Citation: González, G., E. Fujita, B. Shibazaki (2020), A new pathway to untangle the question: Was thevolcanic eruption triggered by the earthquake?, Synopsis of IISEE-GRIPS master report.

A NEW PATHWAY TO UNTANGLE THE QUESTION:WAS THE VOLCANIC ERUPTION TRIGGERED BY
THE EARTHQUAKE?
Gino Steven González Ilama1,2Supervisor: Eisuke FUJITA3 , Bunichiro SHIBAZAKI4

ABSTRACTThe relationship between tectonic earthquakes and volcanoes is one of the most striking, but yet lesswell-understood topics in earth sciences, due to the lack of observational data. When this interaction
occurs, volcanoes may react in the short term (hours to days) to long term (months to decades), causing
an eruption, which suggests that what happens inside the volcano to trigger this new eruption needs time.
In 2012, three large earthquakes struck Central America, and some volcanoes erupted days after, whileothers took erupted months to years after the earthquakes to enter into an eruption. This poses to thequestion: was the eruption triggered by the earthquakes? Here I show that the large earthquakes
contributed to the increment in the number of volcanic eruptions in the region. I found that only
volcanoes were already undergoing a certain degree of unrest and without large eruptions previous to
the large tectonic earthquakes erupted, thus suggesting that the volcanoes were nearly ready to erupt andthat the earthquakes helped, but not necessarily caused the volcanic eruptions. The present research canbecome a tool for forecasting volcanic activity when a large earthquake hits a region if the volcanic
activity is previously well monitored and to communicate and prepare the population and to reduce thevolcanic risk if the protocols are well established.
Keywords: Earthquake and volcano interaction, volcanic eruptions, volcanic unrest, stress, Monte Carlo
method.
1. INTRODUCTION“Was the volcanic eruption triggered by the earthquake?” The answer to this question usually is “maybe”
or “it could be a coincidence”. These ambiguous answers can be the result of the lack of observational
data and/or clear scientific evidence that relates both processes. Darwin (1838), in his expedition to
Chile in 1835, experienced the Concepción earthquake in February of that year, with some volcanoes
increasing their activity on the same day and during the subsequent months. Some studies suggested thatthe reaction of volcanoes after a tectonic earthquake can be on the short term, such as hours or days after
the earthquake (Linde and Sacks, 1998; Manga and Brodsky, 2006) or the medium-long term, such asmonths or some years or even decades after the earthquakes (Hill et al., 2002; Walter and Amelung,2007).
Recently, in 2012, three large earthquakes of magnitudes Mw=7.3 (August 27), Mw=7.6(September 5), and Mw=7.4 (November 11) struck El Salvador, Costa Rica, and Guatemala,respectively, occurred within a period of only 72 days (Figure 1). After the first two earthquakes, some1

Volcanes sin Fronteras, Costa Rica.
IISEE-GRIPS master course student.
3
Senior Researcher, National Research Institute for Earth Science and Disaster Resilience.
4
International Institute of Seismology and Earthquake Engineering, Building Research Institute.
2

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volcanoes resumed volcanic unrest (Figure 1). Two volcanoes (San Cristóbal and Fuego) had large
explosions a few days after the first two earthquakes. Years later, other volcanoes changed their
behavior; some entering in a state of unrest to eventually escalate into large volcanic eruptions (i.e. San
Miguel, Telica, Momotombo, Rincón de la Vieja, Poás, Turrialba volcanoes). With this perspective in
mind, the present research tries to explain whether the three megathrust earthquakes of 2012 promoted
the increment of the volcanic activity in Central America on the short- and long-term.

