Probabilistic neural network tomography across Grane field (North Sea) from surface wave dispersion data

Surface wave tomography uses measured dispersion properties of surface waves to infer the spatial distribution of subsurface properties such as shear-wave velocities. These properties can be estimated vertically below any geographical location at which surface wave dispersion data are available. As the inversion is significantly non-linear, Monte Carlo methods are often used to invert dispersion curves for shear-wave velocity profiles with depth to give a probabilistic solution. Such methods provide uncertainty information but are computationally expensive. Neural network based inversion provides a more efficient way to obtain probabilistic solutions when those solutions are required beneath many geographical locations. Unlike Monte Carlo methods, once a network has been trained it can be applied rapidly to perform any number of inversions. We train a class of neural networks called mixture density networks, to invert dispersion curves for shear-wave velocity models and their non-linearised uncertainty. Mixture density networks are able to produce fully probabilistic solutions in the form of weighted sums of multivariate analytic kernels such as Gaussians, and we show that including data uncertainties in the mixture density network gives more reliable mean velocity estimates when data contains significant noise. The networks were applied to data from the Grane field in the Norwegian North sea to produce shear-wave velocity maps at several depth levels. Post-training we obtained probabilistic velocity profiles with depth beneath 26,772 locations to produce a 3D velocity model in 21 seconds on a standard desktop computer. This method is therefore ideally suited for rapid, repeated 3D subsurface imaging and monitoring.