Earthquake magnitude calculation without saturation from the scaling of peak ground displacement

GPS instruments are noninertial and directly measure displacements with respect to a global reference frame, while inertial sensors are affected by systematic offsetsprimarily tiltingthat adversely impact integration to displacement. We study the magnitude scaling properties of peak ground displacement (PGD) from high-rate GPS networks at near-source to regional distances (similar to 10-1000 km), from earthquakes between M(w)6 and 9. We conclude that real-time GPS seismic waveforms can be used to rapidly determine magnitude, typically within the first minute of rupture initiation and in many cases before the rupture is complete. While slower than earthquake early warning methods that rely on the first few seconds of P wave arrival, our approach does not suffer from the saturation effects experienced with seismic sensors at large magnitudes. Rapid magnitude estimation is useful for generating rapid earthquake source models, tsunami prediction, and ground motion studies that require accurate information on long-period displacements.