Ultra - long period seismic moment of the great December 26 , 2004 Sumatra earthquake and implications for the slip process

Analysis of the longest period normal modes of the Earth, excited by the December 26, 2004 Sumatra earthquake yields a moment of 1. 3 × 10 dyn-cm, approximately three times larger than the 4 × 10 dyn-cm measured from long-period surface wav es. 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 reported. The higher magnitude presumably reflects slow slip not detected by the surface wav es. Although the mode data do not constrain the location of the slow slip, a likely explanation is that it occurred over the entire 1200-km length of the rupture zone shown by aftershocks, of which only about the southern 1/3 to 2/3 appears to have slipped based on body-wav e slip inversions. If so, then accumulated strain on the northern part of the rupture zone has also been released, leaving no immediate danger of a large tsunami being generated by slip on this part of the plate boundary. These results come from analyzing the normal mode multiplets 0S2 , 0S3 and 0S4, with periods of about 3231, 2134, and 1546 s, respectively. The multiplets consist of 5, 7 and 9 singlets or peaks, respectively, which are split, i.e., 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 (Figure 1). Complementary data was obtained from the [unsplit] radial modes 0S0 and 1S0 with periods of 1227 and 613 s, respectively†. The singlets can be described by their spectral amplitude, attenuation, and eigenfrequency. The amplitude of each singlet depends on the location of the earthquake and seismic station, earthquake depth and focal mechanism, and seismic moment [Stein and Geller, 1977]. The decay of energy with time, or equivalently the width of the spectral peak, depends on the mode’s quality factor Q, a measure of attenuation. The singlet eigenfrequencies have been calculated by Dahlen and Sailor [1979]. Using the focal mechanism from the Harvard CMT project (strike 329°, dip 8°, slip 110°) and a focal depth of 15 km, we used two methods to estimate the seismic moment M0 and Q for 0S2 , 0S3 and 0S4 at seven, five and four stations, respectively. One consisted of fitting the amplitude spectra in the frequency domain (Figure 1). A second † The study of 0S0 is preliminary since the proper analysis of its spectral line requires in principle a time series lasting at least 82 days (the product of its period by its quality factor).