Figure 1. The epicenter of the earthquakes, volcanoes with unrest and location of the seismic stations
used to obtain the waveform to calculate the dynamic stress of the 2012 three large earthquakes inCentral America. The legend: Three EQ (gray circle) indicate stations available for the threeearthquakes. Yellow circle, white diamond, and blue square are seismic stations used for the El
Salvador, Costa Rica, and Guatemala earthquakes, respectively. The volcanoes analyzed here are: 1.
Santa María, 2. Fuego, 3. Pacaya, 4. San Miguel, 5. San Cristóbal, 6. Telica, 7. Cerro Negro, 8.
Momotombo, 9. Apoyeque, 10. Masaya, 11. Concepción, 12. Rincón de la Vieja, 13. Miravalles, 14.
Tenorio, 15. Arenal, 16. Platanar, 17. Poás, 18. Irazú and 19 Turrialba.
2. METHODOLOGY
In order to determine why these volcanoes reacted either in a short or in the long term after the large
earthquakes of 2012, I have considered the dynamic and static stress related to these tectonic shocks.
Also, I applied the Monte Carlo statistical method, as explained below:
2.1 Dynamic stress
The pressure's change by the passing of the seismic waves is called the dynamic stress (σD). This can becalculated using the Eq. 1 proposed by Hill et al. (1993):
𝑃𝐺𝑉 ∗ 𝐺
𝜎𝐷 =
𝑉𝑝ℎ
(1)
where PGV is the peak ground velocity of the seismic wave (km/s), G is shear modulus with a value of
30 GPa for the region based on Ye et al. (2016), and Vph is the velocity phase of the wave (km/s). The
dynamic stress considers the maximum peak-to-peak velocity of the waveform.
2.2 Static stress
The static stress is the change in the local stress field after the earthquake. The software used to calculate
the static stress was "Advance FrontSTR" and it is based on a finite element method, following theprocedure described by Fujita et al. (2014).
The calculation of static stress considers the government equation, Eq. (2) and Eq. (3).

