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INTRODUCTION |
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 TOP INTRODUCTION DATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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65 km) and Mexico City ( 270 km); the peak
ground accelerations (PGAs) at soft sites in these two cities were as high as
200 cm/s2 and 12 cm/s2, respectively. This was the first
significant earthquake in Mexico since the recent strengthening of
strong-motion and broadband networks in the country. This was also the first
moderate event for which ground-motion maps for Mexico City were produced and
distributed without human intervention in near real time. In this paper, we
report on the source characteristics and the tectonic implications of the
earthquake and the ground motions that it produced. We also discuss the
performance of the seismic alert system (SAS) and near real-time generation
and distribution of expected ground-motion maps for Mexico City during the
earthquake. |
DATA AND ANALYSIS |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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About 35 aftershocks with M 
3.4 were reported by SSN in the
first four days of the earthquake, the largest being one of magnitude 5.3. The
SSN network is sparse. However, the accelerograph network operated by the II
is relatively dense in Guerrero (Anderson
et al. 1994) where a mature seismic gap has been
identified (Singh et al.
1981). Merged data from both networks permit reliable location of
earthquakes in the region. As the accelerograms from the II network are not
available in real time, two field crews were sent to retrieve them. Much of
this report is based on the data collected up to 17 April 2007. We also
analyze two events that occurred after 17 April.
The mainshock and the largest aftershock were well-recorded by the networks. The accerelograph at Atoyac (ATYC), which is located in the epicentral region (figure 1), also recorded many of the smaller aftershocks. However, only four aftershocks triggered three or more II accelerographs. Here we analyze the mainshock and these four aftershocks (table 1). We also consider six other events that occurred in the region (table 2), as they have some relevance to this study.
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, is smaller
than the depth, h. Figure
2 shows the fit between the observed and synthetic seismograms.
The focal mechanisms and the moments are listed in
table 1. The source parameters
of the mainshock obtained from near-source seismograms and those reported in
the Global Centroid Moment Tensor (CMT) catalog are very similar. The fit
between observed and synthetic P wave on the Z component for
the mainshock at ATYC, however, is poor. ATYC is nearly nodal for the
P wave. The observed P pulse is negative for about 1 s and
then becomes positive, while the synthetic P wave, as expected, is
unipolar (positive). One possible explanation for the change in the polarity
of the P wave is a change in the focal mechanism during rupture so
that the first motion at ATYC changes from dilatational to compressional. For the largest aftershock, which occurred on 13 April at 08:43 (event 1, table 1), and all earthquakes listed in table 2, we performed a regional moment tensor analysis following the procedure of Randall et al. (1995). The method uses a time-domain moment-tensor inversion scheme described by Langston (1981). The inversion is performed on bandpass filtered seismograms over a time window that begins with the P wave and includes surface waves. Synthetic seismograms are computed using the reflection-matrix method of Kennett (1983) and Randall (1994). The best centroid depth is obtained through grid search.
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35-43 km) and occur in the subducted Cocos plate
immediately below the plate interface. It is important to note that these
events reveal downdip compression. Shallow-angle thrust earthquakes occur on
the plate interface at depths of less than about 25 km, updip of this inslab
zone of compression (Pacheco and Singh
2007). As the vertical section in
figure 1(B) illustrates, just
below the zone of downdip compression there occur normal-faulting earthquakes
in the slab whose stress axes show downdip tension. The plate interface above
these zones of downdip tension and compression may define the downdip edge of
the seismogenic, shallow-dipping thrust zone (e.g.,
Tichelaar and Ruff 1993). The
aftershocks of large/great earthquakes may not extend below this edge
(although the seismic slip during large/great earthquakes might). If so, then
the aftershock area should not extend inland much beyond 10 km from the coast.
A bound on downdip extent of rupture during large/great earthquakes in
Guerrero is of critical importance in hazard estimation.
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50 km
over a small lateral extent (<10 km). Further inland, the inslab seismicity
completely ceases and the seismic identity of the subducted plate is lost. We
note that inslab downdip compression has also been reported in subduction
zones of Peru and central Chile (Lemoine
et al. 2002). The seismicity pattern and state of the stress in the region can be explained by the initial bending of the Cocos plate at a shallow angle as its subduction at the middle America trench commences. The plate begins to unbend about 10 km landward from the coast, which gives rise to earthquakes with downdip compression in the upper part of the slab (like those of the Atoyac earthquake sequence) and downdip tension immediately below it. Beyond this point the plate becomes subhorizontal, reaching a depth of 50 km about 180 km from the coast where the plate again bends down. This bending is reflected in normal-faulting earthquakes with downdip tension. Thus, the inslab seismicity is mostly confined to regions of unbending and bending. The state of the stress in the slab is almost neutral in the portion that is subhorizontal. This model is similar to those proposed earlier (e.g., Suarez et al. 1990; Singh and Pardo 1993) but is now much better constrained from improved earthquake locations and focal mechanisms (Pacheco and Singh, in preparation) and from receiver function analysis using data from a linear, portable seismograph array deployed from Acapulco in the south up to 400 km in the north (Pérez-Campos et al. 2007).
