Scaling relationships between catalog magnitude and (a) τpmax and (b) Pdc. Light gray dots are individual station observations for all events in study. Green squares and red and blue triangles are average values for individual earthquakes from the historic/calibration data sets from Japan (JAP), Southern California (SCA), and Northern California (NCA), respectively. Black crosses are average values for earthquakes recorded in real-time by ElarmS across California. In Figure 1a the best fit lines to the regional data sets are shown with colored lines, and the black line is the best linear fit to all the data excluding the real-time-detected earthquakes (equation shown). In Figure 1b the black line (equation shown) is the least squares multiregression fit to the entire data set and represents our preferred global scaling relationship.
We examine five different methods to estimate an earthquake’s magnitude using only P wave data for use in earthquake early warning systems. We test two input parameters: the maximum predominant period of the P wave (τpmax) and the displacement amplitude of the P wave’s vertical component (Pd). We apply our algorithms to 174 earthquakes 3.0 < M < 8.0 from California and Japan that have also been used in previous calibration studies. We also apply them to 1992 0.2 < M < 5.7 earthquakes that were processed by the real-time Earthquake Alarm Systems in California. We find that τpmax does not scale with magnitude for small earthquakes (M < 3) and is less accurate for large- magnitude earthquakes than using Pd alone. We derive a global scaling relation between Pd and magnitude and conclude that this global relationship provides the most accurate and robust magnitude estimate. This relationship could be applied in earthquake source zones around the world.