A Scalable Online Algorithm For Passive Seismic Tomography In Underground Mines

Understanding and monitoring the seismic responses of rock masses to massive mining are crucial for safety and economic viability of ever larger and deeper underground operations. Seismic monitoring can be used to detect stress variations and hazardous instabilities, but its effectiveness requires accurate estimations of the nonhomogeneous propagation velocity of microseismic waves. While predetermined velocity models are not accurate enough and might bias hypocenter localization, using activesource seismic tomography methods to estimate the velocity field provides limited spatial coverage. Thus, passive seismic tomography using first-arrival traveltimes of mining-induced microseisms (of unknown hypocenters) constitutes a promising tool. However, available methods solving this high-dimensional statistical inverse problem do not scale well with the data set size and cannot easily refine or update estimations with new data. We have developed a novel passive seismic tomography method able to dynamically ylearn the nonhomogeneous velocity field from a streaming of noisy first-arrival times, online (in real time) or from catalogs. We have developed a new Bayesian approach that avoids linearizing the forward problem and allows for general 3D velocity models. This is combined with the use of the stochastic gradient descent (SGD) method, which underlies much of the recent progress in machine learning and provides increasing accuracy at a cost scaling linearly with the data set size. Moreover, we introduce an adaptive variant of SGD based on raypath density, which significantly improves the speed of the algorithm, and we implement a parallel version of our method enabling its systematic use in real applications. These include the design of optimal sensor locations, the dynamic update of velocity estimates in production conditions, and the real-time determination of hypocenters and their uncertainty. Our method's reach and effectiveness are illustrated with simulated seismic data on 3D checkerboards, using synthetic and real acquisition geometries, and on a dense 2D velocity grid.