Probabilistic Source Inversion of Seismic Waveform and Geodetic Data Using Neural Networks

Although well-established methods for source parameter estimation exist and are carried out on a routine basis, they are usually based on linear approximations, and a realistic uncertainty quantification is often lacking. Moreover, there is increasing interest in combining conventional seismic waveforms with other datasets sensitive to the seismic source, such as InSAR or continuous GPS recordings. We aim to invert seismic waveform and geodetic data using a neural network approach, which is both fast and provides posterior probability distributions over source parameters. Neural networks can be considered as function approximators, able to learn general mappings to arbitrary accuracy given examples of inputs and results. An extension to standard neural networks, the Mixture Density Network, makes it possible to directly model marginal posterior probability density functions as a mixture of Gaussian kernels. This approach enables us to consistently treat measurement- and modeling-uncertainties in a Bayesian framework and accounts for the possible non-uniqueness of the solutions. As a proof of concept, we train Mixture Density Networks on synthetic seismograms calculated in a 1-D Earth model to output centroid locations and moment tensors. We also show how this flexible approach can readily be extended to other data sources such as static displacement measurements. Furthermore, once a trained network is available, inversions are fast and require only little computational power, which makes the approach suitable for real-time tasks such as early warning.