Constraints on Source Rupture From the Initial Phase and Amplitude of Free Oscillations Excited by the 2004 Sumatra-Andaman Megathrust

The initial phase of a long-period seismic free oscillation, referenced to the onset of an earthquake, can be used to estimate the time centroid of the source rupture process if the rupture duration is short compared to one half-cycle of the oscillation. For the 2004 Sumatra-Andaman megathrust, we estimate the initial phase of several well-excited free oscillations nSl from stations of the Global Seismographic Network, Geoscope, GEOFON and other broadband seismic stations. We apply multiple-taper spectrum analysis to determine amplitude and initial phase of phase-coherent decaying sinusoids via maximizing an F-variance ratio test [Park, Lindberg and Thomson, 1987], using spherical harmonic stacking to isolate individual vibrational singlets. Preliminary results suggest that moment release did not follow a simple symmetric function about a centroid time. The initial phase of the "breathing mode" 0S0 (T=1227 s) corresponds to an apparent centroid time of nearly 400 s. If the source time function is a simple boxcar with 800 s duration, the amplitude of 0S0 should be deficient, relative to the longer-period 0S2 (m=0 singlet, T=3236 s), by roughly 50%. This amplitude deficiency is consistent with the relative amplitudes of the two modes, as predicted for a Mw=9.3 event. However, a simple boxcar time function for the Sumatra rupture does not match the intial phase measurements of either 0S2 (m=0 singlet) or the overtone 1S0 (T=613 s). Therefore the rupture process is more complicated than a simple boxcar or a similar symmetric function about a 400-s centroid time. An asymmetric source rupture time function is not surprising, because high-frequency body wave radiation lasted roughly 500 s, and a simple Sumatra CMT source with 400-s time shift creates surface waves that are very late relative to the data. If the Sumatra fault zone switched to "silent slippage" after 500 sec, the remainder of its moment release may have occurred over a much longer time. Park, J., C. R. Lindberg and D. J. Thomson, Multiple taper spectral analysis of terrestrial free oscillations: Part 1, Geophys. J. Roy. Astron. Soc., v91, 755-794, 1987.