The mechanism of low frequency earthquakes

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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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The mechanism of deep low frequency earthquakes:
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further evidence that deep non-volcanic tremor is
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generated by shear slip on the plate interface
4
Satoshi Ide
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Department of Earth and Planetary Science, University of Tokyo, Japan
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David R. Shelly, Gregory C. Beroza
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Department of Geophysics, Stanford University, USA
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S. Ide, Department of Earth and Planetary Science, University of Tokyo, Japan, 7-3-1
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Hongo, Bunkyo, Tokyo, 113-0033, Japan (ide@eps.s.u-tokyo.ac.jp)
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D. R. Shelly, G. C. Beroza, Department of Geophysics, Stanford University, 397
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Panama Mall, Stanford, CA, 94305-2215, USA (dshelly@pangea.stanford.edu,
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beroza@pangea.stanford.edu)
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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Abstract
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We study the mechanism of low frequency earthquakes (LFEs) in the Nankai Trough in
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western Shikoku, Japan.
4
represent shear slip on the plate boundary.
5
these events.
6
and compare them with the waveforms of nearby earthquakes of known mechanism
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within the subducting Philippine Sea Plate. Analysis of both the focal mechanism
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using P-wave first-motions and the moment tensor using S waveforms indicates that
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LFEs represent shear slip on a low-angle thrust fault dipping to the northwest, namely
10
the plate interface. Together with previous reports that deep tremor consists of a
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swarm of LFEs, our results suggest that deep tremor is generated directly by shear slip
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on the plate interface, and as such represents a seismic signature of the accompanying
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slow slip events.
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Precise locations have previously suggested that they
In this paper we examine the mechanism of
Due to the low signal-to-noise ratio, we analyze stacked LFE waveforms
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
1. Introduction
2
Deep, non-volcanic low-frequency tremors were discovered by Obara [2002]
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along the Nankai trough, Japan, where large (M~8) earthquakes, such as the 1944
4
Tonankai and the 1946 Nankai earthquakes, have occurred repeatedly.
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consists of intermittent weak signals at relatively low frequency (1-8 Hz) that last as
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long as days to a few weeks once activity begins.
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the down-dip limit of megathrust earthquakes in a belt-like distribution, suggesting the
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potential interaction with large inter-plate earthquakes.
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as periodicity and migration, have been reported [Obara and Hirose, 2006]; however,
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the mechanism responsible for tremor generation has been unclear, in part due to the
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very low signal to noise (S/N) ratio of the tremor signal.
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of high tremor activity, slow changes in tilt have been detected [Hirose and Obara,
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2005; Obara and Hirose, 2006]. Hirose and Obara [2005] interpreted these signals as
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originating from a slow slip event (SSE) on the plate interface. Strong temporal and
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spatial correlation between tremor and SSE suggests that tremor may also originate on
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the plate interface.
Deep tremor
The source of tremor is located near
Many aspects of tremor, such
In this area during the period
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While most of the tremor waveform has a chaotic appearance, there are periods
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with relatively impulsive arrivals, which have been identified by the Japan
19
Meteorological Agency as a new class of events termed “low-frequency earthquakes
20
(LFEs)”, [Katsumata and Kamaya, 2003].
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of LFEs [Shelly et al., 2006a]. Shelly et al. [2006b] determined the hypocenters of
Tremor appears to be comprised of swarms
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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LFEs using the double difference tomography and event relocation technique [Zhang
2
and Thurber, 2003]. The hypocentral depths of the LFEs range from 30 km to 35 km,
3
and the hypocenters fall on a surface that is approximately parallel to and ~7 km above
4
the distribution of regular intraplate earthquakes, with a dip of 15-20º to the northwest.
5
The tomography reveals an area of high Vp/Vs anomaly between LFEs and intraplate
6
earthquakes, suggesting the existence of pore fluids.
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hypothesized that the reduction of effective stress due to high pore-fluid pressure may
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facilitate LFEs, tremor and SSEs.
9
Shelly et al. [2006b]
The objective of this study is to determine the mechanism of LFEs and find
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whether it is consistent with this hypothesis.
