Physical Sensitivity Kernels Can Emerge in Data-Driven Forward Models: Evidence From Surface-Wave Dispersion
This work addresses the problem of understanding the physical interpretability of neural network surrogates in geophysics, which is incremental but clarifies conditions for their use in inversion and uncertainty analysis.
The study investigated whether data-driven neural networks used as surrogate forward models in geophysics recover the underlying physical sensitivity structure, not just data mappings, by comparing gradients from a neural network with theoretical kernels for surface-wave dispersion. The results showed that the learned gradients can recover the main depth-dependent structure of physical kernels across a broad range of periods, indicating that neural surrogates can learn physically meaningful differential information.
Data-driven neural networks are increasingly used as surrogate forward models in geophysics, but it remains unclear whether they recover only the data mapping or also the underlying physical sensitivity structure. Here we test this question using surface-wave dispersion. By comparing automatically differentiated gradients from a neural-network surrogate with theoretical sensitivity kernels, we show that the learned gradients can recover the main depth-dependent structure of physical kernels across a broad range of periods. This indicates that neural surrogate models can learn physically meaningful differential information, rather than acting as purely black-box predictors. At the same time, strong structural priors in the training distribution can introduce systematic artifacts into the inferred sensitivities. Our results show that neural forward surrogates can recover useful physical information for inversion and uncertainty analysis, while clarifying the conditions under which this differential structure remains physically consistent.