Envelope Reconstruction of the 0S2 - free Oscillation of the Earth

Abstract: The earthquake in December 2004 caused free oscillations of the Earth. Vibrates the earth in the football mode 0S2, splits the natural frequency due to rotation into five closely adjacent individual components. The sum of these spectral components in the frequency band near 309 {\mu}Hz produces a beat that gives the overall amplitude envelope a characteristic, regular pattern. From the measured envelope the parameters frequency, amplitude, phase and damping of generating sinusoids can be reconstructed. Since the method is extremely sensitive to changes in frequency and phase, these quantities can be determined precisely. The results depend on the geographical location of the site. Further results are the half-life of the amplitude decrease and the resonator Q. It is shown that the interaction of the five individual frequencies can be interpreted as amplitude modulation, which requires a nonlinear process in the Earth's interior.