Advances and New Insights into Real-time Magnitude Estimation for Earthquake and Tsunami Early Warning

The prompt and reliable estimation of earthquake magnitude is paramount for modern earthquake and tsunami early warning systems. In the case of earthquake early warning a reliable estimate is needed ideally within a few seconds, while for a tsunami a few minutes may be acceptable. As a result the optimal methods differ. In the case of moderately large earthquakes (up to ~M7), seismic P-waves offer the earliest information, and seismic methods based on amplitude and period are currently in practical use. We show improvements and further insights into the predominant period methods, including how low frequency noise in small magnitudes will reduce accuracy and how this can be countered by using the damped predominant period (Tpd), how variations in rupture parameters cause scatter, and hints on the causes of apparent predictability. However, for the really large earthquakes, predictions from these seismic methods seem to saturate, significantly underestimating the magnitude. By considering the Mw 9.0 Tohoku-Oki earthquake, we show that inverting for the fault slip from transient GPS displacements provides a timeous and robust estimate of magnitude (Wright et al, GRL, 2012). For magnitudes up to ~M7, methods based on seismic P-wave arrivals are in current use. These exploit the scaling between either the amplitude or the period of the early arrivals and magnitude. (Hildyard and Rietbrock, BSSA, 2010) show that the relationship of predominant period to magnitude can be significantly improved by the use of an amplitude-based damping parameter (Tpd or TpdMax). We show that this damping factor is most effective at removing spurious effects from low frequency noise in small magnitudes, which ultimately weakens predictions for large magnitudes. We also examine a range of different synthetic ruptures, and show that variation in rupture parameters accounts for significant scatter in the magnitude relationship, which cannot simply be removed through denser station coverage. Instead new approaches may be needed which relate an ongoing rupture to a specific subset of historic data. Our synthetic results also hint at new understanding on the causes of predictability of rupture from predominant period. For really large earthquakes, predictions from the above seismic methods saturate. For example, the early warning for the Mw 9.0 Tohoku-Oki earthquake saturated at Mw 8.1 after 120 seconds, significantly underestimating the magnitude. Using real-time deformation data from Japan's dense network of continuously-recording GPS stations, we show that a robust estimate of magnitude can be obtained by performing a simple static inversion on the current displacements at a subset of stations. A key novelty of this approach is that it uses the transient displacements and produces estimates while the earthquake rupture is ongoing. We find that this method produces a robust estimate of magnitude after just 100 s of the onset of rupture. An investigation into the required station density shows that a robust estimate of magnitude is obtained with less than one station every hundred kilometres.