The elastic compliance of a fracture can be spatially varying, reflecting the variation of microscale properties of the fracture, e.g., aperture, contact asperities, and fracture infill. Characterizing the spatial heterogeneity of a fracture is crucial in explaining the apparent frequency dependence of fracture compliance and in addressing the spatially varying mechanical and hydraulic properties of the fractured medium. Apparent frequency dependence of the estimated fracture compliance is caused when the used seismic wavelength is very large compared to the scale of heterogeneity. We perform ultrasonic laboratory experiments, and characterize the spatially varying compliance along a fluid-filled fracture. We simulate a horizontal fracture, and introduce heterogeneous fluid distribution along the fracture. We perform amplitude variation with offset (AVO) inversion of the P-P reflections, in which we obtain the theoretical angle-dependent reflection responses by considering the linear-slip model. The estimated compliance distribution clearly separates the dry region from the wet region of the fracture. The effective bulk modulus of the fluid is estimated using the derived values of the compliance. We find that the obtained bulk modulus is well-explained by the presence of minute quantity of air bubbles in the water. We also find new evidence of the existence of scattered waves generated at the boundary representing a sharp change in fracture compliance. The estimated boundary between the dry and the wet regions of the fracture, which is detected by AVO inversion, is slightly shifted compared with the actual location. This is possibly due to the interference of the scattered waves that are generated at the boundary. The linear-slip model can represent thin structures in rocks in a wide range of scale. Therefore, our methodology, results, and discussion will be useful in developing new applications for assessing laterally varying mechanical and hydraulic properties of thin nonwelded discontinuities, e.g., fractures, joints, and faults.
Experimental verification of spatially varying fracture-compliance estimates obtained from amplitude variation with offset inversion coupled with linear slip theory
