Rethinking Full-Waveform Inversion: A New Era with Neural Networks?

Full-waveform inversion (FWI) has been the cornerstone of geophysical exploration, medical imaging, and non-destructive testing. Its ability to estimate physical parameters from limited measurements is essential. Yet, traditional FWI methods carry a significant Achilles' heel, their sensitivity to initial model accuracy. A new frontier in continuous representation FWI (CR-FWI) might just be changing the game.

The Neural Network Leap

Recent innovations have introduced the idea of using coordinate-based neural networks, like implicit neural representations (INR), to model parameters. This shift potentially mitigates the reliance on initial models. However, one can't ignore the elephant in the room: Why does INR-based FWI have slower high-frequency convergence? The answer lies in the novel wave-based neural tangent kernel (NTK) framework.

Unlike the standard NTK, the wave-based variant isn't constant, neither at the start nor during training. Its nonlinearity is a double-edged sword, explaining both the reduced dependency on initial models and the slower convergence at higher frequencies. This insight paves the way for improved CR-FWI methods, including a hybrid model that marries INR with multi-resolution grids, coined as IG-FWI.

Real-World Implications

Let's talk numbers. Applications in geophysical exploration using models like Marmousi and the 2014 Chevron have illustrated the superior performance of these new methods. Compared to conventional FWI and existing INR-based methods, the advancements are tangible. But here's the burning question: Is this just a flash in the pan, or the dawn of a new era for FWI?

The intersection of AI and geophysical exploration is very real, but as always, ninety percent of such projects aren't worth the hype. Slapping a model on a GPU rental isn't a convergence thesis. Show me the inference costs. Then we'll talk about real-world viability. For now, the CR-FWI methods are promising, but the jury's still out on their long-term impact.