Normalising Flows for Bayesian Gravity Inversion

This work is concerned with applying machine learning to Bayesian gravity inversion. While various Bayesian frameworks have been explored for this application, these methods are not ideal due to the associated long computation time and can become intractable for a high-dimensional parameter space. For many applications, machine learning can offer a faster approach to obtaining posterior approximations, while not sacrificing accuracy. Normalising flows, which are based on the simple principles of the change of variables formula, recently have become a focus of development for a wide variety of applications. They are a popular alternative to other generative Bayesian frameworks due to their relative ease to train and their simple principles and architecture, making them more transparent and trustworthy for researchers. This work explores how this type of architecture can be applied to the common inverse problem in gravimetry and how it can improve on traditional methods. As a first application, results are shown for the inverse modelling of cuboid underground objects from a variety of gravimetry survey configurations. These simple shapes are not defined by a small number of parameters, rather the model is kept as a 3-dimensional density map defined by a grid of single-density voxels. This decision results in a more difficult problem with a high dimensional posterior space, however, it allows the approach to be more flexible and be directly applicable to the modelling of irregular bodies. Finally, it is discussed how the method performs compared to other traditional and Bayesian inversion methods.