# Tsunami Source Inversion Using Tide Gauge and DART Tsunami Waveforms of the 2017 Mw8.2 Mexico Earthquake

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## Abstract

On September 8, 2017 (UTC), a normal-fault earthquake occurred 87 km off the southeast coast of Mexico. This earthquake generated a tsunami that was recorded at coastal tide gauge and offshore buoy stations. First, we conducted a numerical tsunami simulation using a single-fault model to understand the tsunami characteristics near the rupture area, focusing on the nearby tide gauge stations. Second, the tsunami source of this event was estimated from inversion of tsunami waveforms recorded at six coastal stations and three buoys located in the deep ocean. Using the aftershock distribution within 1 day following the main shock, the fault plane orientation had a northeast dip direction (strike \(= 320^{\circ }\), dip \(= 77^{\circ }\), and rake \(=-92^{\circ }\)). The results of the tsunami waveform inversion revealed that the fault area was 240 km × 90 km in size with most of the largest slip occurring on the middle and deepest segments of the fault. The maximum slip was 6.03 m from a 30 × 30 km^{2} segment that was 64.82 km deep at the center of the fault area. The estimated slip distribution showed that the main asperity was at the center of the fault area. The second asperity with an average slip of 5.5 m was found on the northwest-most segments. The estimated slip distribution yielded a seismic moment of \(2.9 \times 10^{21}\) Nm (Mw = 8.24), which was calculated assuming an average rigidity of \(7\times 10^{10}\) N/m^{2}.

## Keywords

2017 Mw8.2 Mexico earthquake tsunami source inversion tsunami numerical modeling## 1 Introduction

The earthquake triggered a tsunami that was reported by the Pacific Tsunami Warning Center (PTWC) with a maximum peak amplitude of 1.68 m at Puerto Chiapas in Mexico. The aftermath of this event, the ground shaking, left at least 98 people dead in Oaxaca, Chiapas and Tabasco. Previous studies have focused on the tsunami hazard risk on the Tehuantepec gap, and some of these researchs (Manea et al. 2017) have previously suggested that a magnitude Mw8.0 type earthquake could potentially occur in this area (Nishenko and Singh 1987). The rupture area of this event was located over the edge between the continental shelf and the continental slope, generating a complex bathymetry region for tsunami propagation.

## 2 Data

### 2.1 Tsunami Waveform Data

Geographical coordinates of the stations used in this study

Station | Latitude (°) | Longitude (°) | Agency |
---|---|---|---|

Lazaro | 17.9406 | − 102.1758 | IOC |

Puerto Angel | 15.6608 | − 96.4892 | IOC |

Huatulco | 15.7458 | − 96.1208 | IOC |

Salina Cruz | 16.1642 | − 95.1958 | IOC |

Chiapas | 14.7142 | − 92.4008 | IOC |

Acajutla | 13.5842 | − 89.8342 | IOC |

DART43413 | 10.8458 | − 100.1375 | NOAA |

DART32411 | 4.9958 | − 90.8542 | NOAA |

DART32413 | − 6.5875 | − 93.5208 | NOAA |

### 2.2 Bathymetry Data

In the computational domain, the employed bathymetry data are resampled from the 30 arcsec grid resolution of GEBCO 2014 DEM (Weatherall et al. 2015). Figure 2 shows the computational domain for the tsunami simulation. For the DART stations, which are located in a deep open ocean, the bathymetry resolution is set to 30 arcsec. At coastal tide stations, where the tsunami signals strongly depend on the interaction of the incoming tsunami waves with the surrounding coastline, we construct a nested grid system of 6 and 12 arcsec for the tsunami numerical simulation. The finest bathymetry resolution (6 arcsec) is for the coastal stations around the source area (Puerto Angel, Huatulco, Salina Cruz, and Chiapas). A 12 arcsec resolution is used for the Lazaro and Acajutla stations. Furthermore, the coastline around all coastal stations was manually digitized from the latest optical satellite image available from the Google Earth platform.

## 3 Methods

In this study, we first investigate the tsunami propagation features, focusing on the tsunami signals recorded at nearby tide gauge stations. For this purpose, we use a single-fault model to perform a nonlinear tsunami simulation. The fault geometry and location are set using the aftershock distribution within 1 day following the main shock and the backward propagation of tsunami travel computed from stations. Moreover, we also use the aftershock distribution to set the appropriate fault plane orientation from the earthquake’s focal mechanism. Second, we estimate the fault slip distribution through the tsunami waveform inversion of six coastal tide gauge stations and three deep-ocean-bottom pressure gauges (Fig. 2).

