iRIC Easy-performable
Long-wave Inundation
MOdel (ELIMO)∗
Users Guide
Ver. 4.0

June 26, 2023∗

©2013 Coastal and Ocean Engineering Laboratory, School of Engineering,
Hokkaido University

Introduction
The 2011 Tohoku earthquake tsunami brought great damages to human
lives, industries and economics in Japan, and provided an important lesson
for disaster reduction and evacuation. We have reconsidered the disasterprevention policy and tried to renew multilateral regional disaster plans for
multiple scenarios of tsunami onsets. The estimation of regional tsunami
heights provide fundamental conditions to design the disaster plans; developing infrastructures, hazard maps and managing evacuation for various
scenarios. While reasonable tsunami computation to predict the tsunami
heights along coasts need to be performed, it requires technical knowledge
and experiences to operate computer simulators as well as expensive highperformance computers. Whereas local government needs to make the local
disaster and evacuation plans to save the local resident against tsunamis, it
may be diﬃcult for them to predict the heights by themselves because theabsence of human and computer resources, which may slow down proceduresof planning.
iRIC-ELIMO has been developed with a motto of ”simple and easytsunami computation” for people with minimum knowledge to operate Window softwares, which is capable of reliable estimations of tsunami generation,
propagation and evolution on coasts on easy-performable GUI environment
provided by iRIC.
ELIMO ver. 4 introduced a submarine mass failure model (Watts etal. 2005) to nonlinear long wave equations to simulate tsunami inducedby submarine landslide, which allows simulataneous evaluation of tsunamis
caused by interplate earthquake and landslide.
Users should carefully conﬁrm the following speciﬁcations of ELIMO
and understand the model assumptions and limits of the applications. Any
applications beyond the model conditions and computational accuracies usedin ELIMO are not supported. It should be noted that iRIC-ELIMO cannot
be held responsible for any disadvantages, loss, cost which may be incurredby ELIMO. Conﬁrm and agree Terms of Conditions before using ELIMO.
i

ii
ELIMO Development Team
Yasunori Watanabe, Hokkaido University
June, 2023

ELIMO 4.0 Speciﬁcation(June 2023)

1. Governing equation; nonlinear long wave equation
2. Coordinate system; Spherical global coordinate
3. Computational method; Euler-Lagrangian ﬁnite diﬀerence method withthird order accuracy (CIP metod + Predictor-Corrector method)
4. Bathymetry; General Bathymetric Chart of the Oceans (GEBCO) altitude data
5. Shore boundary condition; Impermeable condition at shore (no inundation on land area)
6. Open boundary condition; Radiation condition + Sponge zone (additional energy dissipation)
7. Fault model; Elastic rectangular fault model (Okada 1985), Tsunami
generation model including horizontal fault displacements (Tanioka ad
Satake 1996).
8. Submarine mass failure model (Watts et al 2005)

Contents
1 What is ELIMO?
1.1 Governing equation . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Computational methods and boundary conditions . . . . . . .
1.2.1 Impermeable condition at a shore . . . . . . . . . . . .
1.2.2 Open boundary condition . . . . . . . . . . . . . . . .
1.2.3 Initial Conditions . . . . . . . . . . . . . . . . . . . . .
1.2.4 Submarine landside . . . . . . . . . . . . . . . . . . .

1
2
4
4
5
7
11

2 Tutorial
13
2.1 Acquisition of bathymetry data . . . . . . . . . . . . . . . . . 13
2.2 Operations on iRIC . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Generation of computing grids . . . . . . . . . . . . . 16
2.2.2 Setting computational conditions and Executing ELIMO 18
2.2.3 Run computation . . . . . . . . . . . . . . . . . . . . . 22
2.2.4 Visualizing the results . . . . . . . . . . . . . . . . . . 22
3 Examiples of Computations
25
3.1 The 2011 Tohoku earthquake tsunami . . . . . . . . . . . . . 25
3.2 Comparisons with the observed surface elevation . . . . . . . 26
3.3 Submarine landslide tsunami . . . . . . . . . . . . . . . . . . 26
3.4 Scenario tsunami . . . . . . . . . . . . . . . . . . . . . . . . . 27

iii

iv

CONTENTS
Update Records
1. July 2013

Release of ELIMO 1.0

2. November 2013 ELIMO 1.1; Release a format conversion software”gebco conv” for GEBCO 1 minuet altitude grid data that is downloadable from British Oceanographic Data Center. The user’s guide
updated.
3. June 2015 ELIMO 2.0; ”gebco2s2014” for 2014 format of GEBCO
data has been provided. The elastic rectangular fault model by Okada(1985) and the tsunami generation model by Tanioka and Satake (1996)
have been introduced. The arbitrary fault models with asperities canbe used for the ELIMO computation by using a ﬁle input function for
the fault parameters.
4. 2019; Allowing direct input of NetCDF GEBCO data (without preprocessing).
5. June 2023; Introducing a model for submarine landside tsunami.

