A general method for fracture compliance matrix estimation using full-waveform sonic data

Abstract The normal and shear compliances of fractures quantify their deformation in response to the application of a given amount of stress perpendicular and parallel to the fracture plane, respectively. The presence of fractures significantly influences the overall mechanical properties of the host rock. As such, fracture compliance represents an important rock mechanical property with a wide range of applications throughout the Earth, engineering, and environmental sciences. Traditionally, fracture compliance is estimated in-situ through hydraulic testing, which is logistically complex and correspondingly time-consuming and costly. To alleviate this problem, efforts are made to estimate fracture compliance from full-waveform sonic (FWS) log data. In view of this, we have developed a technique for the joint estimation of normal and shear compliances of multiple, closely spaced, and inclined fractures utilizing refracted P- and S-waves from production-type FWS log data. Our approach is based on analytical plane-wave expressions of fracture-induced P- and S-wave phase time delays for inclined compliant fractures and assumes that P- and S-wave phase time delays induced by individual fractures are cumulative. Using this methodological framework, we build an inversion scheme that allows for the joint inference of the normal and shear compliances of multiple closely spaced fractures. We assess and discuss the viability of this new technique by applying it to observed FWS log data acquired along a shallow borehole penetrating naturally fractured granitic rocks.