Different from the conventional approach to tsunami warnings that rely on earthquake magnitude estimates, we have found that coastal GPS stations are able to detect continental slope displacements of faulting due to big earthquakes, and that the detected seafloor displacements are able to determine tsunami source energy and scales instantaneously. This method has successfully replicated three historical tsunamis caused by the 2004 Sumatra earthquake, the 2005 Nias earthquake, and the 1964 Alaska earthquake, respectively, and has been compared favorably with the conventional seismic solutions that usually take hours or days to get through inverting seismographs. Because many coastal GPS stations are already in operation for measuring ground motions in real time as often as once every few seconds, this study suggests a practical way of identifying tsunamigenic earthquakes for early warnings and reducing false alarms.
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 The tragedy of the December 2004 Indian Ocean tsunami has been partially blamed on the initially under-estimated earthquake magnitude and the lack of a tsunami warning system in the Indian Ocean [Kerr, 2005]. Since then, several powerful undersea earthquakes have occurred in both the Indian and Pacific Oceans. In fact, their magnitudes were properly detected, but none of the resulting tsunamis was correctly predicted. Here are the facts: the March 2005 Nias Mw 8.7 earthquake, the June 2005 Mw7.2 west California earthquake, the May 2006 Mw7.8 Tonga earthquake, the November 2006 Mw8.3 and the January 2007 Mw8.2 Kuril Islands earthquakes - all of them created large-scale tsunami alarms/alerts and panic in surrounding countries, but no damaging tsunamis were observed. Surprisingly, two relatively smaller earthquakes, the July 2006 West Java Mw 7.7 earthquake (no early warning was issued out of fear of false alarms [Jouhana and Paddock, 2006]) and the April 2007 Solomon Mw 8.0 earthquake, generated unexpectedly large tsunamis that killed about 600 and 30 people, respectively. The United States Government Accountability Office recently reported that 16 tsunami warnings had been issued in the Pacific Ocean from 1982 to May 2006; however, no damaging waves actually has ever reached U.S. shores [U.S. Government Accountability Office, 2006]. Too many false alarms not only undermine the credibility of the warning system but also have negative economic and societal impact.
 The inability of predicting tsunami potentials from seismic information and the high rate of false alarms indicate that the currently used earthquake-magnitude-based-method for early warnings is not ideal. For example, Sobolev et al.  recently demonstrated that the presence of islands can make tsunamis sensitive by a factor of 5 for earthquakes with the same magnitude but different slip distribution. The key to successful tsunami prediction for saving lives and property during tsunami emergencies is the early detection of not only earthquake magnitudes, but also tsunami scales. Recent studies in this direction have shown promising results from a GPS-based-method [Vigny et al., 2005; Subarya et al., 2006; Blewitt et al., 2006; Sobolev et al., 2006, 2007]. Particularly, Blewitt et al. showed that real-time GPS inversion of the earthquake source was feasible and Sobolev et al. proposed an elegant GPS-shield concept for global oceans.
 Following up on these previous studies, here we introduce an innovative approach to determine tsunami scales directly from GPS displacement measurements for early warnings. Our method focuses on estimating tsunami source energy directly from seafloor motions because a tsunami's potential or scale, no matter how it is defined, has to be proportional to the source energy. Since seafloor motions are the only source of a tsunami, their estimation directly relates to the mechanism that generates tsunamis; therefore, it is a proper way of identifying earthquakes that are capable of triggering tsunamis, while being able to discriminate those particular earthquakes from false alarms.
2. GPS Data
 Instantaneous GPS receivers and other similar instruments can measure ground motions in real time as often as once every few seconds [Bock et al., 2000]. Giant earthquakes often occur where large oceanic plates underthrust continental margins and involve significant lateral displacement of slopes, which are detectable in near-field coastal areas by these continuous GPS stations. To demonstrate our methodology on real earthquake-tsunamis, we have examined three historical tsunamis that have well-documented GPS measurements and tsunami observations. Our first test case is the 2004 Sumatra event which has both continuous GPS (GPS) and campaign GPS (cGPS/geodetic) measurements [Vigny et al., 2005; Subarya et al., 2006], as shown in Figure 1a. Our second case is the 1964 Alaska earthquake (it took 125 lives, in which 110 was due to the tsunami) and the third case is the 2005 Nias earthquake; both have well processed GPS data from Johnson  and Kreemer et al. , as shown in Figures 1b and 1c.
