Fluid injection for geoenergy development and waste disposal can perturb in situ stresses and reactivate pre-existing faults, thereby inducing seismicity. Most existing analytical solutions assume isotropic reservoirs and may overlook the poroelastic anisotropy commonly observed in layered sedimentary formations. This study presents a closed-form analytical model for injection-induced fault reactivation in a transversely isotropic reservoir intersected by a displaced fault. The pressurized reservoir is represented by two trapezoidal inclusions with uniform injection-induced eigenstrain, and the resulting poroelastic stress and displacement fields are derived from Eshelby inclusion theory and orthotropic Green functions. The proposed solution recovers existing isotropic solutions as limiting cases and is verified against finite-element simulations, showing good agreement for fault-parallel shear and normal stresses. Parametric analyses demonstrate that elastic anisotropy has a secondary effect on fault stability, whereas directional Biot coefficients strongly control Coulomb stress changes and the length of potentially unstable fault segments. The vertical Biot coefficient is more influential for gently dipping faults, while the horizontal Biot coefficient becomes more important for steeply dipping faults. Lithology-based comparisons further indicate that clay-rich formations are more prone to reactivation because strong poroelastic coupling is combined with relatively low frictional resistance. The proposed solution provides a rapid and physically transparent tool for first-order assessment of induced-seismicity risk in injection-related subsurface operations, especially where mechanically weak anisotropic formations bound the reservoir.
 

Injection-induced seismicity,Fault,Poroelastic anisotropy,Eshelby’s inclusion theory,Analytical solution