Maximum Energy and Total Fault Slip Estimate of the NVT during the 2006 SSE
To estimate an upper edge of seismic energy released by all nonvolcanic tremor episodes (NVT)
and the entire hypothetical fault slip produced by the NVT during the 2006 slow slip event (SSE)
we assume isotropic S wave energy in a uniform medium. Despite this simplification we only need
to find an extreme upper limit of the NVT radiated seismic energy, Es, during the period of 2006
SSE. The maximum of NVT total coseismic slip may be estimated from Es assuming that all NVT
episodes were occurring on the same interplate thrust fault with the same rake.
We used the algorithm for radiated seismic energy [Battaglia and Aki, 2003; Maeda and Obara, 2009].
The basic equation is
Es=2pi·p·ß·R^2·exp(2pi·fc·R/ß·Q)·Integral(t1->t2)[Un(t)^2+Ue(t)^2+Uz(t)^2]dt , (1)
where Es is the radiated seismic energy, p is the density (2800 kg/cm3), ß is the shear velocity
(3500 m/s), R is the distance between the NVT source and a seismic station, U is the velocity amplitude
of the each component, fc is the center frequency and Q is the quality factor. The amplitude, U, was
summed over an NVT episode lasting from t1 to t2 according to the NVT duration register. When a
background seismic spectrum (seismic records with no NVT or earthquakes) was removed from the seismic
spectrum containing the NVT, the result was the NVT had a peak at ~1.5 Hz (Fig. S1), so this was used
as fc. Q = 276 as determined [Garcia et al., 2004] in central Mexico.
We chose R = 65 km (> sqrt(40^2+50^2)) as a reasonable upper limit on the distance of detected NVT,
where 40 km was assumed to be the maximum possible depth and 50 km was the maximum horizontal distance
of reliable tremor detection. A depth of about 40 km would put all NVT at the interplate interface.
Nearly all of the MASE tremor records show the vertical component much weaker than the horizontal components,
which means that the detected NVT was located close (less than ~20 km) or almost directly below the seismic
stations, suggesting a relatively short horizontal distance from the MASE profile. However, some NVT
were located more distantly from the MASE profile [Payero et al., 2008].
The NVT had been located within a band of ~100 km along the MASE profile [Payero et al., 2008].
The present study shows that the same distance range contains almost all of the NVT energy (Fig. 2).
The edge of the detectable tremor distance was ~50 km, from the NVT peak energy where the NVT
energy was more than an order of magnitude lower than at the peak (Fig. S2). Thus we assumed that
the maximum horizontal distance of the NVT was 50 km from the MASE line, and the entire fault area
of the recorded tremor was about of 10^4 km2.
The seismic records of NVT were filtered in the band of 1-2 Hz where the signal to noise
ratio was the best for all stations ([Payero et al., 2008], and Fig. S1). In order to calculate Es,
it is necessary to know the ratio e of the energy from the total NVT (noise subtracted) spectrum
(Figure S1) to the 1-2 Hz energy band, dEs. This ratio estimated from the spectrum in Figure S1 is
approximately e~10.
The upper limit for radiated seismic energy, dEs, estimated using (1), in the frequency range
of 1-2Hz for all detected NVT during the 2006 SSE was dEs=4.72x10^8 J. Multiplying e to dEs gives
Es=4.72x10^9 J (Me~3.3, [Gutenberg and Richter, 1956]) which is well below the total energy of the
SSE (Mw ~7.0).
The total fault area where all recorded NVT energy, Es, was radiated is about of A=100x100 km2.
NVT stress drop, dS, may vary if the tremor source has a characteristic scale [Watanabe et al., 2007]
but it is apparently as low as the amplitude of the NVT triggering stress dS < 0.4-0.6 MPa [Peng and
Chao, 2008; Rubinstein et al., 2007]. So a rough estimate of the maximum cumulative NVT fault slip
is about d = 2Es/(A dS)~2x10^-3 mm. This dislocation on the 100 km long plate interface at the
depth of 40 km would produce a negligible surface deformation [Savage, 1983], which is at least
two orders of magnitude less than the noise level of the GPS position time series.
We should remind that these upper edge estimates of ES and d would be appropriate only if all
the above taken assumptions were valid. In reality the values of ES and d may be significantly
lower.
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