The 2004 catastrophic Indian Ocean tsunami has strongly emphasized the need for reliable tsunami early warning systems. Another giant tsunamigenic earthquake may occur west of Sumatra, close to the large city of Padang. We demonstrate that the presence of islands between the trench and the Sumatran coast makes earthquake-induced tsunamis especially sensitive to slip distribution on the rupture plane as wave heights at Padang may differ by more than a factor of 5 for earthquakes having the same seismic moment (magnitude) and rupture zone geometry but different slip distribution. Hence reliable prediction of tsunami wave heights for Padang cannot be provided using traditional, earthquake-magnitude-based methods. We show, however, that such a prediction can be issued within 10 minutes of an earthquake by incorporating special types of near-field GPS arrays ("GPS-Shield"). These arrays measure both vertical and horizontal displacements and can resolve higher order features of the slip distribution on the fault than the seismic moment if placed above the rupture zone or are less than 100 km away of the rupture zone. Stations in the arrays are located as close as possible to the trench and are aligned perpendicular to the trench, i.e., parallel to the expected gradient of surface coseismic displacement. In the case of Sumatra and Java, the GPS-Shield arrays should be placed at Mentawai Islands, located between the trench and Sumatra and directly at the Sumatra and Java western coasts. We demonstrate that the "GPS-Shield" can also be applied to northern Chile, where giant earthquakes may also occur in the near future. Moreover, this concept may be applied globally to many other tsunamigenic active margins where the land is located above or close to seismogenic zones. Copyright 2007 by the American Geophysical Union.