Chapter 1

What is ELIMO?
A tsunami computation is a fundamental way to provide tsunami heights andarrival times along coasts for past and future earthquakes, which has beenused for designing disaster prevention plans. The computations have been
generally performed at high performance computers owned by Universities
and research institutes, and commonly used by researchers and engineers
who have scientiﬁc knowledge and experience of the numerical computation.
There may be no computational tool that is accessible to the public. Whilethe disaster prevention and evacuation plans for tsunami inundation are
required to develop by local governments, they have no way to estimate thetsunami properties by their own human and computational resources. Under
these background, we have tried to develop technologies for producing acompact and reliable software to compute tsunami for arbitrary earthquake,
which is executable on home PC. We hope this tsunami software named
ELIMO will be utilized for estimating the tsunami onsets in order to achieve
disaster reduction and eﬃcient evacuation.
iRIC is a computational platform to support computations of river ﬂows
and ﬂoods with the pre-processing functions of computational griding andthe post-processing of visualizing and plotting the results on GUI environment. The tsunami solver ELIMO (Easy-performable Long-wave Inundation
MOdel) is designed to perform fundamental tsunami computations on theiRIC environment.
This users guide for ELIMO is composed of three chapters. In Chapter 1, governing equations to be solved, boundary conditions, assumptions
and numerical methods used in ELIMO are explained. While researchersand engineers who have scientiﬁc knowledge should conﬁrm these technicalinterpretations, general users may skip this chapter. In Chapter 2, the pro-1

CHAPTER 1. WHAT IS ELIMO?

2

Figure 1.1: Spherical global coordinate system.
cedure to acquire bathymetry data, to compute tsunami and visualize theresults is explained. Chapter 3 introduces examples of the tsunami computations, including the 2011 Tohoku earthquake tsunami.

1.1

Governing equation

The depth-averaged long wave equation is used as governing equation in
ELIMO (Fig. 1.1).
τ s − τλb
∂u
u ∂u
v ∂u
1
∂pa
g
∂ζ
+
+
=−
−
+ λ
∂t
R cos ϕ ∂λ R ∂ϕ
ρR cos ϕ ∂λR cos ϕ ∂λ ρ (h + ζ)
(
(
))
2
1
∂ u
1
∂
∂u
+νh
+
cos ϕ
R2 cos2 ϕ ∂λ2 R2 cos ϕ ∂ϕ
∂ϕ()
u
+ 2Ω +
v sin ϕ(1.1)
R cos ϕ

CHAPTER 1. WHAT IS ELIMO?

3

τϕs − τϕb
∂v
∂pa
∂ζ
u ∂v
v ∂v
1
g
+
+
=−
−
+
∂t
R cos ϕ ∂λ R ∂ϕ
ρR cos ϕ ∂ϕ
R cos ϕ ∂ϕ ρ (h + ζ)
(
(
))
2
1
∂ v
1
∂
∂v
+νh
+ 2
cos ϕ
2
2
2
R cos ϕ ∂λR cos ϕ ∂ϕ
∂ϕ()
u
+ 2Ω +
u sin ϕ(1.2)
R cos ϕ
∫ζ ′
∫ζ ′
1
1
where the depth-averaged mean velocities u = h+ζ
−h u dz, v = h+ζ −h v dz
(local velocities u′ , v ′ ), R is the distance from the center of the earth, Ω isthe earth’s rate of rotation，λ longitude, ϕ latitude, pa atmospheric pressure, ζ surface elevation, νh coeﬃcient of horizontal momentum exchange.
Mass conservation for the depth-averaged equation system is written by
1
∂
1
∂
∂ζ
+
u (h + ζ) +v cos ϕ (h + ζ) = 0(1.3)∂tR cos ϕ ∂λR cos ϕ ∂ϕ
Imposing zero gage pressure at the surface and ignoring surface shear, theabove equations are rewritten with an additional dissipation term Ad in asponge zone (explained in the following section) by
τλb
Du
g
∂ζ
=−
−
+ Ad uDt
R cos ϕ ∂λ ρ (h + ζ)
(
(
))
1
∂2u
1
∂
∂u
∗
+νh
+
cos ϕ
R2 cos2 ϕ ∂λ2 R2 cos ϕ ∂ϕ
∂ϕ()
u
+ 2Ω +
v sin ϕR cos ϕ