Inslab earthquakes with downdip compression also occur 10 km north of
Acapulco (Pacheco and Singh
2007). Indeed, events c and d
(table 2) are such earthquakes.
The largest such event so far identified is the 10 December 1994 earthquake,
which occurred about 41 km north of Zihuatanejo
(Cocco et al.
1997).
Table 3 lists the types of seismic sources in the vicinity of Acapulco and other coastal towns in Guerrero. The table also gives observed maximum Mw in Mexico of each type of event. For the purpose of seismic hazard estimation, it will be desirable to split the instrumental seismicity catalog by different types of sources. This, of course, is a very difficult task.
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SOURCE SPECTRUM AND STRESS DROP |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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0(f) and
f2
0(f), of the
mainshock and the largest aftershock of the Atoyac earthquake from the
analysis of the S-wave group recorded at hard sites within a
hypocentral distance of 165 km (19 stations). The Fourier acceleration
spectral amplitude of the intense part of the ground motion at a station,
under far-field, point-source approximation, may be written as
 | (1) |
where
 | (2) |
In the equations above,
0(f) is the moment
rate spectrum so that
0(f) 
M0 as f R = hypocentral distance,
R
= average radiation pattern (0.55),
F = free surface amplification (2.0), P takes into account
the partitioning of energy in the two horizontal components
, β = shear-wave velocity at the
source (3.95 km/s), 
= density in the focal region (2.9
kg/m3), and Q(f) = quality factor, which includes
both anelastic absorption and scattering. The appropriate geometrical
spreading term, G(R), for inslab Mexican earthquakes is
R-1 and the corresponding Q(f) is
251f0.58 (García
et al. 2004). Taking logarithms of equation 1 we obtain
 | (3) |
We solved equation (3) in the least-squares sense to obtain log
[f20(f)].
The source displacement and acceleration spectra of the mainshock and the
largest aftershock are shown in figure
3. We interpret these spectra within the framework of a
2-source model and obtain an estimation of the seismic
moment (M0) and corner frequency (fc).
The stress drop (
) is computed using the Brune
(1970) model. The source
spectra of the mainshock and the aftershock in
figure 3 can be fit by
M0 and of 8.9 x 1017 N-m
and 47 MPa (fc = 0.727 Hz), and 1.2 x
1017 N-m and 29 MPa (fc = 1.19 Hz),
respectively. We note that the stress drop of the mainshock is somewhat higher
than the median of 30 MPa reported by García et
al. (2004) for inslab
normal-faulting Mexican earthquakes.
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RADIATED SEISMIC ENERGY AND APPARENT STRESS |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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a = µ ER/M0 of
11 MPa. If, however, we allow ER to be in the range
of 1 to 3 x 1014 J, then we get
ER/M0 of 1 to 3 x
10-4 and a of 4.5 to 13.5 MPa.
Choy and Kirby (2004)
studied the behavior of a of normal-faulting subduction
earthquakes from a worldwide database. These authors found that the highest
a for inslab events occurred at 35-70 km depth, in proximity
to zones of intense deformation such as sharp bends in the slab. The apparent
stresses of these events were up to 5 MPa, significantly higher than for the
interplate thrust earthquakes. Inslab earthquakes in Mexico are also
significantly more energetic than interplate events
(García et al.
2004). The fact that a of the Atoyac earthquake
is higher than those reported by Choy and Kirby
(2004) for such events probably
reflects the discrepancy between teleseismic and local estimates of the
radiated energy.
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PEAK GROUND MOTIONS |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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PGA and, especially, PGV in figure 4 show a somewhat slower decay than that predicted by the model, which cannot be explained as a source effect. This results in PGAs > 1 cm/s2 and PGVs > 0.1 cm/s even at R > 300 km.
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GROUND MOTIONS IN ACAPULCO |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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60-75 km) are listed in tables
4 and
5. The locations of the
stations are shown in figure 5.
Generally, PGAs during the mainshock at soft sites were about 100
cm/s2, although it reached 200 cm/s2 at Diana (ACAD). At
hard sites (ACAJ and VNTA), the PGA was about 35 cm/s2.
