All Times ET
Keywords: Long-range dependence, Time series, Earthquakes
Low-frequency earthquakes are small magnitude (less than 2) earthquakes, with reduced amplitudes at frequencies greater than 10 Hz relative to ordinary small earthquakes. They are often detected in subduction zones at the plate boundary between a subducting tectonic plate and the overriding plate. They are usually grouped into families of events, with all the earthquakes from a given family originating from the same small patch on the plate interface. They tend to occur in bursts, that is dozen of earthquakes are detected within a few hours or days, followed by weeks or months of quiet, with just a few earthquakes occurring. Long-range dependence is a phenomenon that may arise in the statistical analysis of time series data. It relates to the slow rate of decay of the statistical dependence between two points with increasing time interval between the points. In this paper, I study evidence of long-range dependence in low-frequency earthquake catalogs. For each family of events, the dataset contains the timing (and sometimes the magnitude) of each earthquake associated with this family. I thus translate the list of earthquake occurrence times into a discrete time series defined by the number of earthquakes per unit of time. The time series associated with two different families are correlated, but the study of this correlation is beyond the scope of this paper. In this paper, I analyze each earthquake time series independently from the others. I use several graphical methods to estimate either the Hurst parameter H or the fractional differencing parameter d associated with each time series. Many low-frequency earthquake time series seem to show evidence of long-range dependence, with values of the Hurst parameter between 0.5 and 1 and values of the fractional differencing parameter between 0 and 0.5.