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We use 1944 processors of the Earth Simulator to model seismic wave propagation resulting from large earthquakes. Simulations are conducted based upon the spectral-element method, a high-degree finite-element technique with an exactly diagonal mass matrix. We use a very large mesh with 5.5 billion grid points (14.6 billion degrees of freedom). We include the full complexity of the Earth, i.e., a three-dimensional wave-speed and density structure, a 3-D crustal model, ellipticity as well as topography and bathymetry. A total of 2.5 terabytes of memory is needed. Our implementation is purely based upon MPI, with loop vectorization on each processor. We obtain an excellent vectorization ratio of 99.3%, and we reach a performance of 5 teraflops (30% of the peak performance) on 38% of the machine. The very high resolution of the mesh allows us to perform fully three-dimensional calculations at seismic periods as low as 5 seconds.