(1.4)

τϕb
Dv
g
∂ζ
=−
−
+ Ad vDt
R cos ϕ ∂ϕ ρ (h + ζ)
(
(
))
1
∂2v
1
∂
∂v
+νh∗
+
cos
ϕ
R2 cos2 ϕ ∂λ2 R2 cos ϕ ∂ϕ
∂ϕ()
u
+ 2Ω +
u sin ϕ(1.5)
R cos ϕ
(
)
(
)
Dζ
∂uh
1 ∂vh
tan ϕ
1
∂u
∂v
−
+
=−
+ζ
+ζ
v (h + ζ) (1.6)
Dt
R cos ϕ ∂λ
∂λ
R ∂ϕ
∂ϕ
R
∂
∂
u
v ∂
D
=
+
+
, modiﬁed bottom shear τλb = Cd |u|u
where
Dt
∂t R cos ϕ ∂λ R ∂ϕand τϕb = Cd |v|v. While many values for the drag coeﬃcient Cd have been
proposed for speciﬁc ﬂows, Cd = 5 × 10−3 is used in ELIMO.

CHAPTER 1. WHAT IS ELIMO?

4

Figure 1.2: Impermeable condition at a shore

1.2

Computational methods and boundary conditions

The third order accurate, ﬁnite diﬀerence computations are performed forthe nonlinear equation system Eq. (1.4)-Eq. (1.6) in the same manner as
Watanabe et al. (2012); Constrained Interpolation Proﬁle (CIP) method forthe advection equation in a two-step fractional step framework, predictorcorrector method for the Eulerian terms. We don’t explain the details ofthese numerical methods in this users guide, which can be found in thespecialized literature (Goto, Okayasu and Watanabe, 2013).

1.2.1

Impermeable condition at a shore

The current version of ELIMO simply uses an impermeable condition the
shore; that is, virtual vertical walls are arranged along the shore (Fig. 1.2).
The impermeable condition at a shore is expressed by
∂η
=0
∂n
u·n=0
where n is the normal unit vector (see Fig. 1.2).

(1.7)
(1.8)

CHAPTER 1. WHAT IS ELIMO?

5

Figure 1.3: Computational domain and region to place the sponge zone
(Tokachi area, Hokkaido, Japan).

1.2.2Open boundary condition

When a ﬁnite computational domain is given in ocean area, an open boundary condition imposed at the edges of the domain is important to transmit incident waves across the boundary without any reﬂection. A ﬂawed
condition may induce unrealistic reﬂected waves at the boundaries to form
multiple reﬂection system within the domain, which results in unacceptablecomputations. While a very large domain has been commonly used in theconventional tsunami computation to avoid the diﬃculties, e.g. a whole areaof Paciﬁc Ocean, ELIMO employs a compact domain to reduce computational loads. Therefore, appropriate open boundaries need to be given toachieve an available computation in ELIMO. While any boundary condition
to achieve perfect transmission of incident waves has yet been developed,
Sommerfeld’s radiation condition has been commonly used (Orlanski, 1976);
∂φ
∂φ
+c
=0
∂t
∂n

(1.9)

6

CHAPTER 1. WHAT IS ELIMO?

Figure 1.4: Ampliﬁcation rate for the dissipation term in the sponge zone.
where the arbitrary quantity φ, and the celerity c approximated by the ﬁnite
diﬀerence at the previous time step;
c=−

δφ δφ
/
δt δn

(1.10)

δ is the ﬁnite diﬀerence operator which is constrained by the conditions;(c < 0) 0c(0 ≤ c ≤ ∆x/∆t)c=(1.11)
∆x/∆t (c > ∆x/∆t)
Signiﬁcant reﬂection may appear under this radiation condition in the casethat the celerity and incident angle spatially change near the boundary. In
order to attenuate the incident waves near the boundary and to minimize
the wave reﬂection, a so-called sponge zone is arranged at an inner areaadjacent to the boundary (see Fig. 1.3)．
According to Cruz et al. (1993), the dissipation coeﬃcient Ad is given
by
√
(
)N
+dlayer
if i ≥ imax − dlayer
Ad = Amax hg (N + 1) i−imax
dlayer
(1.12)
Ad = 1else
where N is the oder of the distribution function. N = 1 is used in ELIMO.
As shown in Fig. 1.4, Ad linearly increased in the sponge zone enhances

CHAPTER 1. WHAT IS ELIMO?

