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As the Earth is a finite body, there is a series of arrivals of different seismic phases that constructively and destructively interfere after propagating around the Earth, such that only certain frequencies will resonate over long time intervals (see e.g. http://www.iris.iris.edu/sumatra/GSNwaveforms_second.htm). So, when the earthquake source exceed a minimum magnitude of Mw = 6.5, the Earth « rings » like a bell, at resonant frequencies termed « normal modes ». The gravest normal mode is the spheroidal “football” or “rugby” mode 0S2 (53.8 min period or 0.31 mHz frequency). Figure 1 shows also the “balloon” or “breathing” mode 0S0 (20.6 min period or 0.81 mHz frequency), the 0S3 mode (35.5 min or 0.47 mHz frequency) and three toroidal modes (0T2 is the “twisting” mode). Toroidal oscillations involve only shear motion parallel to the Earth’s surface, whilst spheroidal motions have also a radial component. The great Chilean earthquake of 1960 (Mw =9.5) was the first to provide observations of the Earth’s free oscillations. Numerous large earthquakes have provided opportunities to study normal modes ever since and of course, the free oscillations have been widely excited by the Sumatra earthquake. Mostly, modes are studied in the frequency domain by computing the Fourier transform of the time series, but the Sumatra event was such that the modes can be observed directly on the time series, as this was performed by Stein and Geller in 1978 using the Chilean event Isabella strain record (BSSA, 68 (2) 325332). The Sumatra event is illustrated by the time series of the superconducting gravimeter of Membach spanning from 20041226 to 20050111 (Belgium, 51.6092 N, 6.0067 E) on Figure 2. Above is shown the time series after correcting for tidal and atmospheric pressure effects. The main shock as well as numerous aftershocks can be observed. The aftershocks do not influence noticeably the free oscillations. Below the same time series bandpass filtered to isolate the 0S0 (blue) and 0S2 (green) normal modes (units in nm/s²). The beating effect observed during the first days on 0S0 (0.81 mHz) is due to the neighbouring 0S5 mode (0.84 mHz). The beating effect on 0S2 is due to the beating between the 5 different multiplets of 0S2 (spectrum using 16.5 days on Figure 3). This “Zeeman” splitting is due to the Earth’s small departure from spherical symmetry, i.e. the Earth’s diurnal rotation, ellipticity and 3D structure. The attenuation quality factor of the long–period fundamental modes is high, such that the oscillations of e.g. 0S0 or 0S2 can still be observed in the time series 2 weeks after the event. Figure 4 shows a recording of several hours on 20050111 showing the Earth still vibrating after the Sumatra earthquake, where 0S0 dominates. As gravimeters are only sensitive to vertical motions, they are only able to record spheroidal modes, but due to coupling, toroidal oscillations can be also observed (see e.g. WidmerSchnidrig, BSSA 93, 3, 13701380, 2003).
Credit: Michel Van Camp, Royal Observatory of Belgium Return to SumatraAndaman Islands Earthquake Page