3. Deriving Seafloor Displacements
 It should be noted that GPS stations only measure near-field ground motions of faulting, not the undersea ground motions that generate tsunamis. Although sophisticated GPS-inversion models have been explored [Blewitt et al., 2006; Wang et al., 2006] based on the shear and tensile fault theory in a half-space [Okada, 1985], for tsunami prediction, we only need the seafloor (surface) displacements. Because great earthquakes cause large-scale ground motions, the coastal GPS-measured displacements are part of the major motions at the fault. Therefore, the seafloor displacements near the fault can be projected or extrapolated from the near-field GPS measurements. Based on the three sets of GPS data and the seismically-inverted data, we have developed an empirical profile extrapolation model to project the seafloor displacements.
 Let (ΔEj, ΔNj) be the near-field GPS offsets (horizontal displacements) in the eastward and northward direction, respectively, where Δ represents a small increment. The subscript j labels the GPS stations alongshore (parallel to the fault line), but only for those closer stations. For each j station, a cross-shelf section through the station, usually perpendicular to the fault, is identified (Figure S1 of the auxiliary material). The seafloor displacements along the cross-shelf section are modeled to follow an empirical profile until the fault (the trench):
 Here, r = d/W is the normalized distance such that r = 0 on the fault line and r = rj at the jth GPS station and, d is the physical distance from the fault line perpendicularly, and W is the mean distance of the GPS stations from the fault. An empirical value of W = 320 km is used for the 2004 Sumatra and 1964 Alaska earthquakes and 150 km for the 2005 Nias earthquake. If more GPS stations are available (besides the j labeled stations), a least-square fitting between the model results and the data is used for (Δej2, Δnj2) to correct the model. The vertical uplift/subsidence is determined from the horizontal displacements by conserving mass such that the uplift volume equals the subsidence volume, in which the non-dimensional constant a = 1.5 is used. Notice that r represents a dimension in the cross-shore direction, while j gives the other dimension in the along shore direction. Once the seafloor displacements are derived from the GPS measurements, they are then interpolated onto a quarter-degree grid over the fault area.
 The GPS-projected seafloor motions are shown in Figure 1 in comparison with the seismic inversions for the 2004 and 2005 earthquakes. The seismic solutions, based on Ji et al. , are inversions without using GPS measurements, and therefore provide an independent validation of the GPS results. The GPS-derived displacements are comparable to the seismic inversions in magnitude, but have discrepancies in slip directions, which are shown to have little effect on the predicted tsunami height.
4. Determining Tsunami Scales
 We then used the GPS-derived seafloor motions to calculate the tsunami source energy, which includes both potential energy due to the seafloor uplift and kinetic energy due the horizontal displacements of the continental slope (Text S1 of the auxiliary material). Mathematically, the total tsunami energy can be written as a function of the seafloor displacements: ET = f(ΔE, ΔN, ΔU, Δt, hx, hy), where the seafloor displacements are obtained from equations (1–3), Δt is the rise-time of faulting, hx and hy are the eastward and northward slopes of the subfault surface, respectively. Once the total tsunami energy is derived, the tsunami potentials (scales) can be determined. Based on the linear wave theory in deep oceans (the square root of wave energy is proportional to the wave amplitude), we introduce the following formula to quantify the tsunami scales:
Here, ST is the tsunami scale (between 1 to 10 and any value greater than 10 is set to 10). Table 1 gives the tsunami source energy and scales determined from GPS offsets and seismic inversions for the three cases. The tsunami scale is a quantitative representation of tsunami height in deep oceans or its potential destructive force before reaching coastal regions.
Table 1. Tsunami-Source Energy and Scales
Tsunami Energy, ET
Tsunami Scale, ST
ST = 5 Threshold
2004 Sumatra (Mw 9.2)
6.0e + 15 Joules
5.2e + 15 Joules
1964 Alaska (Mw 9.2)
8.2e + 15 Joules
2005 Nias (Mw 8.7)
2.8e + 14 Joules
2.2e + 14 Joules
 This is consistent with the principle of determining hurricane categories based on the wind speed over open oceans (e.g., Saffir-Simpson scale) and earthquake magnitudes based on seismic moment or earthquake-released energy (e.g., Gutenberg and Richter scale). The energy approach to tsunami scales may be also applicable to other kinds of tsunamis caused by landslides, volcanoes, and meteor strikes, because energy is the universal quantity. No matter what is the cause, the ocean has to receive enough energy to generate tsunamis, so that detecting the energy transferred to the ocean is the key to the determination of tsunami scales. This is different from Abe's  tsunami magnitude based on tide records, which only becomes available after tsunamis hit coastal regions. We believe that early determination of the scale of a coming tsunami is critical for government agencies to take proper actions in minimizing damages by tsunamis on the one hand and reducing false alarms on the other. For example, if we had set the scale of 5 as the threshold for basin-scale early warnings (thresholds determined by ocean-general-circulation-model (OGCM) simulations [Song et al., 2005; Song and Hou, 2006]), a basin-wide warning was obviously needed in the 2004 Sumatra and 1964 Alaska cases, while the large-scale panic evacuation that caused hundreds of lives in the 2005 Nias event could have been avoided.