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𝜕𝜎𝑖𝑗
+ 𝑓𝑖 = 0
𝜕𝑥𝑗(2)
𝜎𝑖𝑗 = 𝐷𝜀𝑖𝑗
(3)where σij is the stress tensor, and fi is the external force vector applied, D is the matrix of elastic constants,and ε is the strain.
2.3 Statistical analysis
After the large megathrust earthquake of 2012, the number of volcanic eruptions in the region increased.
To discriminate whether this increase in volcanic eruptions occurred by chance (i.e. temporalcoincidence) or not (i.e. cause-effect relationship), I used the Monte Carlo simulation method(Metropolis and Ulam, 1949). To apply the Monte Carlo simulation, it is necessary to consider thesefollowing information: a) The number of eruptions from 2000 to 2019: a total of 50 eruptions occurredin 7305 days; b) The Mw=7.6 Costa Rica earthquake struck on day 4632, and at this moment, 22
eruptions had already occurred; c) The analysis yet aims to reveal how many random simulations prior
to day 4632 result in 22 eruptions, to reach 50 eruptions in the 2673 days that followed (i.e., 4632-7305).
To understand this, and following the law of the large numbers, the number of simulations was 104 times.
3. DATAThis research considered the large three tectonic earthquakes that occurred in 2012 in Central America
and the volcanic unrest five years before and five years after these earthquakes. Volcanic eruptions witha VEI≥2 (Newhall and Self, 1987) from 2000 to 2019, were selected because the available data set in
the region is complete.
3.1 Seismic waveforms of the 2012 earthquakes
In the case of the August 27, 2012 El Salvador earthquake, the first of the three, seven waveforms areavailable from IRIS (Figure 1). For the September 5, 2012 Costa Rica earthquake, two waveforms from
IRIS and 16 accelerometer data from LIS-UCR are available (Figure 1). In the case of the November
11, 2012 Guatemala earthquake, nine waveforms are available from IRIS (Figure 1). In the case of IRIS
data, usually broadband seismic signals are available.
3.2 Fault parameter of the 2012 earthquakes
To calculate the static stress it is necessary to set the fault parameters of each earthquake. The referencesused were the information published by USGS and Ye et al. (2016).
3.3 Volcanic unrest between 2007- 2017
This research delimitated a period of five years before and five years after the earthquakes to understandif the earthquakes that occurred in 2012 affected the volcanic activity, similar to the approach by
Nishimura (2017). The catalog compiled included a weekly report of the Global Volcanism Program,
information from internal reports from the local observatories, scientific papers, and personal data. This
research classified the information available on volcanic activity in three different “degrees of unrest”,
based on the energy release of volcanoes from least (unrest 1), to intermediate (unrest 2) to the highest(unrest 3) degree, as discussed by Yokoyama et al. (1992). Each degree of unrest means: Unrest 1=
increase in the seismicity of the volcanic system; Unrest 2= Increase in the temperature, deformation,
degassing, phreatic activity, or small eruptions; Unrest 3= Large explosions with considerable
ashfall/explosion with ballistic and paroxysmal events.
4. RESULTS AND DISCUSSION
4.1 Increasing the number of volcanic eruptions after the 2012 earthquakes
In the period from 2000 to 2019, 50 volcanic eruptions occurred, of which, 22 eruptions (inapproximately 12 years) were before the 2012 three large earthquakes in Central America, and 28
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volcanic eruptions were after (in approximately 7 years). The increment rate was from 1.6 to 4.6
eruptions (three times more) per year before and after the 2012 earthquakes, respectively (Figure 2).
From a visual qualitative comparison, it seems that the observed cumulative change in eruption rate isunlikely caused by a random process. In particular, at the time of the earthquake, the observed curve has
a value lower than most of the simulated ones: this is when the curve changes its slope. In this case, Iapplied the Monte Carlo simulation to discriminate if the increment in the number of volcanic eruptions
is by chance or not. I ran 10,000 random simulations, and only 15 simulations are the same or equal to
our observed data, which means 0.15%. This shows that it is likely that the observed acceleration in thenumber of volcanic eruptions is not due to chance, but instead, it is a significant change induced by theearthquake.
4.2 Dynamic and static stress
The volcanoes San Cristóbal and Fuego erupted three and nine days after the Costa Rica earthquake,
respectively. This quick reaction could be by the disturbance in the system promoted by the dynamic
stress. The El Salvador earthquake (Mw=7.3) had low high-frequency energy radiation and a long
period; this could have induced resonance and sloshing at the volcanoes internal system (Namiki et al.,2018). After, the Costa Rica earthquake (Mw=7.6) struck with a moderately high-frequency energy
radiation. Both earthquakes could have disturbed these volcanoes in the short term.
The Costa Rica earthquake produced the largest stress change. Rincón de la Vieja volcano
received 1.25 MPa of σD and 50 kPa of differential static stress (σdiff). However, I found that the σdiff
increased depending on the alignment system. For example, the W-E alignment direction received more
σdiff compare with the N-S alignment direction. Also, the static stress increased drastically close to thezone between the high and low rigidity, which means, the country-rock and magma chamber,respectively. In the case of San Cristóbal volcano, σdiff of 2 kPa occurred in the upper and lower part ofthe magma chamber, which could have induced cracks propagation.
4.3 Volcanic unrest 2007-2012
The change in the volcanic behavior (volcanic unrest) sometimes escalates into volcanic eruptions, butsometimes can trigger other hazardous events (Phillipson et al., 2013). This research considered thevolcanic unrest of the Central American region from September 2007 to September 2017. The volcanic
unrest is divided into three degrees according to the energy release (Yokoyama et al. 1992).
In this period analyzed, 19 volcanoes were showing signs of unrest before and/or after theearthquakes of 2012 (Figures 1 and 3). Before the earthquakes of 2012, 13 volcanoes were in unrest(Santa María, Pacaya, Fuego, San Miguel, San Cristóbal, Telica, Momotombo, Masaya, Concepción,
Rincón de la Vieja, Arenal, Poás and Turrialba; Figure 3) and from these, the volcanoes Santa María,
Fuego, Pacaya, Masaya, Concepción, and Arenal were erupting. After the earthquakes until 2017, thevolcanoes Pacaya, Concepción, and Arenal did not erupt. In the case of the Pacaya volcano, a large
eruption occurred in May 2010. Concepción volcano erupted in May 2011. The magnitude of the
volcanic eruptions in Arenal volcano was in a constant decrease, and the last explosion was in October2010. After the earthquakes of 2012, these volcanoes showed unrest degrees 1 and 2. A possible reason
that these volcanoes did not erupt after 2012 earthquakes is that the magma volume erupted in theprevious eruptions already released the internal pressure. In the opposite case, as Santa María and Fuego
volcanoes are very active and open systems, for which internal pressure constantly reaches the threshold
and triggers explosions.
Other volcanoes had decades without magmatic eruption, but before the earthquakes, they werealready in unrest degrees 1 and 2 (San Miguel, Momotombo, Rincón de la Vieja, Poás and Turrialba;
Figure 1 and 3). From the 19 volcanoes in a state of unrest in the period of 2007-2017, 10 volcanoes
erupted after 2012 earthquakes. These 10 volcanoes were already in unrest before the 2012 earthquakes.
A question to pose is why the other nine did not erupt. Different answers can be given (Figure 3): 1)
Three of them had large explosions, as explained before (Pacaya, Concepción, and Arenal). 2) Five4

