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A Long Source Area of the 1906 Colombia–Ecuador Earthquake Estimated from Observed Tsunami Waveforms Yusuke Yamanaka1*, Yuichiro Tanioka2 and Takahiro Shiina2

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A Long Source Area of the 1906 Colombia–Ecuador Earthquake Estimated from Observed Tsunami Waveforms Yusuke Yamanaka1*, Yuichiro Tanioka2 and Takahiro Shiina2 Yamanaka et al. Earth, Planets and Space (2017) 69:163 https://doi.org/10.1186/s40623-017-0750-z EXPRESS LETTER Open Access A long source area of the 1906 Colombia–Ecuador earthquake estimated from observed tsunami waveforms Yusuke Yamanaka1*, Yuichiro Tanioka2 and Takahiro Shiina2 Abstract The 1906 Colombia–Ecuador earthquake induced both strong seismic motions and a tsunami, the most destruc‑ tive earthquake in the history of the Colombia–Ecuador subduction zone. The tsunami propagated across the Pacifc Ocean, and its waveforms were observed at tide gauge stations in countries including Panama, Japan, and the USA. This study conducted slip inverse analysis for the 1906 earthquake using these waveforms. A digital dataset of observed tsunami waveforms at the Naos Island (Panama) and Honolulu (USA) tide gauge stations, where the tsunami was clearly observed, was frst produced by consulting documents. Next, the two waveforms were applied in an inverse analysis as the target waveform. The results of this analysis indicated that the moment magnitude of the 1906 earthquake ranged from 8.3 to 8.6. Moreover, the dominant slip occurred in the northern part of the assumed source region near the coast of Colombia, where little signifcant seismicity has occurred, rather than in the southern part. The results also indicated that the source area, with signifcant slip, covered a long distance, including the southern, central, and northern parts of the region. Keywords: 1906 Colombia–Ecuador earthquake, Slip distribution, Inverse analysis, Tsunami waveforms Introduction Inverse analysis of an earthquake slip distribution Te Colombia–Ecuador subduction zone is one of many using observed tsunami waveforms has sometimes been active global subduction zones from which large earth- conducted in cases where an earthquake triggered a tsu- quakes can be generated. Past earthquakes with moment nami (Tanioka et al. 2004). Because the 1906 earthquake magnitudes (Mw) of more than 7.0 occurred in this induced not only strong seismic motion around the region in 1906, 1942, 1958, 1979, and 2016 (Duda 1965; source region, but also a tsunami, sea surface fuctuations Kanamori 1977; Mendoza and Dewey 1984; Sennson and were observed by local eyewitnesses and by tide gages in Beck 1996; Ye et al. 2016; Heidarzadeh et al. 2017). Te some countries that faced the Pacifc Ocean (Honda et al. earthquake properties of these events have been investi- 1908; Soloviev and Go 1975). Source models for the 1906 gated by many previous studies; the most destructive (or earthquake have been assumed/estimated by recent stud- largest) earthquake is considered to be the 1906 event, ies (Mayorga and Sánchez 2016; Yoshimoto et al. 2017). which had a magnitude greater than 8.0 (Gutenberg In particular, a nonuniform slip distribution of the earth- and Richter 1954; Scholz and Campos 2012). However, quake was estimated by Yoshimoto et al. (2017), who estimation of the detailed source process was limited conducted a slip inverse analysis using some tsunami because there were few quantitative datasets to specify it. waveforms observed at tide gauge stations. However, they excluded the tsunami waveforms observed at Naos Island (Panama) from their analysis, even though the tsu- nami was clearly observed there. Te waveforms of Naos *Correspondence: [email protected]‑tokyo.ac.jp Island, located close to the source region, should be cor- 1 Department of Civil Engineering, The University of Tokyo, 7‑3‑1, Hongo, rectly considered in the inverse analysis because more Bunkyo‑ku, Tokyo 113‑8656, Japan Full list of author information is available at the end of the article benefcial information should be contained in waveforms © The Author(s) 2017. 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. Yamanaka et al. Earth, Planets and Space (2017) 69:163 Page 2 of 11 obtained nearer to the observation site. Furthermore, because the observed tsunami height at Honolulu was although their source model was able to reproduce the signifcantly smaller than that at Naos Island. tsunami waveforms observed in Honolulu (USA), the The earthquake was first assumed to consist of consistency of the model with previous studies had not 45 subfault zones (each with a length and width of been confrmed. 