Near-real time 3D seismic velocity and uncertainty models from ambient noise, gradiometry and neural network inversion

Producing seismic wave speed models of the Earth's interior with full uncertainty estimates is a grand challenge of geophysics. It is relatively easy to produce uncertainty estimates by linearising (approximating) the nonlinear physics relating models to data, but in strongly nonlinear problems such estimates can be almost worthless. Nonlinear solutions are usually calculated using Monte Carlo methods, requiring weeks of computation due to the high dimensionality of parameter spaces. In addition, using seismic interferometry to obtain reliable surface wave dispersion data from ambient noise often requires several days of recordings. Clearly both recording and computation timescales must be reduced dramatically to allow ambient noise tomography in near-real time. Recording times must be reduced by changing methods used to obtain dispersion curves. Computation time is constrained by two mathematical results: the 'curse of dimensionality' precludes exhaustive Monte Carlo search in high-dimensional parameter spaces, and “No-Free-Lunch” theorems state that improvements over exhaustive search require substantial additional a priori information. Nevertheless, we show that recording times can be reduced to the order of minutes, and that common a priori physical assumptions plus a separation of up-front and real-time computation allow 3D velocity models and uncertainties to be obtained in less than an hour.