Determination of earthquake magnitude using GPS displacement waveforms from real-time precise point positioning

For earthquake and tsunami early warning and emergency response, earthquake magnitude isthe crucial parameter to be determined rapidly and correctly. However, a reliable and rapidmeasurement of the magnitude of an earthquake is a challenging problem, especially forlarge earthquakes (M > 8). Here, the magnitude is determined based on the GPS displacementwaveform derived from real-time precise point positioning (RTPPP). RTPPP results areevaluated with an accuracy of 1 cm in the horizontal components and 2-3 cm in the verticalcomponents, indicating that the RTPPP is capable of detecting seismic waves with amplitudeof 1 cm horizontally and 2-3 cm vertically with a confidence level of 95 per cent. In orderto estimate the magnitude, the unique information provided by the GPS displacement waveformis the horizontal peak displacement amplitude. We show that the empirical relation ofGutenberg (1945) between peak displacement and magnitude holds up to nearly magnitude9.0 when displacements are measured with GPS. We tested the proposed method for threelarge earthquakes. For the 2010 M_w7.2 El Mayor-Cucapah earthquake, our method providesa magnitude of M7.18 ± 0.18. For the 2011 M_w9.0 Tohoku-oki earthquake the estimatedmagnitude is M8.74 ± 0.06, and for the 2010 M_w8.8 Maule earthquake the value is M8.7 ±0.1 after excluding some near-field stations. We, therefore, conclude that depending on theavailability of high-rate GPS observations, a robust value of magnitude up to 9.0 for a pointsource earthquake can be estimated within tens of seconds or a few minutes after an eventusing a few GPS stations close to the epicentre. The rapidmagnitude could be as a pre-requisitefor tsunami early warning, fast source inversion and emergency response is feasible.