2018American Geophysical Union Poster Session

Assessment using copulas of simultaneous damage
to multiple buildings as a result of tsunamis
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
In this research, we target the Sagami trough earthquake tsunami that could have a big influence around the Japanese capital region and propose a method forsimultaneous damage assessment using copulas that can take into consideration correlation of tsunami depths and building damages between two sites.
First, we simulated the tsunami inundation depths at two sites by using a nonlinear long wave equation. We simulated the tsunami heights by varying the slip amount(5 cases) and the depths (5 cases) for each 10 source of the Sagami Trough. Then, we constructed the response surfaces that can explain tsunami heights. Then, weconducted the Monte-Carlo simulation using copulas in order to consider correlation of tsunami heights between two sites. In this study, we used Survival Gumbel
copula for the region 8 as the results of maximum likelihood estimation of bivariate copula based on the tsunami numerical simulation results. We can properly
evaluate the correlation of tsunami heights by using the copula. Considering the correlation of the tsunami inundation depth at the two sites, the expected value hardly
changed compared with the case of no correlation, but it was calculated largely that the damage rate of 99th percentile value was about 2 % and the maximum value
was about 6 % in case of using the copulas.

① Target 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).
Table.1 Uncertainty of slip rate and fault depth
Office (2013) (see Fig.1). The target points for the tsunami risk assessment areVariables
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 3Region 4

Slip rate
Mw: 8.0
Region 8Fault depth
0.12(log average)[km]
Mw: 8.6

Region 10

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

Mw: 8.2

A Target point (The Hiratsuka port)
P1Frequency

The Tokyo Bay

Figure.4 (a) is the Monte-Carlo simulation results (Black points) of the region 8without considering correlation of tsunami height between two sites. The redpoints are the tsunami simulation results. The black points cannot not be
considered the correlation. Based on the tsunami numerical simulation results (25cases), we conducted maximum likelihood estimation of bivariate copula, thenselected Survival Gumbel copula because AIC is minimum (AIC = -49.54).
Figure.4 (b) is the results of Monte-Carlo simulation results considering thecorrelation using Survival Gumbel copula.

The Sagami Bay② Constructing response surfaces for the target points2.0(a)N = 10,000

1.5

Figure.2 The two target points of this study

sim8_hiratsuka
Hiratsuka

2.5

A Target point (Miura City)

Tsunami height (m)(Hiratsuka City)

P2Frequency

Mw: 8.5

Log normal
Distribution(log standarddeviation)

1000 2000

Region 9

Mw: 8.5

3.0 0

Mw: 8.4

0.651000 2000

Region 7

3.0 0

Region 6

Mw: 8.3

2.5

Region 5

Mw: 8.2

0.10(b)

N = 10,000

2.0

Mw: 7.9

1.00

NormalDistribution

1.5

Region 2

sim8_hiratsuka
Hiratsuka

Region 1

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

Damage probabilityof two buildings

Tsunami inundation depth (m)Tsunami inundation depth (m)

0.5

0.5

1.0

1.0

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 non-linear long wave equation (TUNAMI-N2 model by Tohoku University).
23456 01000 2000
23456 01000 2000
Tsunami height (m) Frequency
Tsunami height (m) Frequency
In order to consider uncertainties of tsunami wave, the tsunami simulations wereP2
P2(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 Survival Gumbel 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 damage
and developed a response surface for tsunami inundation depth.
probabilityofsteelbuilding
attwopoints
usingfragility
curve.
Comparedwith
theY (x1,x2) = a*x1 + b*x2 + c*x1*x2 + d*x1*x1 + ecaseofnocorrelation,theexpectedvalueofthedamageprobability
hardlychanged,x1: Slip rate of the earthquake, x2: Depth of the earthquake100%
No correlation
but it was calculated largely that
Gaussianthe damage rate of 99th percentile
Slip rate
copulaSlip rate
50%
value
was
about2%
and
theP1
P2
Survival
Gumbelmaximum value was about 6 % in
copulacase of using the copulas (see0%
Fig.5).
Figure.5 Damage probability in case of using each copula④ Summary
We proposed tsunami risk evaluation using response-surface method and monteCarlo simulation technique considering correlation of tsunami depth using copulas.
The proposed method is a useful and simple way to evaluate tsunami risk without
conducting many tsunami numerical simulations.
ReferenceTsunami 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

100%

90%
80%
70%
60%
50%
40%
30%20%
10%0%

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)