### 3.1 Tsunami Simulation Model

For the tsunami numerical simulation, we solve the shallow water equation using a finite difference method. A spherical coordinate system is used for wide tsunami propagation, and the planar UTM (Universal Transverse Mercator) system is used for local tsunami simulation. The core finite difference scheme is based on the TUNAMI (Tohoku University’s numerical analysis model for the investigation) code (Imamura 1996). The time step for the time domain in the nested bathymetry system is set to 0.6 s to satisfy the numerical stability condition. Details regarding the settings of the tsunami simulation based on nested bathymetry are available in (Adriano et al. 2016a). Using earthquake source parameters (strike, dip, rake, depth, slip, fault origin, and fault dimension), the initial condition for the tsunami simulation is calculated based on a rectangular fault model (Okada 1985). The time-dependent rupture is not considered. In addition, the vertical displacement due to the horizontal fault motions is added to the initial sea surface displacement (Tanioka and Satake 1996). The nonlinear tsunami simulation assumes a constant coefficient (0.025) for the bottom friction (Adriano et al. 2016a). The combination of dispersion and wave nonlinearity generates that the wave front of a tsunami propagating on a shallow bathymetry becomes steep (Baba et al. 2015). These nonlinear effects are not included in our simulation.

### 3.2 Early Tsunami Simulation

A tsunami response system implemented at the International Research Institute of Disaster Science, Tohoku University (initially developed in Peru (Adriano et al. 2011), for tsunami simulation is activated when a major tsunamigenic earthquake occurs. This system is based on linear tsunami modeling and a single rectangular fault model. The system is activated when a notification email from the US Geological Survey (USGS) is received after a tsunamigenic earthquake (\(Mw>7.0\)) occurs. This email contains the epicenter location, depth, and a preliminary earthquake magnitude. For calculating the initial sea surface displacement, the earthquake parameters strike, dip, and rake are searched in the Global Centroid Moment Tensor and W-phase solutions (GCMT) database. Our system chooses the closest GCMT solution to the epicenter. The fault dimension and slip amount are calculated using the magnitude and a scaling relation with respect to seismic moment (Papazachos et al. 2004). The preliminary tsunami response corresponds to the worst-case scenario from the results of simulating the two nodal planes of the chosen GCMT moment tensor solution. The initial report of the tsunami simulation of the earthquake that occurred on September 8 is available at http://www.regid.irides.tohoku.ac.jp/response/20170908_mexico_eq-en.html.

In our forward tsunami simulation, we assume the second GCMT nodal plane to construct the single-fault geometry. According to the estimated moment magnitude of the GCMT solution (Mw \(=8.2\)), the single-fault dimensions are 150 km × 40 km with a slip amount equal to 9.5 m (Papazachos et al. 2004). Considering that the centroid depth (50.2 km) and the hypocenter depth (58.0 km) are relatively close to each other, we use the centroid depth and the dip to set the top depth (30.7 km). After determining the earthquake parameters, we conduct a nonlinear tsunami simulation and analyze the tsunami propagation characteristics around the source region.

### 3.3 Inversion Methodology

*i*-th station from the

*j*-th subfault, x\(_j\) is the unknown slip on the

*j*-th subfault, and b\(_i\)(t) is the tide gauge record at the

*i*-th station (Satake 1987). Theoretically, each subfault patch behaves independently of the neighboring segments, providing a best fit to the Green’s function (Williamson et al. 2017). Thus, our inversion model does not include any smoothing factor for the slip calculation. In this study, there are nine stations used in the inversion analysis (\(i=9\)).

## 4 Results and Discussion

### 4.1 Tsunami Simulation from Single-Fault Model

The tsunami source area mainly concentrates at the boundary of the continental shelf and the continental slope; this fact is illustrated by the aftershock distribution (Fig. 3a). Furthermore, the associated coseismic deformation is primarily confined to a concave region formed by the headland from the Puerto Angel to Acajutla stations (Gulf of Tehuantepec) and the Mexican trench (between the longitudes 91°W and 97°W). This unique configuration generates singular characteristics on the tsunami propagation (Yamazaki and Cheung 2011) that directly influence the tsunami waveforms recorded at the surrounding tide gauge stations.

