Supplemental Information
Data and Methods
Seismic records for distances between 30 and 85 degrees are chosen to avoid the effects
of scattering due to the upper mantle or D” structures (Shearer and Pearle, 2004). SAC
(seismic analysis code) is used to band-pass (2-4Hz) filter broadband vertical
component seismograms, and the envelope is smoothed with moving average with a
half-width of 8 sec.
Later phases
PP, S and other later phases are substantially suppressed within 2-4Hz band because PP
travels a longer path in the low velocity zone and S has larger intrinsic attenuation. PcP
or ScP can contain considerable amounts of energy at the high-frequency band, but our
data show consistent patterns of envelope shapes for the same azimuth but different
epicentral distances. This suggests that the high-frequency energy coming from PcP
and ScP does not distort the envelop significantly.
The effect of scattering
Because of scattering of P waves, the end of the envelope is not distinct. Nevertheless,
we can measure the end with an error of 30 seconds or less. A picking error as large as
30 seconds would not change our conclusion that the rupture propagated well beyond
the end of slip models based on body waveform inversion using the first 200s data. So
our method is particularly effective for megathrust earthquakes.
Source duration, rupture speed and rupture length
For most earthquakes, the source region is small and we can use the
standard
directivity formula t =(L/Vr)–Lcos()/V (L: rupture length; Vr: rupture speed; V:
apparent velocity;  station azimuth with respect to the rupture direction; t: apparent
source duration at the station). For the Sumatra-Andaman earthquake, the source region
is about 10 degree long, and the approximation used in this formula is not valid
especially for stations at epicentral distances less than 40 degree. We computed the
azimuthal variation of duration by t =L /Vr + T1-T0, where T1 is the travel time from
the end point of rupture to the station, and T0 is that from the hypocenter to the station.
From the standard formula, the range of the azimuthal variation t is given by 2L/V.
Since the phase velocity is known for each station, we can determine L from this
relation independent of Vr. Then, the rupture speed can be estimated by dividing L by
the azimuthal average of t (=L/Vr). The same principle can be used in the more
accurate method described above.
Azimuthal variation of peak amplitude
Directivity typically produces larger amplitudes in the direction of rupture, and smaller
amplitudes in the opposite direction. In our case, no clear azimuthal pattern is observed.
At frequencies of 2Hz or higher, the incoherent rupture propagation, scattering and the
station site effects obscure the pattern.
Table 1: Earthquakes used in this study
Event ID
Date
Mainshock
021102A
Time
Latitude(º)
Longitude(º)
Depth
Mw
12/26/04 00:58:50
3.30
92.78
10
9.0
11/02/02 01:26:10
2.82
96.09
30
7.1
021102B
11/02/02 09:46:46
2.95
96.39
27
6.4
041227
12/27/04 00:49:26
12.98
92.45
10
6.0(mb)
Figure S1:
Observed t's are indicated by plus symbols. Predicted t's for three end points
indicated by squares in Fig. 1A are shown. We computed the P-wave phase velocities
for each station using the IASPEI earth model (Kennett, 1991). The rupture speed is
determined by matching the curves with the observed t at the azimuth of 150. The
curve for L=1200 km and Vr=2.5 km/s (red) matches the data best. The colors of the
curves correspond to those of the squares in Fig. 1. The green line is used to derive the
termination point in Fig. 1a.
5. References:
Kennett, B.L.N. (Compiler and Editor). IASPEI 1991 Seismological Tables, Bibliotech, Canberra,
Australia, 167 pp., 1991