7

Figure 1.5: Input window for computing conditions.
dissipation for Eq. (1.4) and Eq. (1.5). As additional reﬂected waves may
be produced within the sponge zone with too high gradients of Ad , suitable(low) Ad should be provided in the computation. While a wider spongezone provides more dissipation, available computing area becomes smaller;that is, there is tradeoﬀ between computational cost and performance ofthe boundary condition. User should carefully choose suitable number ofthe computing cells comprising the sponge zone (dlayer) and the maximum
dissipation rate （Amax ） in the window for computational conditions (seeFig. 1.5). It should be noted that tsunami is wrongly computed in coastal
area containing the sponge zone as the computation is available except the
sponge zone (see circles in Fig. 1.3). In this case, you should change thelocations of the boundaries and use larger domain.

1.2.3

Initial Conditions

Fig. 1.6 shows the distribution of the vertical displacement of sea ﬂoor due
to the 2011 Tohoku earthquake tsunami, which provided by Japan Meteorological Agency. The vertical displacement of faults directly contributeto sea level rise while the horizontal displacement also results in sea levelvariations over uneven sea ﬂoors.
In general, deformation of the elastic rectangular fault is determined by
the fault parameters; Rupture length (L), Rupture width (W ), Slip length(U ), Rake angle (θ), Strike angle (ϕ), Dip angle (δ), Fault depth (d), Latitudeand Longitude of Fault Top（see Fig. 1.7 and Fig. 1.8）. ELIMO uses theelastic fault model for the rectangular dip-slip deformation source, which
is derived by Okada (1985). This model provides the three-dimensional

CHAPTER 1. WHAT IS ELIMO?

8

Figure 1.6: Displacement of sea ﬂoor due to the 2011 Tohoku earthquake
tsunami; vertical displacement (left) and horizontal one (right) (web pageof Japan Meteorological Agency).
displacements at arbitrary coordinate (x, y).
)
U2 ( q− I3 sin δ cos δ
2π (R
)
U2
ỹq
ξη
= −
+ cos δ arctan− I1 sin δ cos δ
2π R (R + ξ)
qR
(
)
˜
U2
dq
ξη
= −
+ sin δ arctan− I5 sin δ cos δ
2π R (R + ξ)qR

ux = −(1.13)uy(1.14)uz(1.15)(1.16)

CHAPTER 1. WHAT IS ELIMO?

9

Figure 1.7: Fault parameters; slip length, slip angle, strike and dip angle.
where
I1 = −

ξµ() − I5 tan δ
λ + µ R + d˜cos δµlog (R + η) − I3
λ+µ


µ 
ỹ
(
) − log (R + η) − I4 tan δ
λ + µ cos δ R + d˜
)
)
µ
1 ( (
log R + d˜ − sin δ log (R + η)
λ + µ cos δ2
η (X + q cos δ) + X (R + X) sin δµarctanλ + µ cos δξ (R + X) cos δ(1.17)

I2 = −(1.18)

I3 =(1.19)

I4 =I5 =(1.20)(1.21)(1.22)and p = y cos δ + d sin δ, q = y sin δ − d cos δ, ỹ = η cos δ + q sin δ, d˜ =η sin δ − q cos δ, R2 = ξ 2 + η 2 + q 2 = ξ 2 + ỹ 2 + d˜2 , X 2 = ξ 2 + q 2 , U2 is the
dip-slip displacement source. These displacements are evaluated by using
the following relation;f (ξ, η) = f (x, p) − f (x, p − W ) − f (x − L, p) + f (x − L, p − W ).

(1.23)

10

CHAPTER 1. WHAT IS ELIMO?

Figure 1.8: Fault parameters; longitude and latitude of the fault top, andstrike (in the case of the 2003 Tokachi-oﬀ earthquake)
Fig. 1.9 shows the vertical and horizontal displacements of the sea ﬂoor
for the fault parameters for the 2003 Tokachi oﬀ earthquake, estimated by
the Okada’s model. Any sea ﬂoor displacements for arbitrary fault parameters can be determined by this model.
Tanioka and Satake (1995) proposed the tsunami generation model touse as an initial sea level condition (ζ), based on bulk water displacement
due to horizontal sea ﬂoor displacement as well as direct water displacement
by vertical sea ﬂoor displacement;ζ = uz + ux

∂h
∂h
+ uy
∂x
∂y

(1.24)ELIMO determines the initial sea level by the Tanioka-Satake modelusing the Okada’s solutions for the input fault parameters. Users can choose
two options to input the parameters, ‘manual input’ and ‘ﬁle input’, on
ELIMO, and in particular, the latter option is useful for setting up spatiallynon-uniform displacements described by local deformation of multiple fault
segments, which will be explained in §2.2.2.