Another consequence of the bathymetry configuration of the tsunami source region is the observed arrival time at the Salina Cruz and Huatulco stations. Although the distance between the epicenter and the Salina station (∼ 190 km) is much smaller than the distance between the epicenter and the Puerto Angel station (∼ 270 km), the tsunami arrives early at the latter station. The tsunami signals recorded at these locations also illustrate this arrival time difference (Fig. 4b). This fact is due to bathymetry along the path from the epicenter to the stations; while the shallow bathymetry reduced the tsunami speed toward the Salina Cruz station, the speed of the tsunami wave propagating toward Huatulco and Puerto Angel is less affected in the deep continental slope. This arrival time difference cannot be observed at the stations south of the fault area (Chiapas and Acajutla). After the tsunami wave passes Puerto Angel, it propagates over the Mexican trench, following an almost northwest path. The deep bathymetry along the trench reduces and disperses the tsunami wave amplitude, creating a more extended wave period that was recorded at the Lazaro station. In our simulation, the tsunami waveform at the Lazaro station is not fully well resolved, showing a phase difference between the observed and the modeled waveforms. The location of the earthquake fault and the associated coseismic deformation may be the reason for this difference. Figure 4b shows the comparison of the computed and observed tsunami waveforms. In general, the single-fault model reproduced the observed tsunami waveforms reasonably well, particularly at stations near the source area. Conversely, the simulated waveform at the Acajutla station is slightly higher than the observed one.

### 4.2 Fault Slip Distribution

#### 4.2.1 Fault Geometry

Fault slip distribution of the 2017 Mw8.2 Mexico earthquake estimated from tsunami waveforms

No. | Latitude (°E) | Longitude (°W) | Depth (km) | Slip (m) | Error (±) |
---|---|---|---|---|---|

1 | 14.620 | 94.110 | 6.35 | 0.00 | 0.02 |

2 | 14.827 | 94.289 | 6.35 | 0.18 | 0.11 |

3 | 15.033 | 94.469 | 6.35 | 2.83 | 0.13 |

4 | 15.240 | 94.648 | 6.35 | 2.82 | 0.16 |

5 | 15.447 | 94.828 | 6.35 | 2.03 | 0.10 |

7 | 15.653 | 95.008 | 6.35 | 0.39 | 0.15 |

8 | 15.860 | 95.188 | 6.35 | 0.15 | 0.06 |

9 | 14.659 | 94.062 | 35.58 | 0.00 | 0.04 |

10 | 14.866 | 94.241 | 35.58 | 2.93 | 0.10 |

11 | 15.072 | 94.421 | 35.58 | 2.56 | 0.25 |

12 | 15.279 | 94.600 | 35.58 | 5.01 | 0.21 |

13 | 15.486 | 94.780 | 35.58 | 4.63 | 0.33 |

14 | 15.692 | 94.960 | 35.58 | 0.00 | 0.07 |

15 | 15.899 | 95.140 | 35.58 | 0.83 | 0.07 |

16 | 14.698 | 94.014 | 64.82 | 0.00 | 0.03 |

17 | 14.905 | 94.193 | 64.82 | 0.99 | 0.07 |

18 | 15.111 | 94.373 | 64.82 | 6.03 | 0.26 |

17 | 15.318 | 94.552 | 64.82 | 0.00 | 0.02 |

19 | 15.525 | 94.732 | 64.82 | 3.84 | 0.15 |

20 | 15.731 | 94.912 | 64.82 | 5.15 | 0.31 |

21 | 15.938 | 95.092 | 64.82 | 5.68 | 0.29 |

#### 4.2.2 Slip Distribution

Figure 5c shows the slip distribution estimated by inverting tsunami waveform records. Our inversion result shows a similar slip pattern as that published by the USGS (https://earthquake.usgs.gov/earthquakes/eventpage/us2000ahv0#finite-fault), which was calculated using teleseismic data based on the algorithm proposed by Ji et al. (2002). A particular difference among these source models is the maximum slip deformation which differs by about 4 m, with the USGS model having the largest slip on a shallower depth than our model. This suggests that the seismic inversion model generates larger seabed deformation than that shown by our tsunami waveform inversion results on sea surface deformation. The particularities on energy transfer from seabed to sea surface are of interest for future studies. To solve Eq. 1, we select 160 points from the recorded waveform data to build the vector \(b_i(t)\). From the estimated slip distribution, the associated seismic moment, assuming an average rigidity of \(7\times 10^{10}\) N/m^{2}, is \(2.9\times 10^{21}\) Nm, which is equivalent to a moment magnitude of \({\text{Mw}}=8.24\). Our result is slightly larger than the one estimated by GCMT (\(2.65\times 10^{21}\) Nm, Mw = 8.2). This small difference can be attributed to the slips of approximately 5 m that are determined near the coastline. In our calculations, these deepest subfaults show significant slip amounts to reproduce the tsunami waveform observed at Salina Cruz. Table 2 shows the standard error of the computed slip distribution. In general, for subfaults with the largest slip (> 5 m), the corresponding error is approximately ± 0.25 m, which is almost 5% of the slip amount.

