Seismic magnitude estimates for the first hour after the Mw 9.2-9.3 Sumatra earthquake of December 26, 2004 were far too low, incorrectly indicating no danger of a major oceanwide tsunami. However, weeks of GPS data following the earthquake revealed [1-3] that stations as far away as India were permanently displaced >10 mm, indicating Mw 9.0-9.2. We show here that these static displacements, hence the earthquake's true size and tsunami potential, can be determined accurately using only 15 minutes of GPS data after earthquake initiation. We simultaneously reduced data from GPS stations ranging up to 7,500 km from the epicenter, including 37 operated by the International GNSS Service (IGS), plus station SAMP in the near field (~300 km). Using GIPSY-OASIS II software, data at 30-second epochs were reduced to a time series of station longitude, latitude and height, using a customized procedure that simulates a real-time analysis situation. The analysis only used 24 hours of data until 20.4 minutes after the origin time, applying a forward-filtering estimation strategy designed to eliminate sensitivity to information that would not have been available in real time. Simultaneously estimated parameters include the Earth's instantaneous pole position and rate of drift, the Earth's rate of rotation, state vectors of the satellite orbits (initialized using the Broadcast Ephemeris), stochastic solar radiation pressure on the satellites, biases in the satellite and station clocks at every 30-second epoch, random-walk variation in zenith tropospheric delay allowing for stochastic spatial gradients over each station, constant biases plus random steps for each station-satellite arc of carrier phase observables, and coordinates of GPS station positions. Station positions were estimated in two categories: the 28 far-field station positions were estimated as constants over the 24 hour period, and the 10 near- to mid-field station positions were estimated independently at every 30-second epoch. Parameters were estimated using a square-root information filter, a sequential algorithm adaptable to real-time applications. In addition, we applied a position-based sidereal filter using the stacked results of the previous 4 days of position residuals, applying a 4-minute shift each day. The actual processing time for a 38-station network is ~15% of real time on a common 1-cpu PC running Linux, and so should pose no fundamental time limitation for a real-time operational system. The resulting time series of station positions clearly shows that most of the permanent, static displacement occurs within a few minutes of the first detectable arrival of seismic waves, accompanied by strong shaking that initially overshoots the final static position. At 15 minutes after the origin time, rapidly estimated displacements of 10 stations agree to 7-mm RMS with longer-term published estimates [1-3]. By applying F-tests to the misfit of earthquake models (see figure) of various magnitude and rupture length, we can only accept mega-thrust models in the range Mw 8.7-9.3, with the most-probable magnitudes Mw 8.9-9.1, and rupture length 1000 km (propagating northward). To assess the accuracy of our rapid, best-fitting model, we compared its predictions with three published sets of displacements [1-3]. The RMS differences in displacement range from 2.5-4.1 mm, which is at the same level of agreement as between the published displacements themselves, indicating that our rapidly estimated model is accurate at this level. Thus a rapid analysis of the existing GPS network can estimate Mw accurately and provide information on the direction and length of rupture propagation, all of which are important for assessing the potential for an open ocean tsunami. This GPS static displacement technique could be incorporated into tsunami warning systems to augment current methods, which are based on seismology and ocean wave sensors. GPS should particularly help provide timely warnings of major oceanwide tsunamis. Accomplishing this would require the development of real-time GPS networks, operational analysis systems, and the refinement of GPS static displacement methodology to ensure robustness in a variety of potential scenarios. In particular, our results show dramatically enhanced sensitivity to the magnitude of great earthquakes where the global IGS network is augmented by GPS stations in the near field (within a rupture length of the rupture), indicating the advantage of having real-time GPS networks near oceanic subduction zones. Fortunately many such networks exist, or are being planned, and so could be upgraded with real-time communications and incorporated into tsunami warning systems.  P. Banerjee, F. F. Pollitz, R. Burgmann, Science 308, 1769 (2005).  C. Vigny et al., Nature 436, 201 (2005).  C. Kreemer, G. Blewitt, W. C. Hammond, H.-P. Plag, Earth Planets and Space, in press (2006).