The September 19, 2017 (M W 7.1), intermediate-depth Mexican earthquake: a slow and energetically inefficient deadly shock

Abstract

Plain Language Summary
Devastation in central Mexico produced by the intermediate‐depth (magnitude 7.1) Puebla‐Morelos earthquake of 19 September 2017 has raised important questions about the seismic hazard in Mexico City, where more than 20 million people live. Probabilistic hazard in the city from intermediate‐depth and shallower subduction events (i.e., as the 1985 quake that killed 15,000 people in the capital) is about the same despite that the first type of earthquakes is much less frequent. Understanding the source process of intermediate‐depth earthquakes has been a major research topic since decades ago because they occur at depths where mechanical considerations for shallow earthquakes are no longer valid. Recent research has led to unexpected conclusions for this kind of events that were thought to be the consequence of fast and energetically efficient rupture processes. Through a novel technique, we investigate the Puebla‐Morelos earthquake to better understand the generating physics of the strong ground motions. We show that the event was extraordinarily slow and inefficient and that this does not contradict the large ground accelerations. More than 84% of the earthquake energy was dissipated in the source region likely producing rock melting in the geological fault hosting the rupture process.

Full text

The 19 September 2017 (Mw7.1) Intermediate-Depth
Mexican Earthquake: A Slow and Energetically
Inefficient Deadly Shock
Aron Mirwald1, Víctor M. Cruz-Atienza1, John Díaz-Mojica1, Arturo Iglesias1,
Shri K. Singh1, Carlos Villafuerte1, and Josué Tago2
1Instituto de Geofísica, Universidad Nacional Autónoma de México, Mexico City, Mexico, 2Facultad de Ingeniería,
Universidad Nacional Autónoma de México, Mexico City, Mexico
Abstract We investigate dynamic source parameters of the Mw7.1 Puebla-Morelos intermediate-depth
earthquake (h=57 km) of 19 September 2017, which devastated Mexico City. Our simple, elliptical
source model, coupled with a new Particle Swarm Optimization algorithm, revealed rupture propagation
within the subducted Cocos plate, featuring a high stress drop (Δ𝜏=14.9±5.6MPa) and a remarkably
low radiation efficiency (𝜂r=0.16 ±0.09). Fracture energy was large (G=(1.04 ±0.3)×1016 J),
producing a slow dissipative rupture (Vr∕Vs=0.34 ±0.04) with scaling-consistent radiated energy
(Er=(1.8±0.9)·1015 J) and energy-moment ratio (Er∕M0=3.2×10−5). About 84% of the available
potential energy for the dynamic rupture was dissipated in the focal region, likely producing
friction-induced melts in the fault core of 0.2–1.2 cm width due to heat production (700–1200 ◦C
temperature rise). Such source features seem to be a universal signature of intermediate-depth
earthquakes.
Plain Language Summary Devastation in central Mexico produced by the intermediate-depth
(magnitude 7.1) Puebla-Morelos earthquake of 19 September 2017 has raised important questions about
the seismic hazard in Mexico City, where more than 20 million people live. Probabilistic hazard in the city
from intermediate-depth and shallower subduction events (i.e., as the 1985 quake that killed 15,000
people in the capital) is about the same despite that the first type of earthquakes is much less frequent.
Understanding the source process of intermediate-depth earthquakes has been a major research topic since
decades ago because they occur at depths where mechanical considerations for shallow earthquakes are no
longer valid. Recent research has led to unexpected conclusions for this kind of events that were thought
to be the consequence of fast and energetically efficient rupture processes. Through a novel technique, we
investigate the Puebla-Morelos earthquake to better understand the generating physics of the strong ground
motions. We show that the event was extraordinarily slow and inefficient and that this does not contradict
the large ground accelerations. More than 84% of the earthquake energy was dissipated in the source region
likely producing rock melting in the geological fault hosting the rupture process.
