17th World Conference on Earthquake Engineering
Sendai, Japan - September 28 to October 2, 2021
Paper N°C004492

Probabilistic tsunami inundation assessment for the maximum possible earthquake
A case study of the Sagami Trough megathrust earthquake in JapanYo Fukutani1
1 Civil Engineering Department, College of Engineering and Science, Kanto Gakuin University (E-mail: fukutani@kanto-gakuin.ac.jp)

Abstract
The purpose of this study is to conduct a probabilistic tsunami inundation assessment for the maximum possible earthquake magnitude in the Sagami Troughmegathrust earthquake in Japan, showing the uncertainties of the assumed tsunami by performing a numerical simulation of tsunami inundation considering various
uncertainties and reduce the computational costs using the mode decomposition method. First, we developed 9 cases of fault parameters of the Sagami Troughmegathrust earthquake (Mw 8.7) considering these uncertainties, where the reference Mw was changed to ±0.1 and the reference fault depths were changed to -1 km
and +2 km. Then, we evaluated the tsunami inundation areas and depths for all 9 cases using a nonlinear longwave equation. Next, we applied singular value
decomposition to the inundation depth data and evaluated the spatial inundation modes. We can obtain a large number of possible inundation areas and probability
density distributions of tsunami inundation depths in each mesh by combining these inundation modes. Finally, we obtained tsunami inundation hazard curves andtsunami inundation distribution within the next 30 years by applying the Brownian Passage Time (BPT) distribution. The proposed method can be used to evaluate thetsunami inundation area considering the uncertainty of the largest earthquake with a relatively low computational cost and could be an effective method to evaluate theuncertainty of tsunami hazard maps and the probability density function of tsunami inundation depths at each point.

① A target earthquake source and earthquake uncertainties

Mw 8.6
Depth ±0.0 km(a)
Mw 8.7
Depth +2.0 km

Mw 8.6
Depth －1.0 km(b)
Mw 8.7
Depth ±0.0 km(d)Mw 8.8Depth +2.0 km

Control(c)Mw 8.7
Depth －1.0 km(e)

Mw 8.8Depth ±0.0 km(f)Inundation depth (m)Based on the theoretical framework outlined in our paper, we consider the uncertainties inearthquake Mw and fault depth. Figure 1. shows the slip distribution of the generated
Sagami Trough megathrust earthquake.
This was generated based on the fault parametersof the Sagami Trough megathrust earthquake(western model) (Mw 8.7) published by theCabinet Office in 2012. Using the initial waterlevel as an input value evaluated by using thetheory of Okada, we performed tsunami numericalsimulations via nonlinear shallow water equations
and the continuity equation with a time interval of
0.6 seconds and a grid spacing of 270 m - 90 m 30 m - 10 m.
Figure 1. The target sources of this study

Mw 8.6
Depth +2.0 km

Mw 8.8Depth －1.0 km(The Sagami trough earthquake in Japan)

Figure 2. shows the distributions of the maximum tsunami inundation depths for the target
area, Zushi city in Japan, simulated for 9 seismogenic faults with three Mw values andthree fault depths. Changes in Mw were achieved by adjusting the amount of slip.

(g)

(h)

(i)

Figure 2. Tsunami inundation results for Zushi city, Japan② Mode decomposition and Surrogate model

Mode 1Mode 2Mode 3Mode 4Mode 5Mode 6

Mode 7

Mode 8Mode 9We generated data matrix X from the 9 tsunami inundation depth data and decomposed thematrix into singular vectors as following:Singular Value Decomposition:
𝑻𝑿 = 𝑼𝜮𝑽𝑁𝒙𝑗 = ෍𝑘=1

𝑇𝒖𝑘 𝜆𝑘 𝑣𝑘𝑗

𝑁=෍
𝑘=1

𝑁𝜆𝑘 𝑣𝑗𝑘 𝒖𝑘 = ෍𝑘=1

𝛼𝑗𝑘 𝒖𝑘Figure 3. shows the spatial distribution of column vectors 𝒖𝑗 (j = 1, …, 9) comprising theleft-singular vector. These column vectors are called modes, and we can identify 9 mode
distributions corresponding to various tsunami inundation depths. We determined thecoefficients 𝛼𝑗𝑘 using random numbers following probability distribution of the input
parameters (see Table 1.) and randomly generated the inundation depth distribution using
the surrogate model.
Table 1. Probability distribution of slip scale and fault depth for generating tsunami inundation depths

Variables

AverageStandarddev.

Probability
distribution

0.35

Log normal

Fault depth
D [km]

0.00

2.0

Normal(a)(b)(c)Standard deviation (m)1.00

Figure 3. Mode decomposition results for tsunami inundation depth data
Tsunami inundation depth (m)Slip scale
factor S

Basis forvariability setting
Mw is suggested to vary by about±0.1, considering previous
earthquakes with the same fault
area. (The Nuclear Civil Engineering
Committee, JSCE, 2011)
There was a standard deviation ofseveral kilometers based on theresults of research evaluating thedepth of the upper edge of thePhilippine Sea Plate.

Figure 4. (a) Average, (b) maximum and (c) standard deviation of the tsunami inundation depthby Monte Carlo simulation results

Figure 4(a) shows the average inundation depth in each mesh evaluated by using③ Summary
10,000 random numbers, and Fig. 4(b) shows the maximum inundation depth in
We proposed a probabilistic tsunami inundation assessment method using proper
each mesh sampled with 10,000 simulations. The mean values in Fig 4(a) areorthogonal decomposition as a method to determine the buffer zone of tsunami
similar to the inundation depth distribution for the control case in Fig 2(e), andhazard maps. The current tsunami hazard maps are prepared for the largest class ofthe maximum values in Fig 4(b) are similar to the inundation depth distribution
earthquakes, and this method can be effective when considering the uncertainty offor the Mw 8.8 case in Fig 2(g), (h) and (i), indicating that we were able totsunami hazards from the largest class of earthquakes.
reproduce the spatial distribution of tsunami inundation depths produced from thenumerical analysis by using the surrogate model. Fig 4(c) shows the standard Reference
deviation of tsunami inundation depth. This allows us to understand the Yo Fukutani，Shuji Moriguchi, Kenjiro Terada, Yu Otake (2021) Time-Dependent ProbabilisticTsunami Inundation Assessment Using Mode Decomposition to Assess Uncertainty for an
characteristics of the variability of the tsunami inundation depth whenEarthquake Scenario, Journal of Geophysical Research: Oceans, Vol.126(7), e2021JC017250.
considering the earthquake source uncertainty.
DOI:10.1029/2021JC017250.