Trainable geological model under the framework of model-based gravity inversion

Uncertainties in geological modeling have drawn increased attention in recent years. This is due to the fast-evolving computational power and more demanding evaluation of the modeling procedure.

However, these uncertainty quantifications (UQ) often face high dimensionality. Advanced mathematical methods have been developed to significantly improve the efficiency of the UQ process. Still, many of the methods require not only the forward evaluation of the quantity of interest but also the partial derivative information to guide the posterior exploration (e.g., HMC, SVGD). Differentiable geological modeling methods have been introduced and have become an appealing tool to efficiently evaluate the partial derivatives w.r.t. the input parameters using Automatic Differentiation (AD) techniques.

To successfully apply AD to geological modeling several challenges need to be addressed. One of these challenges is the aliased effect due to discretization. In this work, we will introduce a method to generate a trainable geological model under the framework of gravity inversion using the implicit geological modeling method. We present a smooth-step function in the scale value domain and adopt an order-reduction method to provide a visual evaluation of the trainability of the generated model. This work provides the fundamental step to the application of advanced derivative-informed UQ and optimization methods.