1. Introduction
On 19 September 2017, an Mw7.1 intermediate-depth normal-faulting earthquake (IDE) occurred in the
subducting Cocos plate at 57-km depth, with epicentral distance of 114 km from Mexico City (Cruz-Atienza
et al., 2017; Singh et al., 2018; Figure 1). The peak ground acceleration (PGA) at the rock reference site
of Ciudad Universitaria was 57 cm/s2, twice the value recorded at that site during the 1985 devastating
earthquake (29 cm/s2). The earthquake resulted in 369 deaths, of which more than two thirds perished in
the capital, where 57 buildings suffered total or partial collapse. Devastation produced by an IDE in the
country is not unusual. Several past intraslab earthquakes, as the great Mw8.2 rupture offshore the states
of Oaxaca and Chiapas on 8 September 2017 (Okuwaki & Yagi, 2017; Suárez et al., 2019), have also caused
large damage in other regions of Mexico (see; Singh et al., 2018, for a historical overview of IDEs in Mexico).
Despite the hazard that IDEs represent in Mexico and other regions of the globe, the physics of this kind
of events has challenged the seismological community for decades (Frohlich, 2006). At focal depths below
30 km, brittle failure should be inhibited due to the high normal stresses and frictional stability (Green &
Houston, 1995; Scholz, 1998). Yet most IDEs are characterized by unstable slip radiating high frequencies
RESEARCH LETTER
10.1029/2018GL080904
Key Points:
• We performed the dynamic source
inversion of the 19 September
(Mw7.1) 2017 intermediate-depth
Mexican earthquake with a Particle
Swarm Optimization algorithm
• The event was highly dissipative
with a slow rupture propagation and
scaling-consistent radiated energy
• The temperature rise associated with
thespecificfractureenergylikely
produced friction-induced melts in
the fault core
Supporting Information:
• Supporting Information S1
Correspondence to:
V. M. Cruz-Atienza,
cruz@geofisica.unam.mx
Citation:
Mirwald, A., Cruz-Atienza, V. M.,
Díaz-Mojica, J., Iglesias, A.,
Singh, S. K., Villafuerte, C., &
Tago, J. (2019).The 19 September 2017
(Mw7.1) intermediate-depth
Mexican earthquake: A slow and
energetically inefficient
deadly shock. Geophysical
Research Letters,46, 2054–2064.
https://doi.org/10.1029/2018GL080904
Received 16 OCT 2018
Accepted 22 JAN 2019
Accepted article online 7 FEB 2019
Published online 26 FEB 2019
©2019. American Geophysical Union.
All Rights Reserved.
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Geophysical Research Letters 10.1029/2018GL080904
(Frohlich, 2006). Dehydration reactions at those depths have often been invoked to explain brittle fracture
(Hacker et al., 2003). Water release from mineralogical phase transitions could counteract the confining pres-
sure directly (dehydration embrittlement; Jung et al., 2004) or indirectly (dehydration-driven stress transfer;
Ferrand et al., 2017), enabling a brittle fracture.
However, it is also possible that brittle fracture is not responsible for IDEs. Thermal shear runaway in the
focal region can generate highly localized ductile deformation and slip instabilities (Kanamori et al., 1998;
Prieto et al., 2012). This mechanism was shown to be plausible by numerical simulations (Braeck & Podlad-
chikov, 2007; John et al., 2009) and geological evidence (Andersen et al., 2008; Di Toro et al., 2005; John et al.,
2009). Recently, local and global seismological studies have shown that most of IDEs have a low radiation
efficiency, suggesting that thermal shear runaway is the leading source mechanism of IDEs (Díaz-Mojica
et al., 2014; Nishitsuji & Mori, 2013; Prieto et al., 2013, 2017).
Advances in source imaging currently permit the retrieval of some dynamic rupture parameters directly
from ground motion records. After the pioneering work of Peyrat and Olsen (2004), a few other efforts
have led to improved methodologies for inverting the friction and stress changes on seismogenic faults
(Díaz-Mojica et al., 2014; Di Carli et al., 2010; Herrera et al., 2017; Ruiz & Madariaga, 2013; Twardzik
et al., 2014). Since these methods model the spontaneous rupture process to explain the observed seismo-
grams (by solving the elastodynamic equations coupled with a fault-friction constitutive law), they allow
assessment of fundamental properties of the source, such as the energy partition and its relation with the
rupture kinematics.
