An efficient approach to uncertainty quantification for deep learning based microseismic source location

Uncertainty quantification (UQ) remains a pain-point in microseismic source localisation tasks, even more so in recent years with the increased popularity of deep learning-based solutions. While most UQ methods rely on costly procedures, such as Monte Carlo methods, in this study we illustrate how a neural network can be trained to directly estimate the underlying parameters of the probability density function associated with an estimate of the source location. More specifically, by describing the source location with a multi-variate Gaussian distribution and minimizing the negative log-likelihood, the network can efficiently predict the mean (source location) and covariance (uncertainty) of such a probability distribution, while only being constrained by the source location detailed in the training labels. The procedure is validated on two scenarios that are known to commonly introduce uncertainty into the source location estimation process: the use of an incorrect velocity model and the presence of errors in the arrival time selection. In both scenarios, the uncertainty predicted by the networks increases when compared to an ideal scenario.