Learned extensions for wave-based simulation and inversion

We introduce a new method that explores velocities as an operator (extended velocities) for wave-equation based inversion. Through this extended formulation, we obtain the known benefits of working with subsurface offset volumes. The offset-dependence of these volumes has been studied in the linear case, i.e as part of extended Born scattering and extended least-squares reverse-time migration, but has been avoided for non-linear inversion due to computational concderns and challenges. By using techniques from randomized linear algebra, we will show that we can work with extended velocities for inversion while maintaining an acceptable computational cost much lower than solving one PDE per extended velocity model.