A holistic approach to seismic waveform tomography of heterogeneous fractures: from geometric reconstruction to interfacial characterization

University of Minnesota Ph.D. dissertation. August 2016. Major: Civil Engineering. Advisors: Bojan Guzina, Joseph Labuz. 1 computer file (PDF); ix, 197 pages.The primary focus of this thesis is on the development of a comprehensive analytical, computational, and experimental framework for (a) 3D seismic waveform tomography of partially-closed fractures, e.g. hydraulic fractures, and (b) reconstruction of their heterogeneous contact condition. Taking advantage of recent advancements in the theory of inverse scattering, the analytical platform is formulated as a novel 3-step approach where: (i) the fracture geometry Γ (which may be non-planar and/or disconnected) is non-iteratively reconstructed without any prior knowledge about its interfacial condition via either the Generalized Linear Sampling Method (GLSM) or the method of Topological Sensitivity (TS); ii) given Γ, the fracture opening displacement (FOD) profile is computed from the integral equation relating FOD to the observed seismic data; and (iii) given Γ and FOD, the (normal and shear) specific stiffness profiles are resolved from the hypersingular boundary integral equation for a fracture with elastic contact condition. To cater for efficient numerical simulations, a computational platform is developed on the basis of a regularized boundary integral equation (BIE) method for elastic-wave scattering by heterogeneous fractures in 3D, which provided fertile ground for verifying and demonstrating the effectiveness of the 3-step inverse solution. The experimental component of this work makes use of the 3D Scanning Laser Doppler Vibrometer (SLDV) that is capable of remotely monitoring the triaxial motion wave- forms (up to 1MHz) on the surface of rock specimens with 0.1mm spatial resolution and O(nm) displacement accuracy. In this setting, a set of plane-stress laboratory experiments is designed which allow for monitoring the full-field interaction of ultrasonic waves with stationary and advancing fractures in rock. The measured data are then used to: (1) non-parametrically expose the true contact law and its spatiotemporal variations along the surface of stationary and advancing fractures in rock, and (2) extract the linearized contact properties in terms of the (heterogeneous) distribution of shear and normal specific stiffness along the fracture. In turn, such high-fidelity results provide the ground truth toward validating the proposed inverse solution for the geometric reconstruction and interfacial characterization of fractures in rock by seismic waves