50 km) that covered the entire source area, as sug- Terefore, the primary objective of this study was to gested by Kelleher (1972) (Fig. 1). Strike/dip angles estimate the slip distribution of the 1906 Colombia– and the depth of each subfault were assumed based on Ecuador earthquake more accurately using the tsunami slab depths and their coordinates (Bird 2003; Hayes waveform data observed at appropriate tide gage stations et al. 2012). A rake angle was assumed and fixed for and to compare this analysis with the results of previous all subfaults based on a subducting angle to the trench studies including Yoshimoto et al. (2017) and the seismic (Chlieh et al. 2014). The vertical displacement of the history of the Ecuador–Colombia subduction zone. ocean floor due to each subfault was first estimated based on Okada (1985), and sea surface deformation Data and methods was assumed to be equal to that displacement. Fur- Some tide gauge records, including tsunami fuctua- thermore, the effect of horizontal displacement within tions, were obtained from sites near and far from the the bathymetry on the sea surface deformation was source region, such as in Panama, Japan, and the USA. considered based on Tanioka and Satake (1996) using For example, tide gauge stations at Honolulu captured computation bathymetry data with a 90 arc-s spatial the tsunami with heights of several tens of centimeters resolution obtained by resampling the General Bathy- (National Geophysical Data Center/World Data Ser- metric Chart of the Oceans data with a 30 arc-s reso- vice). However, the details of the tsunami arrival and lution (Smith and Sandwell 1997; Becker et al. 2009). fuctuations at some of these tide gauge stations were The propagation of each sea surface deformation gen- not clearly visible because chaotic waveforms with noise erated by each subfault was then simulated with a time comparable to the observed wave height were mixed step of 5 s to specify the tsunami waveforms at each into the observed waveforms. Tus, we decided to use tide gauge station. The occurrence time of the earth- only the tide gauge data from Honolulu and Naos Island quake was assumed to be 15:30 (UTC) on January 31, (Fig. 1), where the tsunami was clearly visible in the data, 1906, based on Soloviev and Go (1975), and the rup- as transcribed by Honda et al. (1908) and Soloviev and ture/rise times of the earthquake were not taken into Go (1975). consideration. For the Honolulu and Naos Island sta- First, these tsunami waveforms were estimated from tions, the propagation computations were conducted the brightness matrix of images obtained through the based on the linear long wave model, which considers digitization and pixelization of the documents of Honda no dispersion, and the linear Boussinesq model, which et al. (1908) and Soloviev and Go (1975). Te time reso- considers high frequency dispersion. Both the high lutions of the estimated data from Honolulu and Naos and the low frequency dispersion effects are expected Island were expected to be 1.9 and 1.6 min, respectively, to significantly influence the waveforms at Honolulu. and height resolutions were expected to be 0.8 and Thus, all dispersion effects are introduced into the 1.5 cm, respectively, in view of the relationship between waveforms simulated by the linear long wave model the data scale and pixel resolution of the matrix. Time based on the phase correction method developed by series datasets with an interval of 0.5 min were made Watada et al. (2014). In contrast, only the high fre- based on the estimated data. Fourier analysis with a band quency dispersion effect is expected to influence the pass flter of 10–120 min was applied to the datasets at waveforms of Naos Island with respect to distance both stations to estimate the water surface elevation relations. Furthermore, although the phase collection change due to the tsunami. Te waveforms estimated method can yield all dispersion effects, some assump- through the above process were then determined to be tions are required, such as propagation distance. the observed waveforms of the tsunami. Therefore, the linear Boussinesq model is more suit- Te inverse analysis of this study estimated the con- able and useful than the phase collection method for strained slip distribution in space using a smoothing fac- estimating the waveforms of Naos Island. The govern- tor, as described in Tanioka et al. (2004). Te intensity ing equations for the propagation computations are as of the smoothing factor for the analysis was determined follows (Goto 1991): with a trial-and-error step. Furthermore, the weight ∂η 1 ∂ ∂N + M cos + = 0 (1) coefcients between the data at the Honolulu and Naos ∂t R cos ∂ ∂θ Island stations were set to 1.5 and 1 for the analysis Yamanaka et al. Earth, Planets and Space (2017) 69:163 Page 3 of 11 3 2 ∂M gh ∂η 1 ∂ h h 1 2 2 + =−fN + F1 + F2 ∂ ∂ v 3 2 F1 = (u cos ) + (4) ∂t R ∂ R ∂ R cos ∂t∂ ∂t∂θ 2 ∂h h (2) − F1 + hF2 1 ∂ 2 ∂ ∂h ∂ ∂h F2 = u cos + v (5) R cos ∂t ∂ ∂t ∂θ ∂N gh ∂η 1 ∂ h3 h2 + = fM + F1 + F2 where η is the water surface elevation, M (= uh) and ∂t R cos ∂θ R cos ∂θ 3 2 N (= vh) are the fux in the λ and θ directions, u and v ∂h h2 are the velocity in the λ and θ directions, h is the still − F1 + hF2 ∂θ 2 (3) water depth, g is the acceleration due to gravity, R is the radius of the Earth, f is the Coriolis parameter, λ is the Fig.
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