Citation:Pulido, G., S. Koshimura (2021), Developing tsunami fragility functions using numericalmodeling and remote sensing data from the 2010 Chile tsunami, Synopsis of IISEE-GRIPS Master’sThesis.

DEVELOPING TSUNAMIFRAGILITY FUNCTIONS USING NUMERICAL
MODELING AND REMOTE SENSING DATA FROM
THE 2010 CHILE TSUNAMI
Geronimo Pulido I1,2

Supervisor: Shunichi KOSHIMURA3
ABSTRACTOn February 27, 2010, a megathrust earthquake of Mw 8.8 (USGS) provoked a destructive tsunami inChile. The tsunami damaged about 600 km area along the coast of Chile, including the coastal towns ofDichato and Tumbes in the Bio-Bio region and Robinson Crusoe Island on the archipelago of JuanFernandez, about 670 km off the coast of Chile. To estimate the structural damage in a quantitative
manner for the areas mentioned, tsunami fragility functions were developed. Using Tohoku University's
Numerical Analysis Model for Investigation of Near-field tsunamis (TUNAMI) for the numericalsimulation to obtain the propagation and inundation depths and visual inspection of satellite images forthe damage data, the fragility curves for Juan Fernandez, Tumbes, and Dichato were constructed. The
obtained curves suggest that for an inundation depth of one meter, the damage probability is 7%, 48%,and 82% for Tumbes, Dichato, and Juan Fernandez, respectively. The similarity of the construction type(wood, masonry, and mixed) indicates that the areas' exposure and building configuration has the mostsignificant impact on the structural damage, considering that Juan Fernandez island was not affected by
the ground motion of the 2010 event.
Keywords: Tsunami, Fragility function, 2010 Maule Earthquake, Chile.
1. INTRODUCTION
Chile is a country that is constantly affected by catastrophic events such as earthquakes and tsunamis.
On February 27, 2010, local time 3:34:08 AM, an earthquake of Mw 8.8 (USGS) attacked the Mauleregion, becoming the second-largest event in the country's history following the great earthquake ofValdivia in 1960, the largest event in our country's history. The 2010 earthquake affected most of thecountry's central zone, where an estimated 13 million people lived at that time. After this event, many
vulnerabilities were exposed, and the need for new and better mitigation measures against tsunamis
became evident. To assess the structural damage, fatality, or vulnerability due to a tsunami attack,Koshimura et al. (2009) proposed tsunami fragility functions as a tool to quantify the damage probability
by constructing them from the integration of satellite remote sensing, field surveys, and numericalmodeling with geographic information system (GIS). In this work, fragility curves are developed for thethree cities, Dichato, Tumbes, and Juan Fernández, affected by the 2010 tsunami using remote sensing
and satellite images for the damage interpretation and numerical modeling to obtain the hydrodynamic
features of the tsunami.
2. DATA
1

Chilean Association of Port and Coastal Engineering (ACHIPYC), Chile.
IISEE-GRIPS Master’s course student.
3
Professor, International Research Institute of Disaster Science (IRIDeS), Tohoku Univ.
212.1. Bathymetry and topography data
For the present work, four-nested grid systems (Figures 1 and 2) were generated for the numericalmodeling using GEBCO's 2021 15 arc-second gridded bathymetric data (GEBCO Compilation Group,2021), bathymetric probes data associated with the Hydrographic and Oceanographic Service of theNavy (SHOA) nautical charts No. 5411, 6000, 6110, and 6120, and LIDAR bathymetric surveys data
provided by Rafael Aránguiz Associate Professor of Universidad Católica de la Ssma Concepción (BioBio region). To characterize the inundation, we used the land elevation one arc-second grid mesh datafrom the Shuttle Radar Topography Mission (SRTM), a topographic survey conducted by the Ministryof National Property of Chile, and LIDAR topographic surveys merged with the bathymetry data for thehighest resolution grids.

Figure 1. Model setting of nested computational grids for Juan Fernández.

Figure 2. Model setting of nested computational grids for Bio-Bio region. The finest grids 4a and 4b
correspond to Dichato and Tumbes, respectively.