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analyses of P- and S-waves consistently show that the LFE moment tensor solution is
12
shear slip on a low-angle thrust fault that has T and P axes azimuths parallel to the plate
13
subduction direction. This mechanism is also consistent with fault models for SSEs
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determined by Hirose and Obara [2005].
In short, the answer is yes.
Independent
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16
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2. Events and Data
We study LFEs identified by the JMA in western Shikoku, Japan using the
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relocated catalog of Shelly et al. [2006b].
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high-sensitivity seismometers maintained by the National Research Institute for Earth
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Science and Disaster Prevention (NIED), Earthquake Research Institute, the University
21
of Tokyo, and Kochi University.
In the present study we use records of
The distribution of LFEs is spatially clustered. We
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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focus on one of these clusters in an area of 5 km x 15 km (Figure 1).
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LFEs has a linear northwest (N35-45ºW) trending alignment, which is comparable to
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the relative plate motion direction in this area (N43ºW) from NUVEL-1A [DeMets et al.,
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1994]. The dip angle is approximately 15º.
This cluster of
5
In this study area intraplate earthquakes within the downgoing Philippine Sea
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Plate are also present, but are approximately 7 km deeper than the LFEs (Figure 1).
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We determine the focal mechanism (strike, dip, and rake angles) and the scalar seismic
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moment for ten of these intraplate earthquakes using polarities and amplitudes of
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P-waves (supplemental table S1). Although the hypocenters of these events are close
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to each other, the mechanisms are quite diverse, which helps in constraining the
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polarities and mechanisms of the LFEs.
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Are the mechanisms of LFEs equally diverse?
To address this issue, we
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calculate cross correlation functions for S-wave arrivals between LFE events that are
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separated by less than 3 km and compare the distribution of maximum positive and
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negative peaks (Figure 2a). Since the mechanisms of intraplate earthquakes are diverse,
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negative correlations are often stronger than positive correlations (Figure 2b).
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mechanism diversity is comparable to that for the intraplate earthquakes, we should
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observe strong negative peaks at many stations; however, for the LFEs we observe no
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such distribution of negative peaks.
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correlations, they are predominantly positive with a complete lack of strong negative
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correlations over the many stations used in the analysis.
If the
Although the low S/N ratio leads to weak
This suggests that the
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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mechanisms of LFEs are very similar and justifies our focus on a specific event to
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investigate the mechanism of LFEs more generally.
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Because the individual original records are noisy, we use stacking to improve
4
the S/N ratio. As Shelly et al. [2006b] explained, the body wave arrivals of LFEs are
5
similar and have good correlations between different events.
6
S-waves are aligned, they were also able to successfully identify and align the P-waves
7
using cross correlation.
Once the large-amplitude
8
For the stacking procedure, we let uk0 (ti ) denote the velocity records of a
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reference LFE at time ti where k = 1-3 denotes a component. We chose waveforms of
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LFEs with maximum cross correlation peaks larger than 0.7, after bandpass filtering
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between 1 and 8 Hz. These waveforms, ukn (ti ) , (n = 1,…, N), are aligned using cross
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correlation and the stacked waveforms for the reference event, uk0 (ti ) , are written as,
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u k (t i )   u kn (t i ) . (1)
N
n 0
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uk0 (ti )   uk0 (t j )uk (t j )uk (ti )
j
2
 uk (t j ) .
(2)
j
15
(1) is simple summation of all waveforms, which is normalized and scaled by the inner
16
product with the waveform of the reference event in (2) to preserve the original
17
amplitude of the reference event.
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Figure 3 shows P-wave portion of the stacked waveforms compared with two
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intraplate earthquakes.
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April, 2005 (JST).
21
the amplitude information from the reference event as determined using equation (2).
The reference event is the one that occurred at 06:50:24 on 19
Although we analyze the stacked waveforms for the LFEs, we use
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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The stacked waveforms of different stations do not share a common shape due to wave
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propagation effects caused by local structure near the stations. On the other hand the
3
waveforms of LFEs and intraplate earthquakes are similar for each station, because the
4
effect of path differences is dominated by effects in the neighborhood of the receiver,
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which is common to the two types of events.
