We use neural networks to find 1-dimensional marginal probability density functions (pdfs) of global crustal parameters. The information content of the full posterior and prior pdfs can quantify the extent to which a parameter is constrained by the data. We inverted fundamental mode Love and Rayleigh wave phase and group velocity maps for pdfs of crustal thickness and independently of vertically averaged crustal shear wave velocity. Using surface wave data with periods T > 35 s for phase velocities and T > 18 s for group velocities, Moho depth and vertically averaged shear wave velocity of continental crust are well constrained, but vertically averaged shear wave velocity of oceanic crust is not resolvable. The latter is a priori constrained by CRUST2.0. We show that the resulting model allows to compute global crustal corrections for surface wave tomography for periods T > 50 s for phase velocities and T > 60 s for group velocities.