Stress inversion of shear-tensile focal mechanisms with application to hydraulic fracture monitoring

Stress inversion methods used to evaluate the state of stress from multiple earthquake focal mechanisms are based on the Bott hypothesis, which assumes that the slip vector lies in the fault plane and is parallel to the maximum resolved shear stress in that plane. This assumption does not consider non-double-couple source components, which may be significant in some scenarios such as hydraulic fracturing, where a large fluid volume is injected to induce tensile rock failure. With the introduction of a modified Bott hypothesis that allows for out-of-plane slip, we develop a stress inversion algorithm that accounts for tensile components of the source mechanism. The composite Griffith Mohr-Coulomb criterion is utilized for fault stability characterization. Synthetic tests are used to quantify the error in stress determination that arises when conventional stress inversion is applied in the presence of non-double-couple sources. A statistical approach is applied to analyse the minimum number of focal mechanisms required for reliable inversion results. We find that at least 30 focal mechanisms with diverse orientations are required in the presence of typical noise levels. We evaluate our method using microseismic data collected from Barnett Shale in the Fort Worth Basin, Texas. The inferred effective stress state is characterized by a subhorizontal maximum principal stress, with intermediate and minimum principal stresses deviating from the vertical and horizontal planes, respectively.