In this work, we present the dynamic source inversion of the 2017 Puebla-Morelos earthquake to investigate
the physics of the source process that originated the devastating ground motion in central Mexico. To this
purpose, we improved the methodology introduced by Díaz-Mojica et al. (2014), by implementing a new
Particle Swarm Optimization (PSO) algorithm (Eberhart & Kennedy, 1995) that takes advantage of parallel
computing, high convergence rates and a thorough exploration of the model space around the best solutions.
2. Dynamic Source Inversion
2.1. Source Model
We model the earthquake rupture as a frictional process on a fault plane embedded in a 3-D elastic full
space. Sliding begins when the shear traction in the nucleation zone (NZ) exceeds the static fault strength.
In nature, the traction builds up gradually due to tectonic loading. Here, the shear traction in the NZ, which
we assume as a 3-km radius circular patch, is prescribed slightly higher than the static strength of the fault so
that the spontaneous rupture initiates with the simulation. To stop rupture propagation, we assume a barrier
model that makes the strength of the rock infinite outside the source. The rupture area has an elliptical
shape, which is a reasonable constraint for moderate-sized IDEs that generally show simpler and localized
slip distributions (Díaz-Mojica et al., 2014; Di Carli et al., 2010; Ruiz & Madariaga, 2013).
We adopt the linear slip-weakening friction law (Ida, 1972) that depends on three constitutive parameters:
the static (𝜇s) and dynamic (𝜇d) friction coefficients, and the slip-weakening distance (Dc). We assume a
constant fault normal traction equal to the lithostatic pressure at 60-km depth (1,564 MPa), although this is
irrelevant for the rupture process because seismic radiation only depends on the relative stress changes. We
fix 𝜇dequal to 0.5 and invert for the change of friction coefficient from the static to the dynamic levels, Δ𝜇.
We also invert for Dc, the last constitutive parameter defining our friction model.
The source model is determined by nine parameters: the initial shear tractions in the NZ and on the fault
outside the NZ, the change of the friction coefficient, the slip-weakening distance, and the five geometrical
parameters of the ellipse (lengths of its two semiaxes, two coordinates of its center with respect to the NZ,
and its rotation angle). From models parameterized in this way, we can derive physical quantities involved
in the rupture process (Díaz-Mojica et al., 2014) such as the fracture energy, G, the radiated energy, Er, and,
hence, the radiation efficiency, 𝜂r=Er∕(Er+G), which tells how dissipative is the rupture process.
2.2. Inversion Method
The dynamic source inversion problem has been solved using heuristic strategies such as the neighborhood
(e.g., Di Carli et al., 2010; Ruiz & Madariaga, 2013) and genetic (Díaz-Mojica et al., 2014) algorithms. In
this work we introduce a new PSO algorithm to invert the rupture dynamics, which has the remarkable
capacity to thoroughly sample the neighborhood of optimal solutions. Problem solving may be seen as a
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Table 1
Inverted and Derived Parameters of Our Preferred Source Model
Symbol Parameter Range Value
Inverted
DcSlip-weakening distance 0.2–1 m 0.6±0.3m
Δ𝜇Increment of friction coefficient 0.015–0.5 0.035 ±0.007
Δ𝜏Stress drop in fault 0–48 MPa 14.9±5.6MPa
Δ𝜏nStress drop in NZ 18–78 MPa 55 ±11 MPa
AArea 80–1,250 km2713 ±250 km2
Derived
GFracture energy — (1.04 ±0.3)·1016 J
ErRadiated energy — (1.8±0.9)·1015 J
𝜂rRadiation efficiency — 0.16 ±0.09
𝜅approximate ratio of strain energy to Gc—1.3±0.2
VrRupture velocity — (0.34 ±0.04)Vs
Note. Columns 3 and 4 provide the search range for the inverted parameters and the obtained mean
values with their standard deviations for both the inverted and derived parameters, respectively.
