# An investigation into the remote triggering of the Oita earthquake by the 2016 Mw 7.0 Kumamoto earthquake using full wavefield simulation

- Masatoshi Miyazawa
^{1}Email authorView ORCID ID profile

**Received: **21 July 2016

**Accepted: **6 December 2016

**Published: **19 December 2016

## Abstract

### Keywords

2016 Kumamoto earthquake Remote triggering Coulomb failure stress change Wavefield simulation## Background

Recent seismic observations have revealed that a single earthquake sometimes comprises slip on multiple faults. The 2009 Mw 8.1 Samoa–Tonga earthquake consisted of multiple large events in the outer rise region and on the megathrust (Beavan et al. 2010; Lay et al. 2010). The 2011 Mw 7.1 Araucania earthquake consisted of two events: a Mw 6.8 thrust event followed 12 s later by a Mw 6.7 event with a normal faulting mechanism and 30 km shallower (Hicks and Rietbrock 2015). The 2011 Mw 6.6 Fukushima earthquake occurred on two subparallel normal faults, where the rupture propagated from one fault to the other (Tanaka et al. 2014). The 2012 M8.6 East Indian Ocean earthquake occurred on multiple planes in an orthogonal conjugate fault system (e.g., Yue et al. 2012). The 2012 Mw 7.3 Sanriku-Oki earthquake occurred in the outer rise region, where a shallower Mw 7.2 normal faulting event was preceded by an Mw 7.1 reverse faulting earthquake about 22 s beforehand (Harada et al. 2013). The slip on the secondary fault in each case seems to result from either static triggering processes driven by permanent fault displacements near the source region (Harada et al. 2013), dynamic triggering processes by transient stress perturbations due to the passage of large seismic waves (Hicks and Rietbrock 2015), or a combination of the two processes (Tanaka et al. 2014). In general, both static and dynamic stress transfers play important roles in triggering slip on the secondary fault plane when the plane is located within one rupture length of the initially ruptured fault.

*M*~6 earthquake in central Oita prefecture, 80 km northeast of the hypocenter of the Kumamoto earthquake. Hereafter, this triggered earthquake is referred to as the “Oita earthquake.” It is well known that in geothermal regions, crustal materials are more sensitive to stress perturbations, and earthquakes are more easily triggered (e.g., Hill and Prejean 2015). In the case of the 2011 Mw 9.0 Tohoku-Oki earthquake, a few small earthquakes were remotely triggered in this area by passing surface waves (Miyazawa 2011; Fukui et al. 2012). Because the Kumamoto and Oita earthquakes were monitored by a dense seismic network, they were able to be distinguished. A triggered earthquake can be identified from observed waveforms near its epicenter (Fig. 1), peak ground motion (PGA) distributions (Fig. 2), and seismicity (Fig. 3). Figure 1 shows that the onset of the Oita earthquake occurred about 34 s after the origin time of the Kumamoto earthquake. Figure 2 shows the distribution of raw three-component PGA values recorded by the K-NET and KiK-net strong-motion networks and thought to be from the Kumamoto earthquake. The PGA values are the maximum amplitudes of the vector acceleration from the three components for a 100-s time window from the origin of the Kumamoto earthquake. The map was generated by smoothing these PGA values. There are two areas of peak PGA values (Fig. 2a), one of which (central Oita prefecture) disappears if the PGA values are calculated for the period prior to the arrival of waves from the Oita earthquake (Fig. 2b); thus, the secondary peak is mainly from the triggered earthquake. The magnitude of the Oita earthquake was tentatively estimated at 5.7 by the Japan Meteorological Agency (JMA), but this value was not well constrained because of overlapping waves from the Kumamoto earthquake. Earthquakes local to central Oita prefecture following the triggered earthquake are described as its aftershocks. Figure 3 shows seismicity for 15 days before and 2 months after the Kumamoto and Oita earthquakes. The seismicity rate in Oita decreased markedly within 1 month, despite the local aftershocks. No

*M*≥ 2.5 earthquakes were observed during the next month.

The correlation between the triggering Kumamoto earthquake and the triggered Oita earthquake can be demonstrated by an integrated seismicity model (Miyazawa 2015), which statistically evaluates the time intervals between consecutive earthquakes. We modeled the seismicity using 30 shallow (depth ≤ 30 km) earthquakes with *M* ≥ 5.0 since 1923 in the area of Fig. 3a and using the integrated seismicity model (more specifically, a stationary Poisson model) under the null hypothesis of no seismicity interaction between the Kumamoto and Oita earthquakes. The estimated probability that at least one earthquake of *M* ≥ 5.0 occurs prior to the Oita earthquake and following the Kumamoto earthquake is only 3.3 × 10^{−5}%. This small value can reject the null hypothesis and statistically indicates that there may exist a causal relationship between the two consecutive events. Then, we need to investigate the physical process for this remote triggering.

