Bayesian inversion of tilt data using a machine-learned surrogate model for pressurised fractures

Abstract

We introduce an innovative inversion approach for deducing subsurface fractures through observations of ground surface tilt. We have constructed, evaluated, and applied a surrogate forward model, crafted using conditional Generative Adversarial Networks (cGAN), to forecast the tilts (displacement gradients) at the ground surface caused by subsurface fractures under pressure. Our findings indicate that this surrogate forward model accurately estimates the tilt vector at the surface resulting from the specified pressurised fracture. Even in complex scenarios involving multiple fractures at various depths, the model, which was initially trained on scenarios with single fractures at a fixed depth, performed well. Subsequently, we employed a Bayesian inversion algorithm to derive the optimised solution (the pressurised fracture) for a given set of surface tilt data, leveraging the surrogate forward model. The outcomes demonstrate that the inversion process with the surrogate model is both effective and significantly faster compared to the traditional finite element model that generated the training data.