NZ=nucleationzone.
population-wide phenomenon, emerging from the behaviour of the individuals through their interactions.
In any case, populations are organized according to some sort of communication structure, often thought
of as a social network. In PSO a number of simple entities—the particles—are placed in the model space,
and each evaluates the objective (or misfit) function at its current location. Each particle then determines its
movement through the space by combining some aspect of the history of its own current and best locations
with those of one or more members of the swarm, with some random perturbations. Eventually, the swarm
as a whole, like a flock of birds collectively foraging for food, is likely to move close to an optimum of the
objective function (Poli et al., 2007). The PSO has proven to be very efficient for a large class of multiparamet-
ric nonlinear problems (Blum & Li, 2008). Our PSO algorithm follows Suganthan (1999) with an increasing
size of the models' vicinity to prevent premature convergence. Its parameters, listed in supporting informa-
tion Table S1, were chosen based on a parametric study we performed for the nine-dimensional Langerman
function (Jamil & Yang, 2013). The size of the population we used was 420 particles (i.e., models), and we ran
the inversions for 50 generations, resulting in 420 ×50 = 21,000 dynamic-source-tested models per inver-
sion. Since we performed 12 inversions per auxiliary fault plane as explained later in section 3, we explored a
total of 504,000 dynamic source models to generate our preferred solution. In Table 1 we provide the search-
ing ranges of the model space. To avoid wasting computational time when solving unfeasible models, we
constrained the parameters in such way that the initial traction was always larger than the static strength in
the NZ, and lower than that in the rest of the fault.
To quantify the quality of the source models, we use a misfit function that involves the cross correlation
between observed and synthetic seismograms (Díaz-Mojica et al., 2014):
𝑓=1
6N∑(𝜏max −𝜏c
2𝜏c
−
cross(xobs −xsyn)
auto(xobs)+auto(xsyn )),(1)
where the sum is over the three components for all (N) seismic stations. The first term on the right-hand
side accounts for the time shift between the signals that depends on the characteristic time, 𝜏c, which is
approximately equal to the source duration halftime (in this case 𝜏c=7s; Díaz-Mojica et al., 2014), and
𝜏max is the absolute value of the time shift for the maximum cross-correlation coefficient. The second term
involves the maximum of the cross-correlation and autocorrelation functions and accounts for the similarity
of waveform and amplitude.
Following Di Carli et al. (2010), the forward problem is solved in two steps. First, the dynamic rupture is
simulated using a highly accurate 3-D traction-at-slip-node finite-difference method (Dalguer & Day, 2007)
as compared with most of the well-established numerical methods (Harris et al., 2018), in a cubic domain
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Figure 1. Map showing significant IDEs in central Mexico. (a) Location of strong motion stations (green squares) used
for the inversion of the Puebla-Morelos event (modified from; Cruz-Atienza et al., 2017). The straight dashed line
depicts the cross section shown below. (b) Cross section showing the tectonic setting of the region and the projection of
some IDEs. IDE = intermediate-depth earthquake.
with 50-km length per side and a grid size of 400 m. We verified that such grid size virtually produces the
same solutions as for 300 m in a wide range of constitutive parameters including those explored in our
inversions (e.g., rupture time errors smaller than 10% in all cases). The time step was adjusted according to
the stability criterion. The cube contains the fault plane where the friction law is imposed. Around the cube,
the outgoing seismic energy is absorbed with a Perfectly Matched Layer (Marcinkovich & Olsen, 2003) to
simulate an infinite space. Second, the output source kinematics is used to propagate the wavefield up to
the stations by convolving the slip rate functions with the double-couple Green's functions computed using
a discrete wavenumber method (Bouchon, 1981) in a layered medium appropriate for the region (Campillo
et al., 1996). The dynamic source inversion methods are very time consuming. In our case, each forward
problem took about 15 min in a single 2.4-GHz Intel Xeon processor. Each inversion was run in parallel with
the PSO algorithm over 210 processors. Considering a population of 420 models and 50 generations, each
inversion lasted about 25 hrs.
