Surface wave tomography: finite-frequency effects lost in the null space

We compared surface wave tomography models obtained using finite-frequency kernels and ray theory. We systematically changed regularization in both cases and plotted data misfit against the number of independent parameters in the solution. Our tests show that models from finite-frequency kernels and ray-theoretical kernels are statistically similar. This means that any model obtained using one forward theory can be obtained using the other one by appropriately changing the damping constant. It is clear that finite-frequency theory is a better forward theory to represent the wavefield, but the associated inverse problem is not less ill posed. Indeed, current data coverage is such that the solution is dominated by the chosen regularization. This prevents us from achieving a resolution of the order of the Fresnel zone, or beyond, and noticing the benefits of a better forward theory.