11

CHAPTER 1. WHAT IS ELIMO?

Figure 1.9: Vertical (left) and horizontal (right) displacements for the 2003
Tokachi oﬀ earthquake.

1.2.4

Submarine landside

Watts et al. (2005) developed a Submarine Mass Failure (SMF) model,
deﬁning initial sea-level displacement when submarine landslide occurs. According to their model, characteristic tsunami amplitude owing to the landslide is given byη0 ≈ 1.74 × 10−5 b (1 − 0.750 sin θ)(b sin θd

)1.75
(1.25)

where b is the length of SMF, d is the water depth at the maximum thicknessof initial SMF，θ is the bed slope．The initial surface form at arbitrary
location (x, y) was approximated by a double Gaussian distribution in xdirection and a soliton-like wave form in y-direction with respect to theinitial location of SMF (x0 , y0 );() ( ( x−x )2() )x−∆x−x0 2
η0y − y0
− λ 0
−
2
′
λ
0
0
η(x, y) ≈ −sech κ
e−κe(1.26)
ηminw + λ0where κ ≈ 3, w is the width of SMF, λ0 is the characteristic wavelength, κ′and ∆x are parameters controling double Gaussian surface forms．ηmin indicates the minimum value of the function on the right-hand side of Eq. (1.26)(excluding the amplitude)．According to characteristic√ √ tsunami scalings,
characteristic time t0 = ut /a0 , terminal speed ut = gb π (γ − 1) sin θ/2Cd ,initial acceleration
a0 = g sin θ (γ − 1) / (γ + Cm ), characteristic wavelength√
λ0 = t0 gd．Here, γ is the speciﬁc gravity, Cd is the drag coeﬃcient, Cm

CHAPTER 1. WHAT IS ELIMO?

12

Figure 1.10: An example of initial surface elevation estimated by Eq. (1.26)；
b=50m, d=5m, κ=3, ∆x=10m, w=25m, λ0 =25m, κ′ =0.8
is the added mass coeﬃcient．The submarine landside tsunami can be simulated through computations of nonlinear long wave equations under the
initial surface elevation deﬁned by Eq. (1.26) with these speciﬁc parameters.

Chapter 2

Tutorial
This chapter describes a whole procedure to simulate and analyze tsunami;acquisition of bathemetry data, import of the bathemetry ﬁle, generationof computing grids, setup of initial conditions (fault rapture parameters,
computing conditions), execution of ELIMO, visualizing and analyzing computed results.

2.1

Acquisition of bathymetry data

ELIMO 4.0 uses netCDF bathmetry data provided by General BathymetricChart of the Oceans (GEBCO). As the GEBCO covers the whole area of theearth, we can simulate tsunamis occurring anywhere in oceans. The data
can be downloaded in the following procedure;
1. In the web site of the General Bathymetric Chart of the Oceans（GEBCO）https://www.gebco.net/, click ‘Download GEBCO’s global
grid’ （bule rectangure bottom on the top left in Fig. 2.1）．
2. Click the world map (Fig. 2.2) bellow ‘Download data for user-deﬁned
areas’．
3. Fill in latitude and longitude of boundaries of the rectangular area todownload in ‘ENTER BOUNDARY’ on the left side of the world map,or specify the rectangular area by dragging mouse with holding ‘Ctrl’.
4. In ｀SELECT FORMATS’ (left input space), click a check box for 2D
netCDF and Grid (top left check box)．

13

CHAPTER 2. TUTORIAL

Figure 2.1: Web site of GEBCO

Figure 2.2: Specify a region to download

14

CHAPTER 2. TUTORIAL

15

Figure 2.3: Download the bathymetry data
5. Click ‘Add to basket’ (bottom button in left input space)．Then, click
the neighboring button ‘View basket’.
6. Click a right bottom button ‘Download your data’ on a popup window(Fig. 2.3)．
7. Move the downloaded data to a folder used for your computation.

CHAPTER 2. TUTORIAL

16

Figure 2.4: Importing bathymetry data ﬁle

2.2

Operations on iRIC

The procedures to compute tsunami and visualize the results are explained
below.

