Real-time estimation of fault rupture extent using envelopes of acceleration

We present a new strategy to estimate the geometry of a rupture on a finite fault in real time for earthquake early warning. We extend the work of Cua and Heaton who developed the virtual seismologist (VS) method (Cua, 2005), which is a Bayesian approach to seismic early warning using envelope attenuation relationships. This article extends the VS method to large earthquakes where fault finiteness is important. We propose a new model to simulate high-frequency motions from earthquakes with large rupture dimension: the envelope of high-frequency ground motion from a large earthquake can be expressed as a root-mean-squared combination of envelope functions from smaller earthquakes. We use simulated envelopes of ground acceleration to estimate the direction and length of a rupture in real time. Using the 1999 Chi-Chi earthquake dataset, we have run simulations with different parameters to discover which parameters best describe the rupture geometry as a function of time. We parameterize the fault geometry with an epicenter, a fault strike, and two along-strike rupture lengths. The simulation results show that the azimuthal angle of the fault line converges to the minimum uniquely, and the estimation agrees with the actual Chi-Chi earthquake fault geometry quite well. The rupture direction can be estimated at 10 s after the event onset, and the final solution is achieved after 20 s. While this methodology seems quite promising for warning systems, it only works well when there is an adequate distribution of near-source stations.