6
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3. P-wave First-Motions
8
To constrain the focal mechanism, we make a plot of P-wave first-motion
9
polarities based on a comparison between the waveforms of LFEs and earthquakes that
10
have clear polarities.
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intraplate events #4 and #8 have up and down polarities, respectively, and these
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waveforms are quite similar.
13
and obtain the polarity distribution on the focal sphere (Figure 3).
For example, the polarity is clearly up at KWBH, because
We qualitatively compare waveforms at several stations
14
Since the mechanisms of all LFEs are similar (Figure 2), we attempt to merge
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all polarity information from individual LFEs to form a composite mechanism using an
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automated polarity determination method.
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using cross correlation measurements with intraplate events of known mechanism.
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measure the maximum and the minimum of the cross correlation functions between
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vertical P-waveforms of the LFEs and intraplate events shown in Figure 1 in the
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frequency range between 1 and 8 Hz. When the absolute value of either the maximum
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or the minimum is larger than 0.5 and the difference between them exceeds 0.1, we
The polarity of LFEs can be estimated
We
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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automatically assign a polarity based on that of the intraplate event.
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poor S/N ratios, some LFE waveforms have a detectable P-wave for which the polarity
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can be extracted by comparing the waveform with multiple intraplate events.
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3 we plot those polarities determined with at least two intraplate events.
5
Despite generally
In Figure
Figure 3 shows up polarities in the northwest and down polarities in the
6
southeast.
7
evenly distributed on focal sphere except for the near-horizontal southeast direction
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(largely offshore), few polarities are determined in the northeast and southwest direction.
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This suggests that this direction is close to one of the nodal planes of P-wave radiation.
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Overall the data are consistent with shear slip on a low angle thrust fault dipping to the
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northwest.
Although the observation directions of the automated analysis are almost
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13
4. Empirical Moment Tensor Inversion
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Next, we analyze S waves, which are generally the dominant arrival in the
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LFEs.
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S-waves, too, and indicates that they share similar propagation effects.
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use the intraplate earthquake records as empirical Green’s functions to determine the
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LFE mechanisms.
The waveform similarity between LFEs and intraplate earthquakes holds for
Therefore we
19
Plicka and Zahradník [1998] and Shomali [2001] presented a method to
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empirically estimate waveforms from a set of basis moment tensors, using earthquakes
21
of known mechanisms. We apply a modified version of their method as follows.
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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There are N earthquakes, each of which has a different moment tensor Mi expressed by
2
a set of basis moment tensors M1, M2, ..., and M5, and coefficients mij,
3
M i  M 0i
 mij M j ,
(3)
j 1,, 5
4
where M 0i is the seismic moment of i-th earthquake. The waveform of this event
5
ui(tk) is considered as the summation of impulse response functions uj(tk) from the basis
6
moment tensors Mj, convolved with a source time function. When we analyze them
7
for frequencies lower than the characteristic frequency of the event, the source time
8
function can be neglected and we can approximate the waveform with some unknown
9
error ei (tk ) as
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u i (tk )  M 0i
 mij u j (tk )  ei (tk ) (i = 1, ..., I). (4)
j 1,, 5
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If the number of events I is larger than 5 and errors are Gaussian, the above equations
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can be used to invert ui (tk ) for u j (tk ) using least squares.
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Once u j (tk ) are determined for many stations, we use them and the records of
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a target event u0 (tk ) to determine the moment tensor of the target event.
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observation equation for a station is written as
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u 0 (tk )   s (tk  tl )
l
 m0j u j (tl )  e(tk ) ,
The
(5)
j 1,, 5
17
where s(tk) is a source time function that is normalized so that the summation s(tk) is
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unity. m0j are five unknown parameters and e(tk ) are errors.
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errors are Gaussian, we solve the observation equations (5) for all stations
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simultaneously as a least-squares problem to determine the parameters m0j and the
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corresponding moment tensor,
Assuming that the
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
M0 
 m 0j M j . (6)
j 1,, 5
2
Using ten intraplate events in Figure 1, we obtained synthetic waveforms from
3
the basis moment tensors for ten stations within an epicentral distance of approximately
4
30 km.