2.2.1

Generation of computing grids

1. Run iRIC.
2. Choose ‘File’ → ‘New Project’. Choose ’ELIMO’ in the window ‘SelectSolver’.
3. Conﬁrm ‘Pre-processing window’ is generated. Choose ‘Import’→‘Geographic
Data’→‘Elevation’.
4. Choose your downloaded GEBCO ﬁle (Fig. 2.4).
5. Click ‘OK’ on a popup window telling ‘To import the geographic data,
specify coordinate system for the project ﬁrst’.
6. Type ‘wgs’ in a search work box on a popup window of ‘Select Coordinate System’. You will then ﬁnd ‘EPSG:4326:WGS 84’ in the list of
coordinates. Click this coordinate (see Fig. 2.5).

CHAPTER 2. TUTORIAL

17

Figure 2.5: Setting coordinates
7. Conﬁrm the imported bathymetry is identical with the area you wantto compute.
8. Menu ‘Grid’→‘Select Algorithm to Create Grid’. Choose ‘Create gridby dividing rectangular region (Longitude-Latitude)’ in the window‘Select Grid Creating Algorithm’.
9. Deﬁne the computational domain by a mouse within the area of theimported bathymetry (Fig. 2.6). Note that the computational domain
has to be smaller than the imported bathymetry area, and should be
inside any bathymetry data boundaries.
10. Choose ‘Grid’→‘Create Grid’. Deﬁne a grid width ‘d’ to be the resolution that you want to compute at. Since the global coordinate system
is used in ELIMO, x-axis represents longitude and y-axis is latitude(i. e. d=0.1 degrees may indicate the grid width over 6 km). As computational costs increase with the resolution, User should choose theoptimal grid width in terms of resolution and cost. The grid width dto be in a range of 0.01 and 0.02 degrees (36 – 72 second) is recommended. As GEBCO has the resolution of 15 sec, user can computeat higher resolution, while there may be interference between the grid
locations of the bathmetry data and computing grids (especially nearshore lines). If you ﬁnd strange computed results (such as strange

CHAPTER 2. TUTORIAL

18

Figure 2.6: Generating a computing domain
waves generated before arriving tsunami), reconsider the grid width d.
11. Click ‘OK’ on the popup window.

2.2.2

Setting computational conditions and Executing ELIMO

Menu ‘Calculation Condition’ → ‘Setting’, then appearing a window ‘Calculation Condition’. Each group in the left box is explained bellow (Fig.
2.7).
File Input of Falut Rapture Conditions
If you answer for ”Which manner to input fault conditions?” is ”Manual Input”, you should manually input fault parameters for interplate earthquake
tsunami. If you select ”File Input”, click the button on the right of ”FileName of Fault Conditions” and select your parameter ﬁle on the dialog box.
Fault Rapture Conditions (Manual)This method is useful to manually input the parameters for one or two
rectangular faults on the input window of ELIMO. For instance, the two
faults models for the 2011 Tohoku earthquake tsunami have been proposedby the Geospatial Information Authority of Japan (Table 3.1). To provide
multiple fault displacements following this model, ﬁll in parameters on the

19

CHAPTER 2. TUTORIAL

Figure 2.7: Window of Calculation Condition
Table 2.1: Rectangle fault model for the 2011 Tohoku earthquake withfollowing parameters provided by the Geospatial Information Authority ofJapan
Fault 1
Fault 2latitude
(o )
39.00
37.21

latitude(o )143.49142.51

length
(km)
199
176

width
(km)
85
82

slip length
(m)
27.7
5.9

strike
(o )
202
201

dip
(o )
18
15

rake
(o )
97
81

Fault depth
( km)
10.0
10.1

ﬁrst fault in ‘First Fault Rupture Conditions’ and parameters on the second
one in ‘Second Fault Rupture Conditions’. Default parameters for the 2003
Tokachi-oﬀ earthquake tsunami have been provided. For any fault modelwith a single rapture, all parameters for ‘Second Fault Rapture Conditions’should be given to be zero. It should be noted that ‘Fault depth’ is deﬁned
by depth of the fault bottom d in ELMO (see Fig. 1.7) while depth at thefault top dtop may be used in some fault models for scenario tsunami. d canbe estimated with dtop byd = dtop + W tan δ sin θ(2.1)

where δ is the dip angle，W is the rapture width and θ is the rake angle.
File input of the fault parameters
Fault models for past and scenario tsunami, commonly provided, are composed by many fault segments to describe asperity and local orientation of

