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This detailed book systematically investigates subsurface geological fractures using rock mechanics, geology, and geophysics. Based on geological fracture mechanisms and fracture boundary conditions, it presents new finite-difference equations for the simulation of seismic wave responses to geological fractures, and proposes innovative AVO inversion equations for the accurate estimation of the rock properties of the fractured medium. It employs schematics, snapshots, color images and charts to demonstrate the mechanical characteristics of the fractures, the seismic wave-field response to the fractures, the seismic data attributes of the fractures and the rock properties of the fractures obtained via inversion. It provides a new methodology for enhancing geological fracture detection technology and for the accurate delineation of fractured reservoirs that ultimately benefits reservoir and mining engineers, geologists and geophysicists in terms of optimizing reservoir recovery, well performance and mining safety.