2019 Asia Oceania Geosciences Society Poster Session

Tsunami Risk Assessment Considering
Tsunami Wave Correlation Using Copulas
1222
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
It is necessary to consider simultaneous damage to multiple buildings when performing probabilistic risk assessment for a portfolio of buildings. In this study, wedemonstrate tsunami risk assessment for two buildings using copulas of tsunami hazards that consider the nonlinear spatial correlation of tsunami wave heights. First,
we simulated the wave heights considering uncertainty by varying the slip amount and fault depths. The frequency distributions of the wave heights were evaluated via
the response surface method. Based on the distributions and numerically simulated wave heights, we estimated the optimal copula via maximum likelihood estimation.
Subsequently, we evaluated the simultaneous distributions of the wave heights and the aggregate damage probabilities via the marginal distributions and the estimatedcopulas. As a result, the aggregate damage probability of the ninety-ninth percentile value was approximately 1.0 % higher and the maximum value was approximately
3.0 % higher while considering the wave height correlation. We clearly showed that the usefulness of copula modeling considering the wave height correlation inevaluating risk of building portfolio. We only demonstrated the evaluation method for two buildings, but the effect of the wave height correlation on the results isexpected to increase if more points are targeted.

① Target earthquake sources and target points③ Tsunami risk assessment using Monte-Carlo simulations and copulas

We used the Sagami trough earthquakes as a tsunami source, which was We conducted Monte-Carlo simulation (N=10,000) using the response surface
published by the study meeting for the Tokyo Inland Earthquakes of the Cabinet considering uncertainty of slip and depth of the earthquake (see Table.1).
Office (2013) (see Fig.1). The target points for the tsunami risk assessment areTable.1 Uncertainty of slip rate and fault depth
Variables
Average Standard deviation
P.D.F
Reason for the variation
located in the Sagami Bay and the entrance of the Tokyo Bay (see Fig.2).
Region 4Slip rate(x1)
Region 6

Region 7

Mw: 8.3
Region 8Fault depth
0.12(x2) [km] (log average)
Mw: 8.5

Mw: 8.6

Figure.1 The target sources of this study(The Sagami trough earthquakein Japan)
Mw: 7.9

Mw: 8.2

A Target point (The Oiso port)
P1

Frequency

The Tokyo Bay

Figure.4 (a) is the Monte-Carlo simulation results (Black points) of the region 8
without considering correlation of tsunami height between two sites. The redpoints are the tsunami simulation results. The black points cannot be considered
the correlation. Based on the tsunami simulation results (25 cases), we conductedmaximum likelihood estimation of bivariate copula, then selected Frank copula
because AIC is minimum (AIC = -49.11). Figure.4 (b) is the results of MonteCarlo simulation results considering the correlation using Frank copula. TheMonte-Carlo simulation results agree well with the tsunami simulation results.

The Sagami Bay② Constructing response surfaces for the target points

2.0
1.5

Figure.2 The two target points of this study

Hiratsuka
sim8_hiratsuka

2.5

A Target point (Miura City)

Tsunami height (m)(Oiso port)

P2

Frequency

Region 10(log standarddeviation)

1000 2000

Region 9

Mw: 8.5

3.0 0

Mw: 8.4

0.65(a)

N = 10,000

1000 2000

Mw: 8.0

3.0 0

Region 5

Mw: 8.2

0.10

2.5

Mw: 7.9

1.00(b)

N = 10,000

2.0

Region 3

1.5

Region 2Hiratsuka
sim8_hiratsuka

Region 1TheNuclear
CivilEngineering
Committee, Japan Society of Civil
Engineers (2016) indicated that there
Normalcan be a variability of ±0.1 Mw
Distribution considering same fault area. In thiscase, a variation range of slip is from0.7 times to 1.4 times.
This variability was calculated based on
the observation errors of fault depths,
Log normal
which are listed in the seismic source
Distribution list of JMA (Data period: 2016/102017/10)

1.0

1.0

0.5

0.5

Tsunami inundation depth (m)Tsunami inundation depth (m)Using the fault parameters of the Sagami trough earthquake, we calculated theinitial displacement of tsunami by Okada’s equation and simulated tsunami wave P1
Monte-Carlo simulation results
Monte-Carlo simulation results
Tsunami numerical simulation results
Tsunami numerical simulation results
by nonlinear long wave equation (TUNAMI-N2 model by Tohoku University). In
23456 01000 2000
2345
6 01000 2000
Tsunami height (m) Frequency
Tsunami height (m) Frequency
order to consider uncertainties of tsunami wave, the tsunami simulations wereP2P2(Miura City)(Miura City)
conducted with changing slip rate and fault depth. The slip were changed fromFigure.4 Monte-Carlo simulation results (a) without and (b) with Frank copula
0.7 times to 1.4 times (5 cases). The fault depth were changed from -1.0 km to+2.0 km (5 cases). Then, we conducted regression analyses using below equation For all regions of the Sagami trough, we conducted same statistical simulations
using above method. Then, we converted the tsunami heights to the damageand developed a response surface for tsunami inundation depth.
probabilityofsteelbuildingattwopoints
usingfragility
curve.
Comparedwith
theY (x1,x2) = a*x1 + b*x2 + c*x1*x2 + d*x1*x1 + e
case
ofnocorrelation,theexpectedvalueofthedamageprobability
hardlychanged,x1: Slip rate of the earthquake, x2: Depth of the earthquake
but it was calculated largely that
Table.1 Aggregate Damage probability
Aggregate damage probability of two buildings
the damage rate of 95/99th
Slip rate
Slip rate
No correlation (A) Correlation (B) Difference (B-A)
percentile
value
wasabout
1%
P1P2Average
58.8%
58.8%
0.0%
and the maximum value was about 95 percentile
66.2%
67.0%
0.9%
3 % in case of using the copulas 99 percentile
68.9%
69.7%
0.8%
Maximum
73.5%
76.7%
3.1%
(see Table.1).
④ Summary
We proposed tsunami risk evaluation using response-surface method and monteCarlo simulation technique considering correlation of tsunami heights using
copulas. The proposed method is a useful and simple way to evaluate tsunami risk
without conducting many tsunami numerical simulations.
Reference
Tsunami numericalsimulation results

a= 0.66, b=0.05, c=0.00, d=0.52, e=0.51
a= 11.11, b=0.00, c=0.00, d=-4.02, e=-3.13
Figure.3 The constructed response surfaces at each point (P1, P2) for the region 8Yo

FUKUTANI, Shuji MORIGUCHI, Takuma KOTANI, Kenjiro TERADA (2018),PROBABILISTIC TSUNAMI LOSS ESTIMATION USING RESPONSE-SURFACE METHOD-APPLICATION TO SAGAMI TROUGH EARTHQUAKE-, Journal of Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol. 74(2), pp.I-463-I-468. (in Japanese)