CHAPTER 2. TUTORIAL

20

Figure 2.8: Input window for fault parameters
the raptures (Fig. 2.9). In ELIMO, arbitrary fault parameters for multiple
segments can be given by a batch ﬁle input. For instance, if the parameters for 12 segments described in Fig. 2.9 are provided by Table 2.2 (These
parameters will be explained again in §4), as shown in Fig. 2.10, the parameters for each segment are described on each line in order of latitude,
longitude, rapture length, rapture width, slip-length, strike, dip, rake andfault depth with space or comma separation. It should be noted that ‘Fault
depth’ is deﬁned by depth of the fault bottom d in ELMO (see Fig. 1.7). If
depth at the fault top dtop is deﬁned in past fault models, d estimated by
Eq. (2.1) needs to be provided in the ﬁle. Add lines for the parameters of
all segments; in the case of Fig. 2.9, every parameters of 12 lines should be
written and saved with arbitrary ﬁle name.
Submarine Mass Failure Conditions (Manual)Parameter input for submarine landslide tsunami using SMF model is explained bellow.
For ”Which tsunami to compute?”, select ”Plate Boundary Earthquake
Tsunami Only”, ”Submarine Landslide Tsunami Only”, or ”Both”. Input
the following parameter (see section 1.2.4);
1. ”Longitude of SMF center (deg)”
2. ”Latitude of SMF center (deg)”CHAPTER 2. TUTORIAL

21

Figure 2.9: Fault segments of the scenario tsunami of Hokkaido oﬀ earthquake.
3. ”Latitude of SMF center (deg)”
4. ”Length of SMF along seabed slope (km)”; b
5. ”Width of SMF (km)”;w
6. ”Characteristic wavelength; lambda0 (km)”; λ0
7. ”Parameter Kappa’”; parameter controlling double Gaussian distribution κ′ （ratio of positive and negative initial surface displacements in
Fig. 1.10）
8. ”Parameter Delta x (km)”; shape parameter of double Gaussian distribution ∆x (km)Here depth of initial SMF d and bed slope θ are automatically estimatedfrom the bathymetry data. κ=3 is given as constant.
Computing Conditions
Input the maximum time step number, time-step interval for saving output
ﬁles (e.g. if 3 is given, the data ﬁles are saved every 3 time steps) , number

22

CHAPTER 2. TUTORIAL

Fault 1
Fault 2
Fault 3
Fault 4
Fault 5
Fault 6
Fault 7
Fault 8Fault 9Fault 10
Fault 11
Fault 12longitude(o )147.5584
146.8476
146.1445
145.4488
144.7606
144.1726
147.0946
146.3802145.6735
144.9746
144.1716
143.5836

latitude(o )42.413542.070341.7226
41.3704
41.0140
40.5693
42.942142.596242.2457
41.890741.460841.0132

length
(km)
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0

width
(km)
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0

slip length
(m)
35.0
35.0
35.0
35.0
35.0
35.0
30.0
30.0
30.0
30.0
30.0
30.0

strike
(o )
235
235
235
235
225
225
235
235
235
235
225
225

dip
(o )
10
10
10
10
10
10
20
20
20
20
20
20

rake
(o )
90
90
90
90
90
90
90
90
90
90
90
90

depth (fault top)
( km)
5.0
5.0
5.0
5.0
5.0
5.0
17.0
17.0
17.0
17.0
17.0
17.0

Table 2.2: Fault parameters for the segments of the scenario tsunami of
Hokkaido oﬀ earthquake (corresponding to Fig. 2.9).
of grids contained in a sponge zone (dlayer in §1.2.2), and the maximum
dissipation rate in a sponge zone (Amax in §1.2.2). dlayer and Amax may be
adjusted if unacceptable reﬂection occurs at the open boundaries (dependingon size and location of the computing domain).
Conﬁrming the computing conditions
Click ‘OK’ on the window of ‘Calculation Condition’.

2.2.3

Run computation

Menu ‘Simulation’ → ‘Run’．Duration from the tsunami generation is displayed on a console screen.

2.2.4

Visualizing the results

How to visualize the results is explained in iRIC Users Manual; such as contours, vector plots, animation of the results. In this chapter, only particular
operations required in ELIMO are explained.
1. ‘Calculation Result’ → ‘Open new 2-D Post-Prosessing Window’
2. Click a check box of ‘SElevation’ in ‘Elimo Grids’¿‘iRIVZone’¿‘Scalar’on Object Browser (Fig. 2.11)．

CHAPTER 2. TUTORIAL

23

Figure 2.10: Parameter text ﬁle for the ﬁle input.
3. Right click on ‘SElevation’ and select ‘Property’ to set up graphycs(color bar, color range and so on)．
4. When you choose one on the list of ‘Background Images (Internet)’ on
Object Browser, your result is superposed on the selected map (Fig.
2.11)．
5. Sequential images of the computed results every output time step aredisplayed if you operate in menu ‘Animation’．

