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Surface wave tomography uses measured dispersion properties of surface wavesto infer the spatial distribution of subsurface properties such as shear-wavevelocities. These properties can be estimated vertically below any geographicallocation at which surface wave dispersion data are available. As the inversionis significantly non-linear, Monte Carlo methods are often used to invertdispersion curves for shear-wave velocity profiles with depth to give aprobabilistic solution. Such methods provide uncertainty information but arecomputationally expensive. Neural network based inversion provides a moreefficient way to obtain probabilistic solutions when those solutions arerequired beneath many geographical locations. Unlike Monte Carlo methods, oncea network has been trained it can be applied rapidly to perform any number ofinversions. We train a class of neural networks called mixture densitynetworks, to invert dispersion curves for shear-wave velocity models and theirnon-linearised uncertainty. Mixture density networks are able to produce fullyprobabilistic solutions in the form of weighted sums of multivariate analytickernels such as Gaussians, and we show that including data uncertainties in themixture density network gives more reliable mean velocity estimates when datacontains significant noise. The networks were applied to data from the Granefield in the Norwegian North sea to produce shear-wave velocity maps at severaldepth levels. Post-training we obtained probabilistic velocity profiles withdepth beneath 26,772 locations to produce a 3D velocity model in 21 seconds ona standard desktop computer. This method is therefore ideally suited for rapid,repeated 3D subsurface imaging and monitoring.

Probabilistic Neural Network Tomography across Grane field (North Sea) from Surface Wave Dispersion Data