We use P-wave velocity records at USArray, filtered between 1.00 and 4.00 Hz.
Signals are realigned according to theoretical arrival time from the
SSN epicenter,
using multichannel cross-correlation – see "Trace alignment".
We use the back projection method described in
Satriano et al. (2012).
Station distribution - Cylindrical Projection
Station distribution - Stereographic Projection
USArray stations used for the back projection analysis.
(click on the images for a larger version)
Back projection resolution is estimated by the array response function (ARF), computed at the lowest
frequency of the band (1 Hz).
The ARF allows to correctly evaluate the beam power images obtained from the back projection analysis.
Here we use to approaches for back projection imaging:
— linear trace stack weighted by trace semblance;
— pure trace semblance.
These two approaches have different resolution and enhance different features.
Linear stack, weighted by semblance
Semblance-weighted linear stack shows a maximum in coherent energy emission at ~80 km to the west, i.e.
downdip of the hypocenter. A secondary maximum is at ~50 km southwest.
Array response function @1Hz
Array response function @1Hz - Linear stack, semblance weight
Maximum beam power over time
Maximum beam power over time - Linear stack, semblance weight
Array response function (left) and maximum beam power over time (right) for semblance-weighted
linear stack. The star is the epicenter. Light and dark gray dots are foreshocks and aftershocks, respectively,
located by SSN.
(click on the images for a larger version)
Pure semblance
Pure semblance stack emphasizes the strong waveform coherency at the hypocenter
(due to the cross-correlation trace realignment). It also shows, as secondary maximum, energy at ~80 km west.
Array response function @1Hz
Array response function @1Hz - Semblance
Maximum beam power over time
Maximum beam power over time - Semblance
Array response function (left) and maximum beam power over time (right) for pure semblance stack.
The star is the epicenter. Light and dark gray dots are foreshocks and aftershocks, respectively,
located by SSN.
(click on the images for a larger version)
We extract over time local maxima of back projection beam power.
These back projection peaks are locations of high-frequency (~1 Hz) coherent energy emitters.
For semblance-weighted linear stack, the circle amplitude is mostly related to the actual signal energy
(with some weighting based on coherency).
For pure semblance stack, the circle amplitude is proportional to waveform coherency.
Back projection peaks - Linear stack, semblance weight
Back projection peaks - Semblance
Back projection peaks - Linear stack, semblance weight
Back projection peaks - Semblance
Time coded back projection peaks for semblance-weighted linear stack (left) and semblance stack (right).
Circle amplitude is proportional to beam power.
The star is the epicenter. Light and dark gray dots are foreshocks and aftershocks, respectively,
located by SSN.
Isolines correspond to the largest slip patch (~6 m), from the
USGS preliminary finite fault solution.
(click on the images for a larger version)
Projected peaks along-dip and along-strike show similar trends for
both back projection methods.
Smblance stack better enhances the rupture start, and shows coherent sources moving donwdip
with initial apparent velocity of ~1.5 km/s and, later, of ~3.5 km/s.
Back projection peaks, projected - Linear stack, semblance weight
Back projection peaks, projected - Semblance
Back projection peaks, projected - Linear stack, semblance weight
Back projection peaks, projected - Semblance
Time coded back projection peaks for semblance-weighted linear stack (left) and semblance stack (right),
projected along-dip (top) and along-strike (bottom).
Circle amplitude is proportional to beam power.
Lines indicate reference rupture velocities.
(click on the images for a larger version)
We look at coherent energy release as a function of time by integrating back projection
beam power on space at every time step.
The function associated to semblance stack is highly distorted, since it enhances waveform coherency
at origin time.
Energy time function - Linear stack, semblance weight
Energy time function - Semblance
Energy time function - Linear stack, semblance weight
Energy time function - Semblance
Space-integrated beam power as a function of time for semblance-weighted linear stack (left) and semblance stack (right).
(click on the images for a larger version)
Trace alignment for semblance-weighted linear stack (left) and semblance stack (right).
Top panel is trace alignment according to theoretical arrival time from origin.
Following panels show trace alignment corresponding to each of the detected
back projection peaks.
Blue curve is semblance function. Vertical blue line is the arrival time corresponding to back projection peak.
(click on the images for a larger version)
C. Satriano, E. Kiraly, P. Bernard, J.-P. Vilotte (2012). The 2012 Mw 8.6 Sumatra earthquake:
evidence of westward sequential seismic ruptures associated to the reactivation of a N-S ocean fabric,
Geophys. Res. Lett., 39(15), L15302, doi 10.1029/2012GL052387.