Differentiable Geomodeling: towards a tighter implementation of structural geological models into geophysical inverse frameworks

Geological models can be constructed with a variety of mathematical methods. Generally, we can describe the modeling process in a formal way as a functional relationship between input parameters (geological observations, orientations, interpolation parameters) and an output in space (lithology, stratigraphy, rock property, etc.). However, in order to obtain a suitable implementation in geophysical inverse frameworks, we have to consider specific requirements. In recent years, a substantial amount of work focused on low-dimensional parameterizations and efficient automation of geological modeling methods, as well as their combination with suitable geophysical forward simulations. In this contribution, we focus on differential geomodelling approaches, which allow for an integration of geological modeling methods into gradient-based inverse approaches.

In this work, we emphasize differential geomodelling approaches. These approaches seamlessly integrate geological modeling methods into gradient-based inverse approaches. To achieve this integration, we actively employ modern machine learning frameworks, specifically TensorFlow and PyTorch. We then incorporate these geometric geological modeling methods into a Stein Variational Gradient Descent (SVGD) algorithm. SVGD is adept at addressing the challenges of multimodality in probabilistic inversion. Moreover, we demonstrate the implementation of these methods in a Hamiltonian Monte Carlo approach.

Our results are promising, showing that treating geological modeling as a differentiable approach unlocks new possibilities. This method facilitates novel applications in the integration of geological modeling with geophysical inversion, paving the way for advanced research in this field.