volcanoes reacted only when the earthquakes occurred, which means that previously they did not show
any unrest (Apoyeque, Miravalles, Tenorio, Platanar and Irazú; Figure 2). From these, only one had
eruptions in historical times (Irazú), and maybe, the other four are far from the recurrence period of new
eruptions. These five volcanoes only showed unrest degree 1 (increased seismicity) some hours or a few
days after the Costa Rica earthquake. This response can be linked to the dynamic stress that triggered
some seismic swarms in the fault systems around these volcanoes. 3) One volcano (Cerro Negro) had
large explosions in August 1999, and the unrest degree 1 was reached on June 4, 2013. These nine
volcanoes showed evidence that the earthquake itself cannot trigger volcanic eruptions, but theearthquakes can promote eruptions by different mechanism only in volcanoes that are already in a stateof unrest; this also implies that dormant volcanoes or volcanoes with low activity cannot erupt just for
the earthquake's shaking/sake, or the change in the stress regime caused by the earthquake.

Figure 2. Volcanic eruptions in Central America during the period 2000-2019. a) Eruptions by size andlocations in Central America. b) The cumulative number of eruptions and the eruption rate increase
after the 2012 earthquakes. The yellow dotted lines correspond to the Costa Rica earthquake on
September 5, 2012.

Figure 3. Volcanic unrest and earthquakes from 2007 (-5) to 2017 (5). Dot line (0) corresponds to the
Costa Rica earthquake on September 5, 2012.
5. RECOMMENDATIONThis study showed the necessity of monitoring all volcanoes to know the degree of unrest prior to thenext large earthquake, to establish future scenarios of increment of volcanic activity and eventually
volcanic eruption on the short (days) or long term (years) considering the previous state of unrest,5

earthquake characteristics and geological history. This kind of surveillance can be a useful forecasting
tool of volcanic unrest to prepare the Civil Protection office, local government, and the Central
Government to take decisions to reduce the risk at different scales. However, it is important to work
quickly with the most vulnerable populations that usually live close to the volcanoes and do not haveenough information or time to prepare before the next volcanic eruption. At the date of submission ofthis synopsis, August 24, 2020, an Mw=6.0 struck Costa Rica and 10 min after, Rincón de la Vieja
volcano located 165 km far from the epicenter, erupted. The previous days, the volcano was in unrest;
this can be a possible case of earthquake and volcano interaction.
6. ACKNOWLEDGEMENTS
This research was conducted during the individual study period of the training course “Seismology,
Earthquake Engineering and Tsunami Disaster Mitigation” by the Building Research Institute, JICA,
and GRIPS. I thank to Professors Eisuke Fujita, Bunichiro Shibazaki, Takumi Hayashida, Dmitri
Rouwet, Giovanni Chiodini and Joan Martí for the support and discussions. I also thank JICA for thefinancial support.
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