 Here we use satellite observations and tide records to validate the GPS-derived tsunami scales. Figure 2 gives the three historical tsunamis replicated from the GPS data using a coupled earthquake-OGCM system (Text S1). The three-dimensional OGCM has a grid of 9 km resolution and 40 vertical levels for the Indian Ocean, which simulated the 2004 and 2005 tsunamis. For the 1964 Alaska tsunami, we used a global ocean grid of half-degree resolution and 20 vertical levels. OGCMs permit simulating both ocean dynamics [Song and Haidvogel, 1994] and tsunami waves [Song et al., 2005]. In each case, the model is initialized by the GPS-derived sea-floor motions and accelerated bottom velocity near the ocean bottom. The model time-step is 5 seconds and takes merely 20 minutes on JPL's supercomputers (the Dell cluster with 1024 Intel Pentium 4 Xeon 3.2 GHz processors) to complete a 12-hour simulation of tsunami propagation.
 The replicated tsunamis have been compared with observations and their corresponding seismic solutions. Figure 3 compares the 2004 tsunami with the satellite observations from Jason-1, Topex, and Envisat. The GPS results are significantly better than the seismic solutions, particularly in catching the leading waves. This is because GPS data is the direct measurement of ground motions, while the seismic inversion is an indirect estimation and can be complicated by simultaneous seismic signals of aftershocks. For the Alaska and Nias cases, we do not have satellite observations, but tide records are available. Figure 4 compares with tides for the two cases. In the 1964 Alaska case, the model agrees well with the tide records. In the 2005 Nias case, the model has reproduced both high waves (∼2 m) near the Sibolga station and low waves near Sri Lanka, suggesting that the GPS measurements are able to detect various tsunami scales.
6. Summary and Discussions
 The successful replications of the three historical tsunamis based on real GPS data have made a convincing case that real-time GPS estimates of earthquake displacements are able to detect earthquake-tsunami genesis and scales directly. The GPS-based method can be summarized in the following steps: (1) Locate an earthquake epicenter from seismometers (available online a few minutes after an initial quake). (2) Collect near-field GPS offsets and derive the seafloor motions (a few more minutes of time may be needed: http://igscb.jpl.nasa.gov/). (3) Calculate the tsunami-source energy and tsunami scales based on the GPS-derived seafloor motions and local topography instantaneously (Text S1). If the oceanic energy scales greater than a threshold, an initial warning can be issued.
 These steps seem achievable within a few minutes after the quake. Such a short period is critical for alerting nearby coastal regions because tsunami peaks can cross a typical ocean margin of about 100 km in 30 minutes. In addition, the GPS-derived tsunami initial conditions—the by-products of the energy scale calculation—can be used in the coupled earthquake-OGCM system to pinpoint remote regions at risk for possible evacuations. As simultaneously demonstrated here, seismic waveform inversion is another independent approach for deriving seafloor motions because modern seismometers can provide earthquake information online a few minutes after the quake. However, the tedious inversion of seismographs is still not real-time, which usually takes hours or days to be completed even on the most powerful computers today [Ji et al., 2002]. We believe that GPS technologies have the advantage to obtain the ground motions directly and rapidly [Blewitt et al., 2006]. A coastal GPS network [Sobolev et al., 2006, 2007], if established and combined with the existing NASA global differential GPS system (http://www.gdgps.net/index.html), can provide a more reliable global tsunami warning system for saving lives and reducing false alarms.
 The research described here was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contracts with the National Aeronautics and Space Administration (NASA). We thank Vala Hjorleifsdottir for providing the seismic inversion data. Constructive comments from John LaBrecque, Richard Gross, Ichiro Fukumori and Geoff Blewitt are appreciated.