Multi-scale generative adversarial networks (GAN) for generation of three-dimensional subsurface geological models from limited boreholes and prior geological knowledge

Delineation of subsurface stratigraphy is an essential task in site characterization. A three-dimensional (3D) subsurface geological model that precisely depicts stratigraphic relationships in a specific site can greatly benefit subsequent geotechnical analysis and designs. However, only a limited number of boreholes is usually available from a specific site in practice. It is therefore challenging to properly construct complex stratigraphic relationships in a 3D space based on sparse measurements from limited boreholes. To tackle this challenge, this study proposes a generative machine learning method called multi-scale generative adversarial networks (MS-GAN) for developing 3D subsurface geological models from limited boreholes and a 3D training image representing prior geological knowledge. The proposed method automatically learns multi-scale 3D stratigraphic patterns extracted from the 3D training image and generates 3D geological models conditioned on limited borehole data in an iterative manner. The proposed method is illustrated using 3D numerical and real data examples, and the results indicate that the proposed method can effectively learn the stratigraphic information from a 3D training image to generate multiple 3D realizations from sparse boreholes. Both accuracy and associated uncertainty of 3D realizations are quantified. Effect of borehole number on performance of the proposed method is also investigated.