It is noted that this two-earthquake sequence is the clearest known example of the remote triggering of a large (*M* > ~6) earthquake during the passage of seismic waves, whereas there were other examples reported previously (e.g., Lin 2012; Miyazawa 2015). The magnitudes of earthquakes triggered remotely by the passage of seismic waves are generally small (*M* < ~4) (e.g., Miyazawa et al. 2005; Miyazawa 2011; Peng et al. 2010; Yukutake et al. 2013). Thus, studying the Oita earthquake could advance our fundamental understanding of the triggering processes of large earthquakes.

## Location of the triggered Oita earthquake and estimation of its mechanism

Because the first arrivals of the Oita earthquake were masked by high-amplitude seismic waves, its hypocenter has not yet been precisely estimated. Therefore, we begin by determining the location and magnitude of the Oita earthquake. A hypocenter is obtained using the program hypomh (Hirata and Matsu’ura 1987), using seismograms from permanent K-NET and KiK-net stations (Fig. 3a) and the JMA2001 velocity model (Ueno et al. 2002). To calculate a local magnitude, we use the largest amplitude of the envelope of the vertical velocity waveform, excluding the amplitude immediately before the P arrival to avoid overestimation.

Parameters of the large, triggered Oita earthquake

Origin time | Longitude (error) | Latitude (error) | Depth (error) | Magnitude |
---|---|---|---|---|

April 16, 2016 01:25:38.0 (UTC+9) | 131.341°E (0.26) | 33.2653°N (0.28) | 8.47 km (0.42) | 5.9 |

A source model for the Oita earthquake is required to resolve temporal stress changes on the fault plane. However, such a source model is not available because of the overlapping waves from the Kumamoto earthquake. Even with the recorded displacements and waveforms at Yufuin, on the basis of a crude rupture size estimate from the magnitude, it is difficult to determine the mechanism and magnitude more precisely because the stations that clearly recorded the Oita earthquake were located very close to the rupture. Therefore, we can neither assume a double-couple source nor constrain the free parameters of the source fault.

The source mechanism of the largest aftershock of the Oita earthquake (M5.4/Mw 5.1, Fig. 3) and the displacements recorded at a global navigation satellite system (GNSS) site on the date of the Oita earthquake are helpful for this purpose. The centroid moment tensor (CMT) solution determined by JMA for the Mw 5.1 aftershock has strike, dip, and rake angles of N243°E, 68°, and −148°, respectively. We assume that the fault of the Oita earthquake strikes WSW–ENE, based on seismicity distributions and mapped fault segments in central Oita (National Institute of Advanced Industrial Science and Technology 2016). The horizontal and vertical displacements at the GNSS site, which is located 0.5 km from OIT009, show 4.2 cm easting, 2.5 cm northing, and 5.5 cm subsidence on April 16 (UTC+9) (Geospatial Information Authority of Japan 2016). The observed subsidence is mainly due to the Oita earthquake. The horizontal displacements are also probably due to this earthquake, but might be partly due to the Kumamoto earthquake. Taking these observations into account, we assume that the Oita earthquake has strike N240°E, dip 70°, and rake −140°.

## Triggering stress changes from the 2016 Kumamoto earthquake

We estimate the stress change in the Oita earthquake’s source region due to the Kumamoto earthquake. Previous studies of remote triggering have approached this problem either by forward techniques with simple layered models (e.g., Rubinstein et al. 2007; Hill 2012) or by inverse approaches using observed waveforms via transport kernels (e.g., Miyazawa and Brodsky 2008; Miyazawa 2015). However, both of those approaches model surface waves. In the present case, such approaches might be inapplicable because it is not clear whether body or surface wave phases triggered the Oita earthquake. To reproduce the observed waveforms and estimate the stress changes at depth, we use SEISM numerical modeling software for elastic wave simulation (e.g., Maeda and Furumura 2013; Maeda et al. 2013), with the Japan Integrated Velocity Structure Model (Koketsu et al. 2012) for the three-dimensional structure. This approach solves the equations of motion in three-dimensional Cartesian coordinates with viscoelastic constitutive equations, using a finite difference method to fourth order in space and second order in time. The spatial grid size is 0.5 km in the horizontal and vertical directions, and the time step is 0.025 s. For the source model of the Kumamoto earthquake, we use the JMA CMT solution (Fig. 3). The advantages of the numerical method include (1) time-dependent changes associated with the far-field and near-field terms are simultaneously considered, and (2) changes in the stress tensor at depth are directly available, even in a heterogeneous three-dimensional structure.

