Automatic slowness vector measurements of seismic arrivals with uncertainty estimates using bootstrap sampling, array methods and unsupervised learning

Horizontal slowness vector measurements using array techniques have been used to analyse many Earth phenomena from lower mantle heterogeneity to meteorological event location. While providing observations essential for studying much of the Earth, slowness vector analysis is limited by the necessary and subjective visual inspection of observations. Furthermore, it is challenging to determine the uncertainties caused by limitations of array processing such as array geometry, local structure, noise and their effect on slowness vector measurements. To address these issues, we present a method to automatically identify seismic arrivals and measure their slowness vector properties with uncertainty bounds. We do this by bootstrap sampling waveforms, therefore also creating random sub arrays, then use linear beamforming to measure the coherent power at a range of slowness vectors. For each bootstrap sample, we take the top N peaks from each power distribution as the slowness vectors of possible arrivals. The slowness vectors of all bootstrap samples are gathered and the clustering algorithm DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is used to identify arrivals as clusters of slowness vectors. The mean of slowness vectors in each cluster gives the slowness vector measurement for that arrival and the distribution of slowness vectors in each cluster gives the uncertainty estimate. We tuned the parameters of DBSCAN using a data set of 2489 SKS and SKKS observations at a range of frequency bands from 0.1 to 1 Hz. We then present examples at higher frequencies (0.5–2.0 Hz) than the tuning data set, identifying PKP precursors, and lower frequency by identifying multipathing in surface waves (0.04–0.06 Hz). While we use a linear beamforming process, this method can be implemented with any beamforming process such as cross correlation beamforming or phase weighted stacking. This method allows for much larger data sets to be analysed without visual inspection of data. Phenomena such as multipathing, reflections or scattering can be identified automatically in body or surface waves and their properties analysed with uncertainties.