2017American Geophysical Union Poster Session

Proposal of a method for evaluating tsunami risk
using response-surface methodology
122
2
Yo Fukutani , Shuji Moriguchi , Takuma Kotani , Kenjiro Terada
1 Civil Engineering Department, College of Engineering and Science, Kanto Gakuin University (E-mail: fukutani@kanto-gakuin.ac.jp)
2 Regional Safety Engineering, International Research Institute of Disaster Science, Tohoku University

Abstract
Information on probabilistic tsunami inundation hazards is needed to define and evaluate tsunami risk . Several methods for calculating these hazards have been
proposed (e.g. Løvholt et al. (2012), Thio (2012), Fukutani et al. (2014), Goda et al. (2014)) . However, these methods are inefficient, and their calculation cost is high,since they require multiple tsunami numerical simulations, therefore lacking versatility.
In this study, we proposed a simpler method for tsunami risk evaluation using response-surface methodology. Kotani et al. (2016) proposed an evaluation
method for the probabilistic distribution of tsunami wave-height using a response-surface methodology. We expanded their study and developed a probabilistic
distribution of tsunami inundation depth. We set the slip (x1) and the depth (x2) of the Sagami trough earthquake fault as explanatory variables and tsunami
inundation depth (Y) as an object variable. We implemented a regression analysis based on the results of 25 tsunami numerical calculations for on the coast ofTokyo Bay and developed a response-surface, which was defined as Y(x1, x2) = 6.744*x1 + 0.069* x1*x2 – 2.025*x1 *x1 – 3.210. Based on the analyses, We
clarified that the expected damage probability of the steel building located in the target area is 49.6%, assuming that an earthquake occurs.

① A target source and a study area

② Response surface for the target point

We used the Sagami trough earthquake (Mw 8.5) as a tsunami source, which was As the result of regression analysis, the following response surface was selected.
published by the study meeting for the Tokyo Inland Earthquakes of the Cabinet
Y (x1,x2) = 6.744*x1 + 0.069*x1*x2 – 2.025*x2*x2 – 3.210
Office in Japan (2013) (see Fig.1(a)). The target point for the tsunami risk Figure. 3 (a) shows the simulation results (Blue point) and the response surface
assessment in this study is located in the Hakkei-jima island, Yokohama-city, (Red area). The developed response surface can explain the simulation results well.
Kanagawa prefecture (see the red points in Fig.1 (a) and (b)). The Hakkei-jima Then, we conducted monte-carlo simulation using the surface considering
island is a welfare facility of the Yokohama City Port Plan. Hakkeijima Sea uncertainty of slip and depth of the earthquake (see Table.2). Figure. 3 shows theParadise, Yacht Harbor are in the place and it is a place for relaxation for the histograms of tsunami inundation height as the results of mote-carlo simulation.
citizens in Yokohama city.
Slip rate

Target point（T.P. +0.2m）

(a)

(b)

(b)

N=10000

Frequency

Hakkeijima, Yokohama-city
Tsunami inundation depth (m)The Sagami trough earthquake

Fault depth (km)(a)

： Tsunami numerical
Calculation results

Tsunami inundation depth (m)Figure.3 (a) The simulation results (Blue point) and the response surface (Red area)(b) The histograms of tsunami inundation height

Figure.1 (a) The source area of the Sagami trough earthquake (Mw 8.5)(b) Target point for tsunami risk assessment

Using the fault parameters of the Sagami trough earthquake, we calculated theTable.2 Uncertainty of slip rate and fault depth
initial displacement of tsunami by Okada’s equation (see Fig.2(a)) and simulated
Variables
AverageStandarddeviation
P.D.F
Reasonforthevariation
tsunami wave by non-linear long wave equation (TUNAMI model by TohokuTheNuclearCivil
Engineering
University in Japan). Figure.2 (b) shows that max tsunami wave height around
Committee, Japan Society of Civil
coastal area of Kanto-region in Japan.
Engineers (2016) indicated that there
Normalcan be a variability of ±0.1 Mw
1.00
0.10
Table.1 shows the tsunami inundation depths simulated from tsunami numerical Slip rate
Distribution considering same fault area. In thissimulations for the target point. Tsunami numerical simulation was conducted withcase, a variation range of slip is from0.7 times to 1.4 times.
changing slip rate and fault depth. The slip were changed from 0.8 times to 1.2
This variability was calculated based ontimes. The fault depth were changed from -1.0 km to +2.0 km.
Fault depth
0.12(log average)
[km]

6.1m

0.65

(log standarddeviation)

Log normal the observation errors of fault depths,
which are listed in the seismic source
Distribution list of JMA (Data period: 2016/102017/10)

-2.8m

(a)

(b)

Figure.2 (a) Initial displacement of tsunami estimated from Okada’s equation(b) Max water height simulated by non-linear long wave equation

Next, we estimated the histograms of damage probability of steel building (seeFig.4 (a)) by using the tsunami inundation deptns generated from monte-carlo
method. In evaluation of the damage probability, we used the fragility curve ofsteel building developed by Suppasri et al.(2013). Finally, we can evaluate
exceedance probability of damage probability when the Sagami trough earthquake
occur (see Fig.4 (b)). From this results, we can estimate the expected value and thepercentile value of damage probability (49.6%) , although it is conditional.

(a)

Table.1 The tsunami inundation depths from tsunami numerical simulations+ 0.5 km

0 km

- 0.5 km- 1.0 km

1.2 times

2.05 m2.01 m1.97 m

1.94 m1.90 m

1.1 times

1.87 m1.85 m1.81 m1.78 m1.73 m

1.0 times

1.58 m1.55 m

1.48 m1.44 m1.39 m

0.9 times

1.28 m1.25 m1.23 m1.20 m1.15 m

0.8 times

0.99 m

0.99 m0.97 m

0.94 m

0.91 mWe conducted regression analyses using below equation and developed a response
surface for tsunami inundation depth.

Y (x1,x2) = a*x1 + b*x2 + c*x1*x2 + d*x1*x1 + e*x2*x2 + f
x1: Slip rate of the earthquake, x2: Depth of the earthquake
Reference

N=10000
Frequency+1.0 km1

Exceedance probability

Max
Tsunamiheight (m)

(b)

0.9

Min. 0.4%

0.8
0.7
0.6
0.5

50 percentile

0.4
0.3

Max. 76.2%

52.5%

0.2
0.1

95 percentile00%

Damage probability

10%

20%

30%

40%

50%

60%

70%

80%

Damage probability 67.9%

Figure.4 (a) Initial displacement height of tsunami estimated from Okada’s equation(b) Max water tsunami height simulated by non-linear long wave equation③ SummaryTakuma KOTANI, Shinsuke TAKASE, Shuji MORIGUCHI, Kenjiro TERADA, Yo FUKUTANI, We proposed tsunami risk evaluation using response-surface methodology. TheYu OTAKE, Kazuya NOJIMA, Masaaki SAKURABA (2016), Numerical-Analysis-Aided
proposed method is a useful and simple way to evaluate tsunami risk using a
Probabilistic Tsunami Hazard Evaluation Using Response Surface, Journal of Japan Society ofresponse-surface without conducting multiple tsunami numerical simulations.
Civil Engineers, Ser. A2 (Applied Mechanics (AM)), Vol. 72 (1), pp.58-69. (in Japanese)