The back-projection method time-reverses seismograms recorded at dense seismic arrays
back to a set of grid points around the hypocenter of the event based upon a 1-D velocity
model [e.g., IASP91, Kennett and Engdahl, 1991]. Corrections for 3-D lateral variations
that are not in the 1-D velocity model are determined using a cross correlation analysis of
the first-arriving P waves [Ishii et al., 2007]. This analysis determines time corrections,
t k , at the kth seismic station that force the initial P waves to align at the hypocenter after
time shifting by the theoretical 1-D travel times. After time shifting the kth seismogram
to the ith grid point, tik , the seismograms are added together to form a stack, si (t) . These
stacks can be expressed as
si (t)   k u(t  t ik  t k ) .
k1 
Here K is the total number of seismograms, and  k is a weighting factor that normalizes
the amplitudes of each seismogram and corrects for polarity changes within the array.
The time corrections t k are usually determined using the first arriving P waves from the
earthquake on which the back-projection analysis is applied. However, when the first
 are difficult to align, one can use time
arriving P waves of the event of interest
corrections from an event in the same region that has more impulsive first-arriving P
is the approach we take for the Mw 9.0 Tohoku-oki earthquake, which has
waves. This
very emergent initial P waveforms. In contrast, a Mw 7.1 aftershock on April 7, 2011
occurred at a depth of 65 km and has very impulsive waveforms that are easier to align
with the cross correlation analysis. The time corrections from the April 7th event are
applied to the sequence of events investigated in this paper. This means that all imaged
energy is with respect to the hypocenter of the April 7th event, and any error in this
location will be reflected in the back-projection results. In addition, by using this
aftershock, we have set the depth of the plane of grid points to 65 km. The fact that this
depth is deeper than most of the events in this study means that the imaged energy will be
slightly shifted towards the seismic array. This will occur because smearing of backprojection results occurs along the ray paths [Kiser et al., 2011]. Both of these sources of
energy mislocation contribute to the imaged energy crossing the trench location (Figure
2c). However, neither contribution should be frequency-dependent, therefore the relative
rupture properties in the main text are robust.
To better image rupture propagation, an additional processing step is taken that
eliminates amplitude information from the back-projection results. This step calculates a
coherency function, xi (t) at the ith grid point as
t T
1 K
x i (t)  
K k1
pk  uk (  t ik  t k )  si ( )
t T
 u (  t
 t k )
t T
 s ( )
This function is the average cross correlation value between individual, time shifted
seismograms and the stack at the ith grid point. T is the time window of the cross
correlation. This time window should include multiple cycles of the waveforms, and
therefore increases when using lower frequency data. pk is the polarity correction at
station k mentioned above.
The frequency-dependent updip shift seen in Figure 2(c) is based upon plotting the center
of the energy kernels at 5-second time increments.
At lower frequencies, the resolution
of the energy kernels degrades, and approximating the location of energy release with a
single point is accompanied by more uncertainty. In Figure S1, the back-projection
results are plotted as a function of longitude and time. This figure shows how resolution
degrades at lower frequencies, but also demonstrates that the updip shift in imaged
energy can still be observed without the point source approximation. An additional test
that investigates if the updip shift in lower frequency energy is an artifact of the backprojection analysis demonstrates that these results are robust (Figure S2).
Auxiliary Figure Captions:
Figure S1: Longitude/Time Plots
From top to bottom: back-projection results of the mainshock with respect to longitude
and time using bandpass-filtered data between 0.8 and 2 Hz, 0.25 and 0.5 Hz, 0.1 and 0.2
Hz, and 0.05 and 0.1 Hz. These images demonstrate how resolution degrades at lower
frequencies. The imaged energy is normalized at each time step, and the white star is the
hypocentral longitude and time. The vertical white lines are the longitudes of the Oshika
Peninsula (left) and the trench location at the epicentral latitude (right).
Figure S2: March 9th Mw 6.4 Foreshock
Back-projection results for a M 6.4 foreshock (centers of the energy kernels) using data
filtered to 0.8-2 Hz (red dots) and 0.1-0.2 Hz (green dots). This result shows that for this
particular earthquake the high-frequency energy is imaged updip of the lower-frequency
energy. This shift is opposite of that of the Mw 9.0 mainshock, and demonstrates that the
frequency-dependent behavior reported in the main text is a real feature of the rupture
and not an artifact caused by a processing step in the back-projection analysis. The white
star is the epicenter of the Mw 6.4 foreshock.
Figure S3: Rupture Areas of Foreshocks and Aftershocks
Rupture areas (white contours) of foreshocks and aftershocks between March 9th and
April 7th. All earthquakes have been identified in the JMA catalogue and have
magnitudes greater than or equal to 6. The red contour is the energy kernel of a synthetic
point source for reference. The yellow line is the location of the Japan Trench. The
white star is the epicenter of the Mw 9.0 mainshock.
Figure S4: Subduction Interface Failure
(a) Similar to Figure S3 except that we have selected foreshocks and aftershocks with
rupture areas that do not overlap significantly with previous foreshocks and
aftershocks. All symbols are the same as in Figure S3.
(b) Average seismicity rate of the regions within the contours of (a) for the 48 hours
surrounding each large event. Time is with respect to the hypocentral time of
each event. This graph shows that seismicity within the contours dramatically
increases following these large earthquakes, which lends support to the idea that
the interface becomes active through a cascading series of large aftershocks,
whose rupture areas are spatially and seismically distinct from the rupture area of
the mainshock.
Auxiliary References:
Ishii, M., P.M. Shearer, H. Houston, and J.E. Vidale (2007), Teleseismic P wave imaging
of the 26 December 2004 Sumatra-Andaman and 28 March 2005 Sumatra earthquake
ruptures using the Hi-net array, J. Geophys. Res., 112, B11307.
Kennett, B.L.N., and E.R. Engdahl (1991), Traveltimes for global earthquake location
and phase identification, Geophys. J. Int., 105, 429-465.
Kiser, E., M. Ishii, C.H. Langmuir, P.M. Shearer, and H. Hirose (2011), Insights into the
mechanism of intermediate-depth earthquakes from source properties as imaged by backprojection of multiple seismic phases, J. Geophys. Res., 116, B06310.