缝的界面条件的一个特定参数是所谓的比刚度，例如量化其在剪切或压缩下的刚度。 除了与岩体稳定性分析的直接相关性（例如，在采矿作业期间）之外，已发现断裂特定刚度：i）与断裂的水力特性（例如，管理增强型地热系统的性能）密切相关，ii）用作沿沿着岩石不连续面剪切破坏的前兆，以及iii）有助于理解浅层地震的机制。 然而，一般来说，裂缝对给定激活的响应同样由其几何形状驱动，这本质上不限于平面条件。 因此，地下裂缝的整体表征，揭示其几何和力学特性，是至关重要的。为了帮助迎接挑战，本研究的目的是建立一个全面的分析，计算和实验平台的几何重建和力学特性的任意形状的岩石中的不连续性的地震波的方式。 重点是开发和验证一个强大的框架，能够解决其三维几何形状和空间分布的具体刚度没有迭代的裂缝的波形层析成像。 通常，由于裂缝特征和地震观测之间的高度非线性关系，波形层析成像的方法需要递归。 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，如拓扑灵敏度法。 通过建立在这样的进步，这项研究将满足弯曲骨折的成像和表征，同时允许在传感安排方面的显着灵活性。 这通过创新的3步方法成为可能，其中地震波形用于顺序地和非迭代地重建：i）裂缝几何形状，ii）裂缝开口位移轮廓，以及iii）非均质比刚度。将利用最近购置的扫描激光多普勒测振仪在实验室环境中对这些发展进行验证，该测振仪能够以极高的分辨率和准确度远程监测岩石样本表面的三轴波形。

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.