Equalized Plot Scales for Exploring Seismicity Data

Abstract

Online Material: Alternate magnitude versus time plots and FORTRAN code. All earthquake catalogs share three features: the earthquakes cluster in space and time, the small earthquakes greatly outnumber the big ones, and many earthquakes that actually happened are missing. The first two features are natural, but the third, the incompleteness of the catalog, is not: which earthquakes are missed depends both on such natural features as attenuation and noise and on such man‐made ones as where data are collected and how they are converted to a list of earthquakes. For almost all catalogs, the complicated history of the data collection and analysis causes the catalog completeness to vary with time. Because the completeness affects all other analyses, any study of an earthquake catalog must first determine it, by finding an earthquake magnitude above which no earthquakes are thought to be missing. Many different methods have been proposed to determine this value (Mignan and Woessner, 2012). Some use the catalog itself, comparing the distribution of magnitudes with the Gutenberg–Richter distribution (for example see Wiemer and Wyss, 2000; Kagan, 2003; Woessner and Wiemer, 2005; Mignan et al. , 2011; Mignan, 2012; Michael, 2014) or examining the daily variation in seismicity caused by time‐varying noise (Rydelek and Sacks, 1989). Others use additional information, whether measurements of noise levels (Gomberg, 1991; Kvaerna et al. , 2002a,b) or the record of which earthquakes were detected at each station (Schorlemmer and Woessner, 2008; Nanjo et al. , 2010). All these methods implicitly assume a constant completeness magnitude over whatever time period is analyzed—an assumption that must itself be checked before estimating this magnitude. Some statistical methods (Albarello et al. , 2001; Hakimhashemi and Grunthal, 2012) seek to estimate time‐varying completeness, but such an initial step should probably be regarded as …