Learning Earthquake Sources Using Symmetric Autoencoders

This study examines almost 30 deep-focus earthquakes, magnitudes starting from Mw 6.0 and higher, with the aim of accurately determining the source time function (STF) of P arrival and its azimuthal dependence. We use the variational symmetric autoencoder (SymVAE)—a neural network architecture designed to automatically isolate earthquake information from far-field seismic waves. Our findings suggest that the STFs produced by the network uncover weak secondary episodes in numerous deep-focus earthquakes, hinting that these earthquakes release bursts of seismic moment. This study is the first to generate high-resolution STFs without requiring traditional path-effect deconvolution—a process that usually introduces substantial uncertainties and hinders achieving high-temporal resolution. Our unsupervised learning method for obtaining STFs does not require labeled seismograms and is based on the principle of scale separation, which allows the accumulation of earthquake information from nearby receivers. This principle states that the variations in far-field bandlimited seismic measurements resulting from finite faulting occur across two spatial scales: a slower scale associated with the source processes and a faster scale corresponding to path effects. This research compares the STFs obtained from SymVAE with those gathered by stacking envelopes and traditional deconvolution. We show that the principal features of SymVAE-derived STFs align with those of envelope stacking, especially in dense seismic networks that record large-magnitude earthquakes with high signal-to-noise ratios (SNRs). However, SymVAE can effectively extract source details from fewer stations or in situations with low SNRs, for which envelope stacking may not work; this capability is vital for directivity analysis. We evaluated the quality of the SymVAE output and performed a synthetic experiment to recover the source in the presence of path scattering.