A surrogate model for predicting ground surface deformation gradient induced by pressurized fractures

Fast and reliable estimation of engineered fracture geometries is a key factor in controlling undesirable fractures and enhancing stimulation design. Measuring the surface deformation gradient (tilt) for engineered fractures in shallow depths (<1000 m) has been proven a reliable source of data to infer fracture geometry, thanks to the impressive resolution of tiltmeter units (in the order of nano-radians). However, solving the inverse problem requires reliable and fast forward models. In this study, we present a fast and reliable machine-learned surrogate model to estimate the ground surface tilt induced by pressurised fractures. The proposed surrogate model, based on Conditional Generative Adversarial Networks (cGAN), receives a fracture aperture map in XY and XZ planes as input and predicts the corresponding surface tilts (in X and Y directions). The surrogate model with Wasserstein loss and gradient penalty has been trained using 11,000 samples and tested for a range of input parameters such as depth, dip angles, elastic properties, fluid pressures and fracture shapes. The testing results show excellent performance of the surrogate model compared with the forward finite element model for both single and multiple pressurised fractures, while running hundreds to potentially thousands of times faster.