Coupled Inversion of Pressure and Tiltmeter Data for Mapping Hydraulic Fracture Geometry

Pressure and tilt data are jointly inverted to simultaneously map the orientation and dimensions of a hydraulic fracture. The deformation induced by a fracture under internal pressure is modeled using the distributed dislocation technique. The planar fracture is represented by four quarter ellipses, joined at the center and sharing semi-axes. This configuration provides a straightforward model for characterizing asymmetric fracture geometry. The inverse problem of mapping the fracture geometry is formulated using the Bayesian probabilistic method, combining the a priori information on the fracture model with updated information from pressure and tilt data. Solving the nonlinear inverse problem is achieved by pseudo-randomly sampling the posterior probability distribution through the Markov chain Monte Carlo method. The resulting posterior probability distribution is then explored to assess uncertainty, resolution, and correlation between model parameters. Numerical experiments are conducted to verify the accuracy and validity of the proposed analysis method in mapping the fracture geometry using synthetic pressure and tilt data.