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Normal modes show that the December 26, 2004 Sumatra earthquake was even bigger than previously thought. Analysis of the longest period normal modes of the earth, 0S2 and 0S3, yields a moment of 1.3e30 dyn-cm, approximately three times larger than the 4e29 dyn-cm measured from long period surface waves. Hence the earthquake's ultra-long period magnitude, Mw = 9.3, is significantly larger than the previously reported Mw = 9.0, making the earthquake the second largest ever instrumentally recorded. These results come from analyzing the normal mode multiplets 0S2 and 0S3, with periods of about 3231 and 2134 s. The multiplets consist of 5 and 7 singlets or peaks, respectively, which are split - have distinct periods or eigenfrequencies - due to the rotation and ellipticity of the earth. Great earthquakes like the Sumatra earthquake excite these long period multiplets sufficiently that they can be observed by Fourier analysis of long seismograms. Fitting the spectral amplitudes (red is synthetic, black is data) gives both the seismic moment - which controls the peak hight - and the quality factor Q, a measure of attenuation, which controls the width of the spectral peak.
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Credit: Seth Stein and Emile Okal, Department of Geological Sciences, Northwestern University