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2.3. Data and Focal Mechanism
We used accelerograms of six strong motion stations belonging to the National University of Mexico (UNAM)
with an epicentral distance smaller than 110 km (Figure 1a). We selected the stations avoiding those with
large site effects, while maintaining a good azimuthal coverage. The seismograms were aligned with the
theoretical Pwave arrival times predicted by the regional velocity model (Campillo et al., 1996). Then, the
accelerograms were band-pass filtered between 0.05 and 0.15 Hz and integrated twice to obtain the dis-
placements that were inverted. The inverted frequency band contains the corner frequency of the event,
fc∼0.08 Hz (supporting information Figure S1; consistent with the source duration of ∼13 s reported by the
U.S. Geological Survey), and thus essential information of the source finiteness. We choose the upper cutoff
frequency to avoid unmodeled effects due to the simplicity of both the source model and the 1-D velocity
structure, which prevent us to solve for source details that are not critical for capturing the overall physics
of the rupture process.
For an 𝜔2Brune source model, the radiated energy contained in frequencies f<2∗fc(i.e., below 0.16 Hz in
this case) is less than 42% of the total (Singh & Ordaz, 1994). However, since low frequencies are intrinsically
linked to high frequencies through the downscale causal relationship given by the elastodynamic and fault
constitutive equations governing the propagating crack, the source energy partition is reasonably well solved
provided that the fault mechanical model we assumed is a good proxy. This has been proven to be so by
Díaz-Mojica et al. (2014) and can be seen in supporting information Figure S1 for this event, where the
spectrum of our preferred source model above 0.16 Hz is consistent with two other functions determined
independently and slightly above the 𝜔2Brune's prediction.
Since it was not possible to determine unambiguously the fault plane using the small aftershocks sequence,
we inverted the source process for both auxiliary planes (Figure 1). The inversions yielded similar model
parameters for both planes, so we decided to discuss only the results for the fault dipping to the south (𝜙=
108◦,𝛿=47◦,𝜆=−98◦), which yielded 20% better fits with the observed waveforms.
3. Results
Because of the stochastic nature of the optimization method, we decided to run multiple inversions in the
same model space. Although the best misfit values from all inversions were of the same order, we noticed
that the associated parameters were different to some extent and that they were interdependent. As expected,
(a) larger stress drops were generally associated with smaller rupture areas and larger Dc, and (b) lower
rupture velocities were often associated with larger Dc. Ruiz and Madariaga (2013) noticed similar trade-offs
between these parameters in their dynamic source inversions. However, the variation range of the preferred
models from our inversions is relatively small. More importantly, there are quasi-invariant metaparameters
across the solutions such as the radiated energy, fracture energy, radiation efficiency, and rupture velocity.
This means that all models essentially share the same energy partition and rupture kinematics.
Our solution models correspond to the best fit individuals from 12 independent inversions, whose misfit val-
ues are smaller than 0.15. We took as the final, preferred solution (Table 1) the average of these models along
with their standard deviation per parameter. The seismogram fits are shown in Figure 2, where we compare
the observed waveforms (black curves) with the average waveforms from the selected models (red curves)
along with the associated standard deviations (pink band). Despite the simplicity of the source model and
the velocity structure, most of the waveforms and amplitudes are well reproduced in the three components,
which gives us confidence to our solution models.
In Figure 3a we show the average final slip distributions from the 12 selected models and the geometry of
the best fit solution whose misfit value is 0.11 (white dashed ellipse). Rupture predominantly propagates to
the northwest and updip with an average final slip of 2.1±0.3m, which is a reasonable value for earth-
quakes of this size. If we project the rupture path from the NZ to the left extremity of the rupture into
the Earth's surface, rupture directivity points roughly toward Mexico City (Figure 1a), suggesting that the
anomalously high ground accelerations and velocities observed in that direction could be due to source
directivity (Singh et al., 2018). It is worth mentioning that a consistent direction of rupture directivity was
found for all solutions obtained from the inversions done for the other auxiliary fault plane, dipping to the
north (not shown).
