We present a neural network approach to invert surface wave data for a global model of crustal thickness with corresponding uncertainties. We model the a posteriori probability distribution of Moho depth as a mixture of Gaussians and let the various parameters of the mixture model be given by the outputs of a conventional neural network. We show how such a network can be trained on a set of random samples to give a continuous approximation to the inverse relation in a compact and computationally efficient form. The trained networks are applied to real data consisting of fundamental mode Love and Rayleigh phase and group velocity maps. For each inversion, performed on a 2 degrees x 2 degrees grid globally, we obtain the a posteriori probability distribution of Moho depth. From this distribution any desired statistic such as mean and variance can be computed. The obtained results are compared with current knowledge of crustal structure. Generally our results are in good agreement with other crustal models. However in certain regions such as central Africa and the backarc of the Rocky Mountains we observe a thinner crust than the other models propose. We also see evidence for thickening of oceanic crust with increasing age. In applications, characterized by repeated inversion of similar data, the neural network approach proves to be very efficient. In particular, the speed of the individual inversions and the possibility of modelling the whole a posteriori probability distribution of the model parameters make neural networks a promising tool in seismic tomography.
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