Determination of the structure of the Earth's core using normal mode of the Earth

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We calculate normal modes for the Earth model, which has a slight rigidity layer at the base of the liquid outer core. We show that such a layer with thickness about 40 km and the shear wave velocity of 0.017 km/sec can produce a normal mode, which has a close eigenfrequency to that of liquid core model, without affecting fundamental modes and most of the higher modes. Our results indicate that the thin finite rigidity layer at the base of the outer core might explain the anomalous splitting of the Earth's normal modes, which has not been fully explained by the anisotropy in the inner core. We also have shown that we may interpret that the soft core mode, which appeared at _3S_2 , may arise as a result of coupling between those trapped modes within thin finite rigidity layer at the bottom of the oute core and the ordinary normal modes. For a preparation of confirmation of the existence of this thin finite rigidity layer at the bottom of the outer core by using body wave, we have set up a computer program to calculate synthetic seismic waveform for fully three dimensional Earth model. We use a spectral element method on the Earth Simulator. We use 243 nodes(1944 CPUs) of the Earth simulator and calculate synthetic seismic wave which is accurate up to 5 seconds. This synthetic waveforms consider all of the heterogeneity inside the Earth and its effect to the seismic wave propagation. Thus we should be able to use these waveforms to study fine structure of Earth's core.