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Figure 2. Observed (black) and synthetic (red) seismograms in the frequency band 0.05–0.15 Hz. The black lines are
the average of the 12 solution models from independent inversions, and the shaded pink areas depict 2 times the
associated standard deviation.
Although rupture velocity is remarkably low across large parts of the fault (average speed of 0.34 ±0.04 of
the shear wave speed; Table 1), it is also highly variable (Figure 3b). Just after nucleation, rupture propagates
with speed around 0.5Vs along ∼10-km updip from the NZ and then slows down rapidly, specially along
strike, where it almost stops a few kilometers to the northwest (i.e., with speeds of 0.1–0.2 Vs). Rupture
finally accelerates around 20 km from the NZ to reach again values around 0.5Vs close to the northwest
fault extremity. We notice that the relatively high front velocity just after nucleation may be an artifact of
the highly stressed NZ required to sustain the rupture process in the whole fault.
Dynamic crack theory predicts that the faster the rupture front, the larger is the radiation efficiency. This is
shown in Figure 4a for the three different fracture modes (gray lines). Since fracture energy for a given model
is almost constant across the fault because of the slip-weakening friction law (i.e., it is constant except in a
narrow belt next to the fault edge where the final slip is smaller than Dc), rupture speed variations should
map bulk regions where radiation of seismic energy (or the seismic moment rate) is enhanced. Figure 3c
confirms such expectation by revealing two maxima of the peak slip rate that spatially correlate with fault
regions where Vris maximum (compare with panel b). Accordingly, the average moment rate function (black
line in Figure 3d) shows the associated bumps centered at 1 and 9 s, as well as a total source duration close to
16 s. Although the stress drop in the nucleation zone has been inverted, we notice that the timing and width
of the first peak could be biased to some extent by the initial kick imposed to initiate rupture. However, as
seen in Figures 3b and 3d, such effect should not be preponderant in the relatively long (∼13 s long) rupture
history after the first 2–3 s of rupture propagation.
Our preferred model exhibits a stress drop of 14.9±5.6MPa, which is high compared with typical values
for shallow earthquakes, but consistent with IDEs in Mexico (García et al., 2004) and at global scale, which
have a mean value around 15 MPa (Prieto et al., 2012; Poli & Prieto, 2016). From the model parameters, we
derived the radiated energy Er=(1.8±0.9)·1015 J, the fracture energy G=(1.04 ±0.3)·1016 J and a
remarkably low radiation efficiency 𝜂r=0.16 ±0.09. All the inverted and derived parameters from our
preferred model are reported in Table 1.
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Figure 3. Averages of the 12 solution models where the dashed ellipse corresponds to the best fit model geometry. (a)
Final slip, (b) rupture velocity normalized by a shear wave speed of 4.7 km/s along with the rupture time contours (in
seconds) of the best fit model, (c) peak slip rate, and (d) moment rate function along with the standard deviation in
gray. All models share the same nucleation zone geometry (black dashed circle).
4. Discussion
Similar to the analysis of the 2011 Zumpango IDE (Mw6.5) in Guerrero, Mexico (Díaz-Mojica et al., 2014),
the inversion of the Puebla-Morelos event revealed that the average rupture speed (Vr∕Vs ∼0.34) and the
radiation efficiency (𝜂r∼0.16) were also remarkably low (Figure 4a). As expected for intraslab Mexican
earthquakes, the stress drop (Δ𝜏∼15 MPa) was relatively high. Similar results for IDEs have been reported
in the Japan subduction zone (Nishitsuji & Mori, 2013), and more recently at a global scale (Poli & Prieto,
2016) and below the Wyoming Craton, USA, in a completely different tectonic setting (Prieto et al., 2017),
suggesting that slow, inefficient processes characterize the source of IDEs.