5
S-waves.
6
calculate the cross correlation of waveforms with those from the first event, and arrange
7
them based on the time that gives the maximum of the absolute value of the cross
8
correlation function. Then, the estimated waveforms from the basis moment tensors
9
are used to determine the moment tensor of the LFEs. The data are the S-wave portion
10
11
The waveforms of different events must first be aligned on the arrival times of
Therefore, we first apply a bandpass filter (1-5 Hz) for all waveforms,
of three components of the stacked signals.
Figure 4 shows the beach ball of the calculated moment tensor and comparison
12
between the data and calculated waveforms.
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= 279º; dip = 25º, and rake = 151º). The seismic moment of the reference LFE is
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measured to be 2.9 x 1011 N-m (Mw 1.6), which is significantly larger than would be
15
estimated based on the JMA magnitude of this event, MJMA 0.3. The source time
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function is chosen empirically as an isosceles triangle of 0.3 s. There is also some
17
ambiguity about the timing of data and calculated waveforms, which we modified
18
empirically to improve the variance reduction, which is defined as,
19
VR  1   e(tk )
k
2
 u0 (tk ) .
2
The best double couple solution is (strike
(7)
k
20
The final VR is 49%, which is far from perfect.
21
are well explained by the calculated ones, stations with small amplitudes, are often not
Although the large amplitude waves
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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fit well.
2
assumption that the LFE and intraplate events share the same path and site effects, and
3
the estimation errors of synthetic waveforms for the basic moment tensors.
4
This is attributable to relatively large noise for these components, the
To investigate the solution stability, we carried out the inversion using different
5
subsets of eight of the ten stations.
6
slightly different solutions as shown in Figure 4; however, in most case, P and T-axes
7
are within 30º in azimuth. These are almost parallel to the direction of relative plate
8
motion (N43ºW), suggesting that the LFEs act to accommodate the subduction of the
9
Philippine Sea plate. The dip angle is better constrained, with a shallow angle from
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15º to 25º, which is also consistent with the dip angle of the LFE cluster, 15º. The sign
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of the non-double couple component is not stable, hence this component is not
12
considered well constrained and may be zero.
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are consistent with the independently determined P-wave first-motion distribution
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(Figure 3), which enhances the reliability of this solution.
The different combination of stations yields
Nevertheless, all possible mechanisms
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5. Discussion and Conclusion
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We analyze the waveforms of LFEs in western Shikoku, Japan, to estimate the
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mechanism of these events.
19
events.
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mechanisms using both P-wave polarity and S waveforms.
21
have a variety of mechanisms, the mechanisms of the LFEs are nearly identical.
We increase the S/N ratios of the LFEs by stacking similar
The combination of LFEs and intraplate events enable us to constrain the LFE
While the intraplate events
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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Therefore, we can estimate a moment tensor solution that represents general mechanism
2
of LFEs. The resultant moment tensor is a shallow dipping thrust fault that is entirely
3
consistent with the subduction of the Philippine Sea Plate.
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Hirose and Obara [2005] determined the fault plane for six SSE, two of which
5
partially overlap our study area.
6
events.
7
difference of the strike and rake angles is not significant considering the errors in the
8
two solutions.
9
with the SSE mechanisms.
Figure 4b shows the focal mechanisms of these
All three mechanisms in Figure 4 are similar low angle thrust fault. The
We conclude that the moment tensor solution for the LFE is consistent
10
Shelly et al., [2006a] demonstrated that deep tremor in western Shikoku can be
11
represented as a swarm of LFEs. Thus, SSEs, LFEs, and deep tremor appear to be
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different manifestations of the same process, viz. relatively slow, but accelerated shear
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slip on the plate interface.
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events, which are directly down-dip of the locked zone, mean that it will be important to
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monitor them closely and to understand better their earthquake triggering potential
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including their relationship to the megathrust earthquake recurrence.
