Velocity model building from seismic images using a Convolutional Neural Operator

The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators for the mapping. Thus, we propose a novel inversion framework that relies on learning to map the velocity model to a seismic image using a Convolutional Neural Operator (CNO), and then we use optimization to invert for the velocity that matches the image. The key to the success of our network is that we use the initial and true velocity models as input in the training, then we invert for the true velocity starting from the initial velocity at inference. Specifically, we first train a neural operator to accurately learn the forward mapping from seismic velocity models to RTM images, using synthetic datasets that include high-frequency structural information. Once trained, the neural operator is embedded into an inversion loop, where its differentiable nature enables efficient gradient computation via automatic differentiation. This allows us to progressively inject high-wavenumber information from RTM images into the background velocity model, thereby improving resolution without the need for traditional adjoint-state solvers. The proposed framework is validated on both synthetic and field data. Results demonstrate that the neural operator generalizes well to real seismic scenarios, maintains high inversion accuracy, and significantly reduces computational cost. This work highlights the potential of neural operators as flexible and scalable tools for efficient, data-driven seismic imaging and inversion.