Although such rupture properties are typical of tsunami earthquakes (see Figure 4a), the 2017 Mw7.1shock
produced a Fourier acceleration spectrum at Ciudad Universitaria between 1 and 2 s 2 times larger than
observed for previous Mexican IDEs with similar magnitude reduced to the same hypocentral distance
(Singh et al., 2018). This shows that despite the highly dissipative source process and the slow rupture prop-
agation, the event generated high radiation of relatively short period waves. This is opposite to tsunami
earthquakes, which are characterized by large MS-Mwdisparities and anomalously low values of the ratio
Er∕M0(Ammon et al., 2006; Newman & Okal, 1998). In the case of the Puebla-Morelos IDE, our inversion
yielded Er∕M0=3.2×10−5, which is consistent with the value found from the dynamic source inversion
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Figure 4. (a) Radiation efficiency (𝜂r) as a function of rupture velocity (Vr) normalized by the shear wave speed (Vs)
for different types of earthquakes including the Puebla-Morelos and Zumpango events in central Mexico. Reported
IDEs (red dots) share the same properties as tsunami earthquakes, with very low rupture velocity and radiation
efficiency. Gray lines depict theoretical predictions for the three different fracture modes (modified from; Kanamori &
Brodsky, 2004). (b) Energy-moment ratios for global earthquakes as a function of magnitude Mwtaken from Kanamori
and Brodsky (2004) along with values found for the Puebla-Morelos and Zumpango IDEs. The straight lines depict the
best linear fit (solid) and the 60th percentile (dashed). (c) Horizontal components geometric mean of the observed and
synthetic (best fit model) peak ground accelerations below 1 Hz. (d) Temperature rise as a function of the fault core
width according to equation (2). The green dashed lines depict the temperature range associated to our fracture energy
uncertainty, and the red dashed lines the range where peridotites and gabbroic rocks melt at the earthquake depth.
IDE = intermediate-depth earthquake.
of the Mw6.5Zumpango IDE in the region (Díaz-Mojica et al., 2014), and with those of many earthquakes
at a global scale (Figure 4b).
Careful examination of the waveforms does not reveal a preponderant source directivity as clearly seen for a
similar IDE in the region (Singh et al., 2014). As a matter of fact, in the absence of strong directivity such as
in our preferred source model, strong motions below 1 Hz can be satisfactorily explained with the dynamic
rupture properties described in the last section. The peak focal-particle acceleration in the two patches with
maximum slip rates (Figure 3c) are significantly higher than 0.5g (i.e., between 415 and 585 cm/s2). These
values in the source region are consistent with most of the PGAs observed at the stations including RABO,
the closest site (hypocentral distance of 65 km), for periods longer than 1 s as shown in Figure 4c. Model
underestimations in the strike-parallel direction (i.e., at stations YAIG and FTIG) are certainly due to the
source model simplicity, specially at FTIG toward the southeast, where even kinematic source inversions
poorly fit the waveforms (Melgar et al., 2018). Two main features of our moment rate function are consistent
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with previous estimates (Figure 3d): the duration of about 16 s and two peaks in the moment release
(between 1 and 4 s, and between 5 and 12 s). Although the source time functions are remarkably different
among each other in the timing of the main peaks, they share similar amplitudes except for the solution
reported by Melgar et al. (2018), which significantly underestimates the scalar moment. Integration of the
moment rate functions gives scalar moments of 1.0520 Nm (Mw=7.28), 3.519 Nm (Mw=6.96), 7.6319 Nm
(Mw=7.18), and 5.819 Nm (Mw=7.11), for our preferred model, and the solutions from Melgar et al.
(2018), Ye (2018), and Vallée and Duet (2016), respectively.
Most interplate earthquakes have radiation efficiencies larger than 0.5 (Venkataraman & Kanamori,
2004; Figure 4a), which implies G<Er. Since 𝜂r∼0.16 for the Puebla-Morelos event, then G=5.3Erin
this case. This means that ∼84% of the available potential energy for the dynamic process of faulting was
dissipated in the focal region. Energy dissipation during an earthquake may involve different processes such
as off-fault fracturing, plastic deformation, or heat production. Among them, heat production is certainly a
preponderant dissipative mechanism that may translate into pseudotachylytes generation (friction-induced
melts) in the fault core (Di Toro et al., 2005; Kanamori et al., 1998). Since most of the mechanical energy
during rupture is converted into work against frictional stresses, it has been shown that about 90% of the
energy partition goes into heat production for most large earthquakes (Cocco et al., 2006). Could fault core
melting have happened during the Puebla-Morelos event? At the tip of the rupture front (i.e., in the stress
breakdown zone), the temperature rise, ΔT, is related to the specific fracture energy, Gc(or breakdown work
density, namely, Wb=G∕A), as (Prieto et al., 2013)
ΔT=Gc
C𝜌w,(2)
where C∼1J·g−1·◦C−1is the heat capacity, 𝜌∼3230 kg/m3, and wis the fault core width. This equation
assumes that the whole fracture energy is dissipated into heat. In our model, Gcis equal to (1.7±0.9)·
107J/m2in average. Figure 4d shows the temperature rise for different widths predicted by equation (2).
