2017American Geophysical Union Poster Session Probosal of a method for evaluating tsunami risk ustnd response-surface methodology Yo Fukułani', Shuti Mortguchi², Takuma Kołani², Kentro Terada’ " Civi Engineering Department, Colege of Engineering and Science, Kano Gakuin Un versity  E-mail okuan@kano-gakuin.ac.p) ² Regional Safety Engineering, International Research Institute of Disaster Science, Tohoku University ADStract Information on probabilistic tsunami inundation hazards is needed to define and evaluate tsunami riak . 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 bigh. 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 isunami wave-height using a response-surface methodology. We expanded their study and developed a probahilistic distribution of isunami inundation depth. We set the slip (x/) and the de th (x2) of the Sagami frough  carthquake fault as explanatory variables and tsunami inundation depth (¥) as an object variable. We implemented a regression analysis based on the results of 25 tsunami numerical calculations for on the coast of 'lokyo Bay and developed a response-surface, which was defined as ¥(x1, x2) = 6.744*x1 + 0.069* x/*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 Sagam trough earthquake (Mw 8.5) as a tsunami source, which was  As the result of regression analysis. the following response surface was sclected. 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 the Paradise, 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. 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 the initial displacement of tsunami by Okada’s equation  (see Fig.2(a)) and simulated tsunami wave by non-linear long wave equation (TUNAMI model by Tohoku University in Japan). Figure.2 (b) shows that max tsunami wave height around coastal area of Kanto-region in Japan. Table.1 shows the tsunami inundation depths simulated from tsunami numerical simulations for the target point. Tsunami numerical simulation was conducted with changing slip rate and fault depth. The slip were changed from 0.8 times to 1.2 times. The fault depth were changed from -1.0 km to +2.0 km. Figure.2   (a) Initial displacement of tsunami estimated from Okada’s equation (b) Max water height simulated by non-linear long wave equation
We 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
Takuma KOTANI, Shinsuke TAKASE, Shuji MORIGUCHI, Kenjiro TERADA, Yo FUKUTANI, Yu  OTAKE,  Kazuya  NOJIMA,  Masaaki  SAKURABA  (2016),  Numerical-Analysis-Aided Probabilistic Tsunami Hazard Evaluation Using Response Surface, Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)), Vol. 72 (1), pp.58-69. (in Japanese) Figure.3    (a) The simulation results (Blue point) and the response surface (Red area) (b) The histograms of tsunami inundation height Table.2   Uncertainty of slip rate and fault depth
Next, we estimated the histograms of damage probability of steel building (see Fig.4 (a)) by using the tsunami inundation deptns generated from monte-carlo method. In evaluation of the damage probability, we used the fragility curve of steel 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 the percentile value of damage probability (49.6%) , although it is conditional.

③  Summary
We proposed tsunami risk evaluation using response-surface methodology. The proposed method is a useful and simple way to evaluate tsunami risk using a response-surface without conducting multiple tsunami numerical simulations.