(Auto) Differentiating geophysics: gravity modelling with spatio-temporal neural fields

Implicit neural representations (INR) have emerged as a flexible tool for implicit modelling of subsurface structures. Works such as GeoINR (Hillier et al., 2023), and curlew (Kamath et al., 2025) have laid the foundation for building increasingly complex geological models with neural fields. Linking these modelling approaches to geophysical forward models would enable better constraints on the 3D structural geological models (SGM) widely used to predict subsurface geometry for mining, engineering and energy applications.

Specifically, within curlew, geological structures are defined as distinct neural fields. Each field can “learn” arbitrary geometries that fit the available constraints, including geological and petrophysical data. The different fields are then chained together with offsetting and overprinting relationships to derive geological complexity. In this contribution, we combine the spatio-temporal model building capabilities of curlew with a highly optimized FFT-quadrature based gravity forward model (Wang et al., 2023) to generate gravity data from implicit fields. The entire framework is built within PyTorch, which allows us to update SGMs of subsurface geometry populated with property distributions through inversions of gravity datasets. Our preliminary results show that the ability to incorporate several different kinds of losses, as well as constrain both the geometry and property, dramatically improve the inversion results compared to standard inversion techniques.

References:

Hillier, M., Wellmann, F., de Kemp, E. A., Brodaric, B., Schetselaar, E., and Bédard, K.: GeoINR 1.0: an implicit neural network approach to three-dimensional geological modelling, Geosci. Model Dev., 16, 6987–7012, https://doi.org/10.5194/gmd-16-6987-2023, 2023.

Kamath, A., Thiele, S., Moulard, M., Grose, L., Tolosana-Delgado, R., Hillier, M., & Gloaguen, R. (2025). Curlew 1.0: Spatio-temporal implicit geological modelling with neural fields in python. doi:10.31223/x5kx81

Wang, X., Liu, J., Li, J. et al. Fast 3D gravity and magnetic modelling using midpoint quadrature and 2D FFT. Sci Rep 13, 9304 (2023). https://doi.org/10.1038/s41598-023-36525-2.