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2-source model. Apart from the seismic moments of the EGF
and the target event, the only other needed parameters are their stress drops,
which we take as 20 MPa. The results are not very sensitive to reasonable
choice of this parameter. Synthesized PGA at ACAJ and ACAD as a function of
Mw is shown in figure
6. The figure indicates that an Atoyac-type
Mw 6.5 earthquake could cause horizontal PGA of
1/2 g at soft sites such as the Acapulco Diana. |
DAMAGE |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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No damage to roads and bridges was recorded, except for a nine-ton rock that fell on a road in Atoyac de Álvarez.
As has occurred in other earthquakes, the population of Acapulco and Mexico City overreacted to the real intensity of the earthquake. It has been observed that even a moderate earthquake triggers fear and anxiety among people who immediately recall the consequences of the devastating 19 and 21 September 1985 earthquakes.
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PERFORMANCE OF THE SEISMIC ALERT SYSTEM FOR MEXICO CITY |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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6 and 5 
M < 6, respectively
(Espinosa-Aranda and Rodríguez
2003). An evaluation of the SAS's performance by Iglesias et
al. (2007) for the period
1991-2004 reveals a surprisingly high failure rate. This poor performance
results from an inadequate detection algorithm and the limited area covered by
the SAS. Iglesias et al.
(2007) propose an alternative
strategy for detecting potentially damaging earthquakes to Mexico City. One
month of seismic activity in the Guerrero region, beginning 31 March, 2007,
provides a further test of the present SAS algorithm and the proposed
alternative strategy. A restricted alert was issued by the SAS for the earthquake of 31 March, which was located near Acapulco (Mw 4.7; event c in table 2). This was a false alert since the magnitude was less than 5. The alert caused annoyance to the alert subscribers since the earthquake was felt by very few people in the city. A public alert was issued for the Atoyac mainshock. In a strict sense, this alert was also a failure, since Mw was less than 6. However, since the earthquake was widely felt in the city, it clearly merited a public alert. In this context, we also note that the initial estimate of the magnitude by the SSN was 6.3. The SAS correctly issued a restricted alert for the largest aftershock (Mw 5.3, event 1, table 1). Although the 19 April earthquake near Petatlan qualified for a restricted alert (Mw 5.0, event e, table 2), none was issued by SAS. Since Mw of the earthquake of 28 April near Acapulco was 5.0 (event d, table 2) the SAS should have issued a restricted alert but did not. More important, it is not clear why SAS did not issue a restricted alert for this event while it did for the 19 March earthquake (Mw 4.7). The events were located very near each other, the 28 April earthquake was greater, and it gave rise to larger accelerations at near-source stations, including those in Acapulco.
In the alternative strategy proposed by Iglesias et al.
(2007), the alert is based on
expected peak acceleration at station CU, Ared, which is
computed from root-mean-square acceleration (Arms) at
near-source stations using the relation
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where RS and RCU are hypocentral
distances to near-source stations and station CU, respectively. CU is located
in the hill zone of Mexico City. This station has been in continuous operation
since 1964. The equation is based on extensive strong-motion recordings
available at CU. In the above equation, Arms is computed
over a 10-s window on bandpass-filtered (0.2-1.0 Hz) accelerograms.
Ared is the expected maximum acceleration at CU in the
same frequency band. Experience shows that if observed peak acceleration in
CU, Acu, is 2 cm/s2, then the earthquake
is widely felt and may cause damage in the city. Iglesias et al.
(2007) propose a single level
of alert and suggest this should occur when Acu 2
cm/s2. If we require that the probability of missed alert at this
threshold be 1% and that of false alert be 30%, then the alert would have to
be issued if Ared 0.8 cm/s2.
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0.8
cm/s2. |
NEAR REAL-TIME GROUND-MOTION MAP FOR MEXICO CITY |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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The system, presently in its first stage, relies on recordings of a single station. It is triggered by the detection of an earthquake at the station CU. As mentioned in the previous section, this station, located in the hill zone of Mexico City, has been in operation since the 1960s and has been used as a reference site to compute spectral amplifications of all the other instrumented sites throughout the city (see figure 8).
Once the end of the motion is detected, the system computes the response spectra (pseudoaccelerations, 5% damping) of the horizontal components and decides, based on their absolute size and the ratio between the spectral ordinates at 1 s and the corresponding PGA, whether it is a significant event or not.
If the system decides that it is dealing with a significant event, a process starts to compute estimated average horizontal response spectra at the nodes of a grid of 1,600 points with separation of approximately 500 m, using response spectral transfer functions that are precomputed and stored in the system. These transfer functions have been obtained using those computed from previous earthquakes at the approximately 100 strong-motion stations of the Mexico City Accelerographic Network (figure 8) and a Bayesian interpolation scheme that uses the transfer functions at instrumented sites, plus information from about 2,500 points in which the predominant site period has been measured. Previous studies have shown that the response spectra thus estimated at sites in the Valley of Mexico are very close to the exact response spectra (e.g., Ordaz et al. 1988).