The estimated slip distribution has the most significant slips around the center of the fault area (30 km northwest of the epicenter) with a maximum value of 6.03 m along the deepest subfaults (Fig. 5c, d). The inversion result also shows substantial slips in front of the Salina Cruz station. Two considerable slips of 5.01 m and 4.63 are located at the center of the fault area within the middle segments. The slip on the shallowest subfaults is approximately 2 m, also at the center of the fault plane. The resulting slip configuration indicates a large patch, which is mainly concentrated around the GCMT’s centroid and extends toward the Salina Cruz station. Figure 5d shows the computed seafloor deformation using the estimated fault slip distribution. Because of the normal faulting, similar to the single-fault model, the associated subsidence deformation faces the coastline and is contained mainly over the continental shelf. The absolute maximum displacements are 1.43 and 0.96 m at the lowest and highest points, respectively (Fig. 5d). Note that the uplift region is affected by the vertical deformation due to the horizontal motion of the fault mechanism, as shown by the red contour lines. This effect is not observed in the subsidence region because of the low slope of the ocean bottom (Tanioka and Satake 1996).

#### 4.2.3 Maximum Estimated Tsunami Height

## 5 Conclusions

The tsunami generated by a normal-fault Mw8.2 earthquake on September 8, 2017, was investigated using tsunami signals that were recorded at several coastal and deep ocean stations. A simple fault based on the GCMT solution (dimensions of 150 km × 40 km, slip \(= 9.5\) m, strike \(= 320^{\circ }\), dip \(= 77^{\circ }\), and rake \(=-92^{\circ }\)) satisfactorily explained the tsunami signal observed at the coastal tide stations near the tsunami source region. The single-fault model also showed that due to the location of the rupture area, the tsunami arrived approximately 10 min earlier at areas much farther from the epicenter, such as near the Puerto Angel station. Furthermore, the tsunami waves propagated toward the coastline over the continental shelf, delaying the arrival time at the Salina Cruz station, which is much closer to the epicenter. A cross-sectional analysis of the aftershock distribution supported the assumption of the northeast dip direction plane. This plane orientation was also adopted by the USGS model. The aftershock also revealed that the rupture extended northwest from the epicenter.

For our inversion analysis, a total of six tide gauge stations and three DART stations were used to compute the fault slip distribution. The estimated fault area was 240 km × 90 km in size (divided into 24 subfaults of 30 km × 30 km size). The maximum slip was 6.03 m from a 64.82 km deep segment, at the center of the fault area. The estimated slip distribution showed the main asperity at the centermost of the fault area, with maximum slips of 2.83 m and 2.93 m in the shallowest and middle segments, respectively. The second asperity with an average slip of 5.5 m was also found on the northwest-most subfaults, near the Salina Cruz station. The estimated slip distribution yielded a seismic moment of \(2.9\times 10^{21}\) Nm (assuming an average rigidity of \(7\times 10^{10}\) N/m^{2}), which was associated with a moment magnitude of Mw \(=8.24\). This result was slightly larger than the one published by GCMT (\(2.65 \times 10^{21}\) Nm). Our result, however, represents a reasonable estimation considering that only tsunami data were employed. The coseismic deformation associated with our slip distribution produced a seafloor subsidence, in the lowest point, of 1.43 m and a maximum uplift of 0.96 m. Using the estimated seafloor displacement, we calculated the maximum tsunami height along the coastline. We ran 3 h of nonlinear tsunami propagation. We found that a significant portion of the tsunami energy was kept between the source area and the headlands. This phenomenon generated tsunami amplitudes up to 4 m in areas approximately 100 km east of the Salina Cruz station. The propagation nature was mainly due to the bathymetry configuration of the rupture area.

## Notes

### Acknowledgements

The tide gauge and DART data were downloaded from the Sea Level Station Monitoring Facility website and the NOAA Center for Tsunami Research website, respectively. The pre-processing of the waveform data and construction of all figures in this paper were performed using the Generic Mapping Tools (Wessel et al. 2013). This research was supported by the Japan Society for the Promotion of Science (JSPS) under the project: Fusion of Real-time Simulation and Remote Sensing for Tsunami Damage Estimation to Latin America (JSPS-Grant: P16055) and the JST/JICA, SATREPS (Science and Technology Research Partnership for Sustainable Development) Mexico Project.

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