According to thermal models of the subducted Cocos plate, the temperature of the slab where the earthquake
took place is between 600 and 700 ◦C (Manea & Manea, 2011; Perry et al., 2016). The melting temperature of
peridotite and gabbroic rocks at those depths (i.e., at 1.5–2 GPa) range between 1400 and 1800 ◦C (Katz et al.,
2003; Nielsen et al., 2010; Philpotts & Ague, 2009; Takahashi & Scarfe, 1985). Therefore, we expect melting
to occur at fault core widths between 0.2 and 1.2 cm (see red line in Figure 4d). Field observations show
that exhumed fault core widths are variable, but most fault veins and pseudotachylites related to subduction
earthquakes are between 0.1 and 3 cm (Andersen & Austrheim, 2006; Obata & Karato, 1995). Therefore, the
temperature rise at the rupture front (estimated between 700 and 1200 ◦C) may indeed have resulted in rock
melting as suggested for other IDEs (Prieto et al., 2013). Note that we did not consider the heat generated
by the total slip involving the dynamic friction level in large parts of the fault, as done by Kanamori et al.
(1998), that would yield to a higher temperature rise.
Our heat production estimates suggest that melting may have happened at the rupture tip of the
Puebla-Morelos earthquake (absolute temperatures at the tip of 1300–1900 ◦C), supporting the idea that a
thermal runaway process could be a preponderant mechanism enhancing unstable slip through lubrication
effects despite the high confining pressures of the focal region. Dehydration from water-rich minerals could
also have played a role in the source region, which does not preclude the existence of the thermal runaway
process (John et al., 2009).
5. Conclusions
We performed the dynamic source inversion of the 2017 intermediate-depth Puebla-Morelos earthquake
with a new PSO algorithm. Our results indicate that the rupture was highly dissipative and remarkably slow.
More than 84% of the available potential energy for the dynamic rupture propagation dissipated in the focal
region. Considering the preexistent slab temperature and heat production during the rupture process, cre-
ation of pseudotachylytes (friction-induced melts) in the fault core is a plausible process that could enhance
the slip instability by lubricating the fault core. Despite the large energy dissipation and the slow rupture
propagation, our dynamic model explains most of the observed PGAs below 1 Hz (i.e., the excitation of rela-
tively short period waves), which were responsible for the extreme ground motion observed in Mexico City.
Independent estimates of IDEs energy balances in Guerrero and different tectonic settings across the globe
MIRWALD ET AL. 2062

Geophysical Research Letters 10.1029/2018GL080904
suggest that slow, inefficient ruptures with scaling-consistent energy radiation may by a universal feature
of most earthquakes at intermediate depths.
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Acknowledgments
This work was supported by the
CONACyT grant 2017-01-6471, the
UNAM-PAPIIT grant IG100617, the
Japan-Mexico SATREPSproject funded
by JST/JICA/UNAM/CONACyT, and
the graduate school scholarships
program of CONACyT. We thank the
“Servicio Sismológico Nacional” and
the “Instituto de Ingeniría,” both
belonging to the “Universidad
Nacional Autónoma de México”
(UNAM), for the acceleration records
used in this work. Seismic records can
be obtained upon request to these
institutions through the websites
(http://www.ssn.unam.mx/contacto/
and http://aplicaciones.iingen.
unam.mx/acelerogramasrsm/
redacelerografica.aspx).
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