*μ*′ is assumed to be 0.4 and Δ

*τ*and Δ

*σ*

_{ n }are the shear stress change in the slip direction and the normal stress change on the fault plane (negative for compression), respectively. The Lamé parameters,

*λ*and

*μ*, are each set to 30 GPa.

Figure 5b shows the volumetric strain changes at the hypocenter, the values of which are independent of the uncertainties in the triggered source mechanism. The triggering strain change varies about from 4 × 10^{−7} to 7 × 10^{−7}, and the corresponding static strain change is about 1 × 10^{−7}. Because the Oita earthquake was not triggered by the preceding peak strains, which exceeded the strain at the origin time, it is inferred that the volumetric strain change was not the only important parameter in the triggering process.

## Discussion

Assuming that the source of the Oita earthquake is similar to that in the reference model and that the stress changes caused by the Mw 7.0 Kumamoto earthquake contributed to the occurrence of the Oita earthquake, the following scenario may describe the physical process of triggering. Frictional stress transiently increased by about 0.7 MPa because of the Kumamoto earthquake, about one order of magnitude less than the stress drop of a typical earthquake, but enough to exceed the frictional strength required to trigger an earthquake on the generating fault. The large transient stress change required for triggering may suggest that the background stress difference was relatively low. On the other hand, this fault was closer to failure than other faults in this region, because there were no triggered earthquakes on the other faults. Although the relationship between triggering stress and triggered event magnitude has been thoroughly investigated only for tectonic tremors (e.g., Miyazawa and Mori 2006; Miyazawa and Brodsky 2008), there have been case studies that suggest earthquakes of *M* > 4 can be triggered by large transient stress changes. For example, the 2011 Mw 9.0 Tohoku-Oki earthquake remotely and dynamically triggered *M* ~4 earthquakes at Hakone volcano, Japan, with triggering stresses of ~100 kPa, a location where no earthquake of *M* > 4.0 had been recorded since 1995 (Yukutake et al. 2011, 2013). In the present case, too, large stress changes on the fault are thought to have directly triggered the large earthquake. Parsons et al. (2012) used simulated wavefields to show that dynamic stress changes from surface waves rarely trigger *M* > 5 earthquakes and concluded that there is an inconsistency between target fault rake and imposed stress change direction and that the window in which the dynamic stress field change favors triggering is temporally short and spatially small. In the present case, because the rake of the imposed slip matched the rake of the triggered fault, and because the resolved triggering stress was sufficiently large, it might have been easy for a rupture to propagate in the favorable direction. Stress transfer from the Oita earthquake then triggered aftershocks to an extent, but seismicity abruptly returned to background levels within a month. Since aftershocks are in general triggered by stress changes caused by the mainshock, this may indicate that the static stress changes caused by the Oita earthquake could not have remarkably exceeded the triggering threshold with a low background stress difference. These observations suggest the following: (1) The fault of the Oita earthquake was not originally close to failure at the time of the Kumamoto earthquake, but the large transient stress changes from the Kumamoto earthquake triggered the Oita earthquake and/or (2) the apparent quiescence of aftershocks following the Oita earthquake is temporary, and eventually there will be significant seismicity.

## Conclusions

This study used a full wavefield simulation to investigate the triggering process of the M5.9 Oita earthquake, which was remotely triggered by passing seismic waves from the Mw 7.0 Kumamoto earthquake of April 16, 2016. At the hypocenter of the Oita earthquake, the change in Coulomb failure stress increased by as much as 0.7 MPa at the origin time and likely played an important role in triggering. Taking the scarcity of the aftershocks of the Oita earthquake into consideration, the generating fault might not have been close to failure before the Kumamoto earthquake; alternatively, there may eventually be significant seismicity.

## Declarations

### Acknowledgements

We used the seismicity catalog of the Japan Meteorological Agency (JMA). Seismic waveform data are from K-NET and KiK-net stations operated by the National Research Institute for Earth Science and Disaster Resilience (NIED), Japan. Plots were made using the Generic Mapping Tools (Wessel and Smith 1998). For data analysis, we used the computer systems of the Earthquake and Volcano Information Center of the Earthquake Research Institute (ERI), University of Tokyo, Japan. This study was partially supported by ERI under Joint Usage Research Project (B) 2015-B-01. We thank Dr. Hector Gonzalez-Huizar and an anonymous reviewer for careful and thoughtful reviews.

### Competing interests

The author declares that he has no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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