The strategic location of these episodic accelerated slip
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Acknowledgements.
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Ministry of Education, Sports, Science and Technology, Japan and by National Science
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Foundation Grant EAR-0409917.
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This work is supported by Grant-in-Aid for Scientific Research,
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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References
2
DeMets, C., R. G. Gordon, D. F. Argus, S. Stein (1994), Effect of recent revisions to the
3
geomagnetic reversal time scale on estimates of current plate motions, Geophys.
4
Res. Lett., 21, 2191-2194.
5
Hirose, H. and Obara, K (2005), Repeating short- and long-term slow slip events with
6
deep tremor activity around the Bungo channel region, southwest Japan, Earth
7
Planets Space, 57, 961-972.
8
Katsumata, A., and N. Kamaya (2003), Low-frequency continuous tremor around the
9
Moho discontinuity away from volcanoes in the southwest Japan, Geophys. Res.
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Lett. 30, doi:10.1029/2002GL015981.
Obara, K. (2002), Nonvolcanic deep tremor associated with subduction in southwest
Japan, Science, 296, 1679-1681.
13
Obara, K. and H. Hirose (2006), Non-volcanic deep low-frequency tremors
14
accompanying slow slips in the southwest Japan subduction zone, Tectonophysics,
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417, 33-51.
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Plicka V., and J. Zahradník (1998), Empirical Green's functions calculated from the
inversion of earthquake radiation patterns, Geophys. J. Int., 132, 471-478.
Shelly, D. R., G. C. Beroza, and S. Ide (2006a), Non-Volcanic Tremor and Low
Frequency Earthquake Swarms, submitted to Nature.
20
Shelly, D. R., G. C. Beroza, S. Ide, and S. Nakamula (2006b), Low-frequency
21
earthquakes in Shikoku, Japan, and their relationship to episodic tremor and slip,
14
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2
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
Nature, 442, 188-191.
Shomali, Z. H. (2001), Empirical Green's functions calculated from the inversion of
earthquake radiation patterns, Geophys. J. Int., 144, 647-655.
4
Zhang, H., and C. H. Thurber (2003), Double-difference tomography: The method and
5
its application to the Hayward fault, California. Bull. Seismol. Soc. Am. 93,
6
1875-1889.
7
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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Figure Captions
2
Figure 1. Map (top) showing the study area and the locations of LFEs (crosses) and
3
regular intraplate earthquakes (circles), determined by Shelly et al. (2006b). The study
4
area of southwest Shikoku is shown in the inset.
5
hypocenter distribution within the thick gray rectangular is shown in lower panel.
6
mechanisms of ten intraplate earthquakes are shown by beach-balls (lower hemisphere
7
projection).
8
stations.
Cross sectional view of the
Star represents the reference LFE, 20050419065024.
The
Triangles are
9
10
Figure 2. Comparison of the maximum and minimum of cross correlation functions
11
(a) between the reference LFE, 20050419065024, and all LFEs within 3 km of it and (b)
12
between the intraplate events shown in Figure 1.
13
calculated for three component waveforms bandpass-filtered between 1 and 8 Hz. Size
14
of symbol scales with S/N ratio in dB.
Cross correlation functions are
15
16
Figure 3. The distribution of polarities of P-waves, up (U, black circles), down (D, open
17
circles), and unknown (?) estimated by comparison to the waveforms of regular
18
earthquakes of known polarity.
19
sphere using the equal-area projection.
20
are shown for a stacked wave (top), as well as the intraplate events #4 (middle) and #8
21
(bottom). Each waveform is normalized by the maximum amplitude and aligned at the
22
onset time of the P-wave. Gray circles and open triangles are polarities determined by
Stations are plotted in lower hemisphere of focal
In each box 3 s windows around the P-waves
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
1
an automated analysis (see text).
2
consistent observations. Dots show data for which the polarities cannot be judged.
Size of the symbol increases as the number of
3
4
Figure 4. a) The moment tensor determined for LFEs by EGF analysis.
5
of stations are also shown in the lower hemisphere projection.
6
(thin black lines) and calculated seismograms (thick gray line) are shown for each
7
station. The amplitude scale (nm/s) is shown for each station.
