The Matrix Profile in Seismology: Template Matching of Everything With Everything

Template matching has proven to be an effective method for seismic event detection, but is biased toward identifying events similar to previously known events, and thus is ineffective at discovering events with non-matching waveforms (e.g., those dissimilar to existing catalog events). In principle, this limitation can be overcome by cross-correlating every segment (possible template) of a seismogram with every other segment to identify all similar event pairs, but doing so has been previously considered computationally infeasible for long time series. Here we describe a method, called the 'Matrix Profile' (MP), a "correlate everything with everything" calculation that can be efficiently and scalably computed. The MP returns the maximum value of the correlation coefficient of every sub-window of continuous data with every other sub-window, as well as the best-correlated sub-window location. Here we show how MP methods can obtain valuable results when applied to months and years of continuous seismic data in both local and global case studies. We find that the MP can identify many new events in Parkfield, California seismicity that are not contained in existing event catalogs and that it can efficiently find clusters of similar earthquakes in global seismic data. Either used by itself, or as a starting point for subsequent template matching calculations, the MP is likely to provide a useful new tool for seismology research. Detecting and cataloging earthquakes through analysis of seismic data-the shapes of seismic waves, recorded by seismometers-is foundational to our understanding of Earth's interior structure and processes, as well as geological hazards such as earthquakes. Methods to improve the efficiency and sensitivity of earthquake detection while maintaining accuracy are critical, as seismic data volumes have grown exponentially in recent decades. Recently, methods that use recorded earthquakes as template patterns to identify in seismic data, have proven capable of detecting several times more earthquakes than traditional methods. However, such methods require knowledge of the template earthquakes ahead of time, and are best at identifying earthquakes whose waveforms are similar to the templates. We present here a new method, called the 'Matrix Profile' (MP), that takes short windows of data from a seismic data stream, and compares them to all other parts of that data stream, identifying parts of the data that are highly similar. The MP effectively identifies earthquakes, even those which are hidden within noise, does not require any templates to be provided upfront, and can be efficiently calculated. We demonstrate its success at detecting earthquakes in different types of seismic data, and provide practical guidelines for applying the method and interpreting the results. The matrix profile finds the maximum autocorrelation of every subsequence in a time series Peaks of high similarity in the matrix profile can be used to identify seismic events and similar event pairs The matrix profile method has similar sensitivity to template matching but does not require a priori templates