An efficient, probabilistic neural network approach to solving inverse problems: Inverting surface wave velocities for Eurasian crustal thickness

Nonlinear inverse problems usually have no analytical solution and may be solved by Monte Carlo methods that create a set of samples, representative of the a posteriori distribution. We show how neural networks can be trained on these samples to give a continuous approximation to the inverse relation in a compact and computationally efficient form. We examine the strengths and weaknesses of this approach and use it to determine the full a posteriori distribution of crustal thickness from surface wave velocities. The solution to this inverse problem shows significant asymmetry and large uncertainties due to trade‐off with shear velocity structure around the Moho. We produce maps of maximum likelihood crustal thickness across Eurasia which are in agreement with current knowledge about the crust; thus we provide an independent confirmation of these models. In this application, characterized by repeated inversion of similar data, the neural network algorithm proves to be very efficient.