8
circles, P: triangles, and N: crosses) of moment tensor solutions determined by different
9
subsets of the data from eight stations. b) The focal mechanisms for SSEs in this area
10
determined by Hirose and Obara (2005). Strike, dip, and rake angles are shown in
11
parentheses.
12
The directions
Observed seismograms
Three principle axes (T:
17
1
2
3
4
5
6
7
8
9
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
Figure 1. Map (top) showing the study area and the locations of LFEs (crosses) and regular
intraplate earthquakes (circles), determined by Shelly et al. (2006b). The study area of southwest
Shikoku is shown in the inset. Cross sectional view of the hypocenter distribution within the thick
gray rectangular is shown in lower panel. The mechanisms of ten intraplate earthquakes are shown
by beach-balls (lower hemisphere projection). Star represents the reference LFE, 20050419065024.
Triangles are stations.
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
1
2
3
4
5
6
7
Figure 2. Comparison of the maximum and minimum of cross correlation functions (a) between
the reference LFE, 20050419065024, and all LFEs within 3 km of it and (b) between the intraplate
events shown in Figure 1. Cross correlation functions are calculated for three component
waveforms bandpass-filtered between 1 and 8 Hz. Size of symbol scales with S/N ratio in dB.
19
IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
1
2
3
4
5
6
7
8
9
10
11
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Figure 3. The distribution of polarities of P-waves, up (U, black circles), down (D, open circles), and
unknown (?) estimated by comparison to the waveforms of regular earthquakes of known polarity.
Stations are plotted in lower hemisphere of focal sphere using the equal-area projection. In each
box 3 s windows around the P-waves are shown for a stacked wave (top), as well as the intraplate
events #4 (middle) and #8 (bottom). Each waveform is normalized by the maximum amplitude and
aligned at the onset time of the P-wave. Gray circles and open triangles are polarities determined
by an automated analysis (see text). Size of the symbol increases as the number of consistent
observations. Dots show data for which the polarities cannot be judged.
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
1
2
3
4
5
6
7
8
9
10
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Figure 4. a) The moment tensor determined for LFEs by EGF analysis. The directions of stations
are also shown in the lower hemisphere projection. Observed seismograms (thin black lines) and
calculated seismograms (thick gray line) are shown for each station. The amplitude scale (nm/s) is
shown for each station. Three principle axes (T: circles, P: triangles, and N: crosses) of moment
tensor solutions determined by different subsets of the data from eight stations. b) The focal
mechanisms for SSEs in this area determined by Hirose and Obara (2005). Strike, dip, and rake
angles are shown in parentheses.
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IDE ET AL.: THE MECHANISM OF DEEP LOW FREQUENCY EARTHQUAKES
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2
3
Supplements
4
5
# ID
[YYYYMMDDhhmmss]
Table S1: Hypocenters and mechanisms of intraplate earthquakes
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
16
17
†
18
20021017035327
20021018114122
20021019180208
20021104152800
20030610213612
20030713192152
20030822201103
20040903163409
20050730081702‡
20060213014645‡
Lat.
[º]
Lon.
[º]
Depth
[km]
M†
33.501
33.501
33.501
33.501
33.503
33.504
33.509
33.498
33.519
33.488
132.635
132.636
132.638
132.637
132.634
132.642
132.628
132.638
132.638
132.625
40.6
40.3
40.9
42.0
40.1
38.6
40.0
40.8
39.7
43.1
1.8
1.7
1.3
3.1
1.4
1.1
1.5
2.2
1.4
2.7
Magnitude determined by JMA.
JMA catalog.
‡
Strike
[º]
150
−40
−51
160
−33
−11
−57
25
−101
146
Dip
[º]
40
23
28
11
37
24
37
39
49
76
Rake Mo
[º] [1012 Nm]
−83
−109
−129
84
−125
−89
−99
−75
−164
−175
1.15
1.57
0.55
33.83
0.62
0.34
0.83
3.11
0.76
13.19
Not included Shelly et al. (2006b). Locations are from the
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