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As an example, figure 9 shows two spectral acceleration maps of the 19 September 1985 earthquake. These maps, of course, have been recreated, a posteriori, using the recordings obtained at station CU at that time.
Although the system had been triggered by several minor events, the earthquake of 13 April 2007 was the first moderate event for which ground-motion maps were produced without human intervention. The total time employed by the system was seven minutes after it first detected the motion. In figure 10 we present the maps corresponding to PGA and the spectral acceleration response at 2 s. Note that the general color of the maps is blue, indicating moderate accelerations throughout the city. Compare the colors of these maps with those of the 1985 maps in figure 9.
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CONCLUSIONS |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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Shallow-dipping thrust events on the plate interface cease to occur at a
depth of 25 km, just above the zone of Atoyactype earthquakes. This may
define the downdip edge of the seismogenic, shallow-dipping thrust zone. It
has been suggested that aftershocks of large/great earthquakes may not extend
any farther below this edge. If so, then the aftershock area should not extend
inland much beyond 10 km from the coast. A bound on downdip extent of rupture
during large/great earthquakes is of critical importance to seismic hazard
estimation in Guerrero.
The source spectrum of the earthquake is reasonably well-fit by the
2-source model along with a stress drop of 47 MPa.
This stress drop is somewhat larger than the median value of 30 MPa estimated
for inslab normal-faulting Mexican earthquakes. This relatively large stress
drop also explains larger than predicted PGA and PGV recorded during the
earthquake.
Radiated seismic energy, ER, during the earthquake was in the
range of 1 to 3 x 1014 J. This yields
ER/M0 of 1 to 3 x
10-4 and apparent stress of 4.5 to 13.5 MPa. These values are
higher than those reported for inslab earthquakes in subduction zones using
teleseismic data (a < 5 MPa). The difference
probably reflects systematic error in teleseismic estimation of
ER.
The damage in the epicentral region was minor and limited to adobe houses.
Synthesis of ground motion in Acapulco from a postulated Atoyac-type
Mw 6.5 earthquake suggests that such an event might give
rise to a horizontal PGA of 1/2 g at soft sites such as the Acapulco
Diana.
The performance of the seismic alert system (SAS) during a one-month period beginning 31 March 2007 was mixed. Public and restricted alerts for the Atoyac mainshock (Mw 5.9) and its largest aftershock (Mw 5.3), respectively, may be considered successes. The system, however, issued a false restricted alert for the Acapulco earthquake of 31 March (Mw 4.7) and missed restricted alerts for the earthquakes of 19 and 28 April (Mw 5.0). We tested a recently proposed alternative strategy for SAS (Iglesias et al, 2007) on the same earthquake sequence and found that it performed well. We think that this alternative strategy merits serious consideration.
Estimated ground-motion maps for Mexico City were automatically generated and distributed in seven minutes after an accelerograph at CU, a station in the hill zone of the city, first detected the earthquake. Presently in the first stage of its development, this project will provide quick and reliable assessment of possible damage in the city.
The Atoyac earthquake demonstrates that permanent seismic instrumentation in some parts of Mexico, especially Guerrero, is reasonably dense for fruitful research in seismology and earthquake engineering. The near real-time availability of strong-motion and other geophysical data (e.g., GPS and tide-gauge), however, still remains elusive and a goal to strive for.
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ACKNOWLEDGMENTS |
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TOPINTRODUCTIONDATA AND ANALYSISSOURCE SPECTRUM AND STRESS...RADIATED SEISMIC ENERGY AND...PEAK GROUND MOTIONSGROUND MOTIONS IN ACAPULCODAMAGEPERFORMANCE OF THE SEISMIC...NEAR REAL-TIME GROUND-MOTION MAP...CONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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1 Instituto de Geofísica, Universidad Nacional Autónoma de
México, C.U., Coyoacán 04510, Mexico City, Mexico 
2 Instituto de Ingeniería, Universidad Nacional Autónoma de
México, C.U., Coyoacán 04510, Mexico City, Mexico
3 Seismological Laboratory, Mackay School of Mines, University of Nevada, Reno,
Nevada 89557
4 Centro Nacional de Prevención de Desastres, Delfin Madrigal 665,
Coyoacán 04360, Mexico City, Mexico
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Instituto de Geofísica
Universidad Nacional Autónoma
de México
C.U. 04510. México
D.F.
krishna{at}ollin.igeofcu.unam.mx
(S.
K. S.)
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