S U M M A R YThe determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(m|d), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)-a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as 'committees', we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 M W 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account.

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The robust and automated determination of earthquake source parameters on a global and regional scale is important for many applications in seismology. We present a novel probabilistic method to invert a wide variety of (waveform) data for point-source parameters in real time using pattern recognition. Inferences are made in the form of marginal probability density functions for point-source parameters and incorporate realistic posterior uncertainty estimates. The neural-network-based method is calibrated using samples from the prior distribution, which are synthetic data vectors, and corresponding sources located in a predefined monitoring volume. Once a set of trained neural networks is available, inversions are fast with very moderate demands on computational resources: an inversion takes less than a second on a standard desktop computer. Uncertainties in the layered Earth model are taken into account in the Bayesian framework and increase the robustness of the results with respect to neglected 3D heterogeneities. Moreover, we find that the method is very robust with respect to perturbations such as observational noise and missing data and therefore is potentially well suited for automated and real-time tasks, such as earthquake monitoring and early warning. We demonstrate the method by means of synthetic tests and by inverting an observed high-rate Global Positioning System displacement dataset for the 2010 M w 7.2 El Mayor-Cucapah event. Our results are compatible with published point-source estimates for this event within the respective uncertainty bounds.Online Material: Additional information on the neural network methodology and implementation details, tables on neural network parameters, crustal model and reference double-couple solution, and figures showing prediction error, crustal models, normalized displacements, and histograms of weighted parameters.

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