Application of normal Morlet wavelet transform method to the damped harmonic analysis: On the isolation of the seismic normal modes (0S0 and 0S5) in time domain

Previous studies indicated that the seismic breathing normal modes S-0(0) (period similar to 20.5 min) and S-0(5) (period similar to 19.8 min) were excited by the 26th December 2004 Sumatra-Andaman earthquake. These two modes may present a beating-pattern in a wavelet time-frequency spectrum due to their close frequencies. Using superconducting gravimeter (SG) data covering 20 days after the Sumatra event, this work shows that a periodic amplitude-varying signal with an similar to 20.2 min period due to beating between the S-0(0) and S-0(5) modes is displayed in the normal Morlet wavelet transform (NMWT) spectrum, and this signal can be quantitatively extracted from the NMWT spectrum. Furthermore, the NMWT spectrum also clearly shows that this beating-pattern disappeared at time t similar to 9 x 10(3) min (when the S-0(5) mode vanished) after the Sumatra event occurred, since S-0(5) mode decays much faster than the S-0(5) mode. Using this information, we can separately isolate the S-0(0) and S-0(5) mode signals and further estimate their respective parameters (i.e., frequency-f(0), initial amplitude-A(0), and quality factor-Q) in the time domain rather than in the frequency domain only. The temporal-varying behaviour of the oSs mode in the time domain obtained in this work can be thoroughly explained by two damped harmonic signals due to the splitting of the S-0(5) mode. In brief, we can isolate S-0(0) and S-0(5) mode signals in the time-frequency domain using the NMWT method, which is different from the traditional method used in the frequency domain.