22.2. Damage data collection
The Chilean Air Force (SAF) has sets of aerial photographs before and after the day of the tsunami
impact at a scale of 1:10,000. The identification of the destroyed houses for Juan Fernández Island wasmade by comparing frame No. 55409 dated 21-01-2009 with frames No. 324454 to 324457 dated 2802-2010. For the Bio-Bio region, high-resolution satellite images dated 03-06-2010 were obtained fromthe web site (http://www.digitalglobe.com) and compared with Google Earth satellite images of 09-102009.
3. METHODOLOGY
3.1. Building structure damage data set
The interpretation and classification of the structures affected by the tsunami were carried out visually
by inspecting high-resolution satellite images before and after the tsunami. The high resolution of theimages is critical to distinguish the degree of damage of the structure only through the state of the roofs.
This method has the advantage of allowing us to visually understand structural damage and its extent ona regional scale. To obtain a damage statistic set, the structures are spatially sampled in the calculated
inundation zone and sorted by inundation ranges. With the number of structures for each inundation
range and the number of wash-away/destroyed buildings, we can determine the damage probability
associated with each inundation group.
3.2. Tsunami simulation
In this study, the numerical modeling was carried out using the TUNAMI code, the version compiled
by Yanagisawa (2021). This software is a tsunami numerical simulation program that uses the linear
wave theory for deep-sea and the shallow wave theory for simulation near the coast. The program runs
with bathymetry/topography data and fault parameters as input, and outputs several sea states at different
times and locations.
The slip distribution inverted from DART, tide gauge, GPS, and coastal geodetic data byYoshimoto et al. (2016) was used. In this model, 44 subfaults (11 x 4) were assumed with the subfault
areas of 50 km x 50 km and 50 km x 25 km for the shallowest ones, the rake and strike angles were setto 16° and 105°, respectively, the depth-dependent dip angles of 10°, 18° and 24° were set from thetrench towards downdip, and the depths of the subfaults ranged from 0 to 28.4 km in the down-dip
direction.
3.3. Tsunami fragility
It is defined as the structural damage probability related to the hydrodynamic features of the tsunami
flow. Developing the fragility functions, we used the same approach that researchers in the tsunami risk
assessment field took from the earthquake engineering studies of risk analysis to construct the tsunami
fragility curves. In those studies, the fragility functions are defined by the following Eq. (1) or Eq. (2);
𝑃 𝑥

𝑃 𝑥

ɸln 𝑥 𝜆𝜉

√2𝜋𝜉𝑡𝑥1ɸ𝜇𝜎

1√2𝜋𝜎𝑒𝑥𝑝

𝑒𝑥𝑝

𝑙𝑛𝑡 𝜆
2𝜉𝑡𝜇2𝜎𝑑𝑡

𝑑𝑡

(1)

(2)

, where PD(x) is the damage probability, ɸ the standardized lognormal or normal cumulative distributionfunction, λ (or μ) is the mean of ln x (or x), and ξ (or σ) is the standard deviation of ln x (or x).

3

Once we compile the set of damage probability data related to its hydrodynamic feature
obtained from the inundation model, we plot them versus ln x or x from Eq. (1) or (2) and invert the ɸfunction by applying the least-square fitting to the plot. We can obtain the mean and the standard
deviation from these plots and finally construct the fragility function.
4. RESULTS AND DISCUSSION
The slip distribution by Yoshimoto et al. (2016), which was obtained using only the tsunami waveformrecords at 26 DARTs reproduces a better agreement with inundation areas and depths at the study sites(Figure 3). The tsunami travel times in the model are similar to those reported on February 27 (Fritz etal., 2011), reaching to the Juan Fernández bay in approximately 49 minutes.

Figure 3. Tsunami maximum inundation depths obtained from the source model (Yoshimoto et al.,2016) inverted from DART data at (a) Juan Fernandez, (b) Dichato, and (c) Tumbes.
Once the tsunami hazard estimation was obtained, we spatially related the damage data
determined by comparing the before and after images of the study sites and compiled the damage
probability data related to its hydrodynamic feature, inundation depth in this study (Figure 4).

Figure 4. Histograms of the numbers of washed-away and survived structures in terms of inundation
depth ranges within the tsunami inundation zones at (a) Juan Fernández, (b) Dichato, and (c) Tumbes.

4Following the steps mentioned in the section 3, the damage probabilities were obtained forthe median values of inundation depths. Through a linear regression analysis, the relation between thesedamage probabilities and the inundation depths were explored. Plotting ln x from Eq. (1) and the ɸ-1function, we obtained the statistical parameters (Table 1) to construct the fragility functions.
Table 1. Statistical parameters of tsunami fragility curves.
SiteStandard deviation ξMean λJuan Fernández
DichatoTumbes

0.49380.27380.8445-0.3399
0.3862
1.0586

Eq. (1) and Eq. (2) are expressed in terms of the standard lognormal or normal cumulative
distribution functions, respectively. The selection of which distribution to apply depends on the best
fitting of the constructed curve and the data set. The fragility functions for Juan Fernández and Dichatowere created using the lognormal distribution and the normal cumulative function for Tumbes, whichshows a better agreement with the data obtained. The fragility functions obtained for the different areas
with the respective damage probability distributions are shown in Figure 5.

