Bayesian inference of geological properties from induced seismicity data using an energy-based poromechanics model

Deep water injection related to shale gas extraction is increasingly relevant for the energy sector. Injected fluids in porous deformable elastic media increase pore pressure, reduce normal effective stress, and change the available friction along factures and faults. Consequently, slip can occur, causing seismic events. Understanding this mechanism and identifying the stress field around the injection wellbores play a central role in assessing the seismic hazard. One of the crucial steps is inferring the unknown model parameters (i.e. poroelastic properties) from the noisy data of injection sites. Due to the indirect relation between the uncertain parameters and the empirical observation (i.e. number of earthquakes and stress drop variations in injection sites) and the high dimension of parameters' domain, the inverse problem is computationally expensive.

In this work, we develop a nonlinear forward model by formulating a variational continuum framework of multi-component poromechanics to characterize the evolution of stress, pore pressure, and other mechanical quantities. This is coupled to a probabilistic model that we develop to process collected data, to identify the critical points for crack initiation and to estimate the increasing probability of an earthquake. We adopt a Bayesian inference framework to integrate the partial differential equations (PDEs) of the forward mechanical model with models of uncertainty for observation and parameters. Using this approach, we can project approximate hazard assessments by exploring scenario ensembles generated from the posterior knowledge.

The Bayesian framework provides a probabilistic characterization of the unknown parameters of the physics-based model, by updating the prior knowledge of these parameters based on the noisy measurements of injection sites. Maximizing the updated probability distribution or the posterior distribution provides the solution of high-dimension inverse problem. In order to quantify the uncertainty and predictability of the solution of the Bayesian method, we will adopt a Hamiltonian Monte Carlo method to take samples of the posterior distribution.