Figure 5. Fragility functions for structural damage in terms of the inundation depth at (a)Juan Fernandez, (b) Dichato, and (c) Tumbes.
Figure 6 compares the fragility functions
obtained by combining the Tumbes and Dichato's data
against the one from Juan Fernández. Since Juan Fernández
Island is located at 670 km apart from the coast of Chile, theisland was not suffered from the effects of the strong groundmotion, and the observed structural damage is only due tothe action of the tsunami. As the study sites consist of asimilar construction type (wood, masonry, and the mixedtype), the factors that possibly contributed to the moresignificant destruction in Juan Fernández can be related tothe inundation flow velocity, which is directly influenced by
the building distribution. In Juan Fernández, the town center
is located within 200 meters from the coastline, where thehorizontal
inundation distance was up to 300 meters in someFigure 6. Fragility functions at Juanplaces,andthe building density is very low compared withFernández (red symbols and line) andthe other study sites. Consequently, the tsunami flow reaches
Tumbes + Dichato (green ones).
greater velocities because it does not have obstacles thatslow down the flow and therefore causes more significant damage to the structures. The differences5between the two fragility functions can be clearly seen. For example, damage probabilities at two metersof inundation depth are 39% and 94% for the combined sites (Tumbes and Dichato) and Juan Fernández
alone, respectively.
5. CONCLUSIONS
Tsunami fragility functions were developed to quantify the damage probability of structures within an
exposed area from a tsunami attack. Using numerical tsunami modeling and high-resolution satellite
images of before and after the event, the tsunami fragility functions for the 2010 Maule earthquake andtsunami in terms of the inundation depth were constructed for Dichato and Tumbes in the Bio-Bio region
and Juan Fernandez Island. Two levels ("survived" and "destroyed") for classification of structural
damage were used. The numerical modeling results spatially referenced were compared with fieldsurvey measurements to obtain some grade of validation of the calculations. In the case of Tumbes andJuan Fernandez, the field survey measurement data were few, so the overall correlation may not be
reliable even if most of the survey points show less than one meter of difference from the calculations.
At Dichato, on the other hand, the numerical modeling presents a correlation of about 60% with the fieldsurvey measurements. This difference may be explained by the resolution of the topography andbathymetry data, the approximation of building structure type, and the overall exposure of the city.
A comparison between the tsunami fragility functions of earthquake-affected (Tumbes andDichato) and non-earthquake-affected areas (Juan Fernandez) was proposed to identify possible
influence factors in the damage probability. The latter shows the higher damage probability for the lower
inundation depths, i.e., 79% of damage probability for one meter of inundation depth, pointing that even
if the strong motion previously degraded the buildings of the areas affected by earthquakes, local effects
like building distribution and exposure have significant impacts to the tsunami damage probability
estimation. Many other factors not mentioned in this study may dramatically impact the analysis of thedamage probability, so the tsunami fragility functions should be taken as one piece of a toolkit for acomprehensive tsunami hazard estimation.
ACKNOWLEDGEMENTS
This research was conducted as the individual study of the training course “Seismology, Earthquake
Engineering and Tsunami Disaster Mitigation” by IISEE/BRI, JICA, and GRIPS. The author would liketo thank the supervisors of this work, Dr. Shunichi Koshimura, Professor, International ResearchInstitute of Disaster Science (IRIDeS) of Tohoku University; Dr. Erick Mas, Associate Professor,IRIDeS of Tohoku University; and Dr. Yushiro Fujii, senior research scientist, IISEE, BRI, for all theguidance and advice through this work.
REFERENCES
Fritz, H.M., Petroff, C.M., Catalán, P.A. et al. (2011). Field Survey of the 27 February 2010 ChileTsunami. Pure Appl. Geophys. 168, 1989–2010. https://doi.org/10.1007/s00024-011-0283-5.
GEBCO Compilation Group (2021) GEBCO 2021 Grid (doi:10.5285/c6612cbe-50b3-0cff-e0536c86abc09f8f).
Koshimura, S., Namegaya, Y., & Yanagisawa, H. (2009). Tsunami Fragility-A New Measure to Identify
Tsunami Damage.
Yanagisawa, H. (2021). Numerical simulation of Tsunami inundation and its application [Code].
Retrieved from IISEE Lectures notes, Disaster Management Program 2020-2021.
Yoshimoto, M., Watada, S., Fujii, Y., & Satake, K. (2016). Geophysical Research Letters, 43(2), 659–665. https://doi.org/10.1002/2015GL067181.

6