CHAPTER 2. TUTORIAL

Figure 2.11: Visualized surface elevation 「SElevation」

24Chapter 3

Examiples of Computations
3.1

The 2011 Tohoku earthquake tsunami

Figure 3.1: Propagation of the 2011 Tohoku tsunami (10 min interval fromtsunami generation)．
The Geospatial Information Authority of Japan provided the rectangle
fault model for the 2011 Tohoku earthquake with following parameters. In
this model, the depth of fault is deﬁned at the top of fault. The fault depths,
deﬁned at the bottom in ELIMO, are estimated by Eq. (2.1) to be 37.4 km
25

26

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

Fault 1
Fault 2latitude
(o )
39.00
37.21

latitude(o )143.49142.51

length
(km)
199
176

width
(km)
85
82

slip length
(m)
27.7
5.9

strike
(o )
202
201

dip
(o )
18
15

rake
(o )
97
81

Fault depth
( km)
10.0
10.1

and 31.8 km. Therefore, the estimated depths, 37.4 and 31.8, need to be
described on ‘First and Second Rapture Condistions’ instead of 10.0 and
10.1 in Table 3.1. As many fault models using the depth of fault top havebeen proposed, Use should conﬁrm the deﬁnition of the parameter used in
the model.
Fig. 3.1 shows the contours of the surface elevation of the tsunami until
one hour after the earthquake. It is seen that the tsunami radically spreads
at an early stage, arrives to Iwate prefecture at 10 – 15 minutes, Hokkaido
and Kita-Kanto areas after one hour. These computed arrival of the tsunami
are consistent with the observed ones.

3.2

Comparisons with the observed surface elevation

Kawai et al. (2013) reported the surface elevation of the 2011 Tohoku
tsunami measured by GPS buoys installed Tohoku oﬀ. Fig. 3.2 shows theobserved surface elevations presenting rapid evolution of the tsunami wave
shapes.
Fig. 3.3 shows the initial stage of the computed surface elevations at
the corresponding locations to the GPS stations. We ﬁnd overall features of
the computed tsunami evolution are consistent with the observed ones despite that the simplest rectangular fault model are used in the computation.
Improvement of accuracy is expected by introducing polished fault models
with asperity.

3.3

Submarine landslide tsunami

M 7.5 earthquake occurred on Sulawesi, Indnesia o the 28th of September,
2018. Tsunami has been observed around coast of Palu Bay after 30 min
later the earthquake. The analyses of this tsunami conclude submarine
landslides induced by the earthquake generated the tsunami (Nakata et al.
2020).
While there have been many studies on magnitude and area of landslide,
as an application of SMF model, the computed tsunami based on a scenario

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

27

Figure 3.2: Observed surface elevations at the GPS tide stations (After
Kawai et al. 2013)．
that a submarine landslide occurred oﬀ Palu is shown here.
Fig. 3.4 shows evolution of the submarine landslide tsunami. While
resolution of bathymetry data is not enough to compute local tsunami near
the coast, overall features of the propagation with reﬂection in the bay canbe found from the results.

3.4

Scenario tsunami

Many fault models for scenario tsunamis, expected to occur in future, havebeen proposed by the governments and research institutes, which provides
possible tsunami heights along coasts of Japan. Most models composed ofmultiple fault segments can be used on ELIMO by the function of the batch
ﬁle input.

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

28

Figure 3.3: Computed surface elevations at the GPS tide stations.
The government of Hokkaido, Japan, deﬁned the scenario tsunami that
may cause the maximum inundation on Paciﬁc coasts of Hokkaido, andprovided the fault model. In this model for the extreme tsunami, 12 fault
segments with the parameters in Table 3.1 are assumed to adjacently locate
as shown in Fig. 3.5.
The text parameter ﬁle for Table 3.1 are shown in Fig. 3.6. The line
number corresponds to the fault number. The parameters for each segment,latitude, longitude, rapture length, rapture width, slip-length, strike,
dip, rake and fault depth with space or comma separation, are describedon each line. As already explained, ‘Fault depth’ is deﬁned by depth of thefault bottom d in ELMO (see Fig. 1.7). If depth at the fault top dtop is
deﬁned in past fault models, d estimated by Eq. (3.1) needs to be provided
in the ﬁle.
d = dtop + W tan δ sin θ(3.1)
where δ is the dip angle，W is the rapture width and θ is the rake angle.
For example, for Fault 1 – 6, 5+70 ×tan(10×π/180)×sin(90×π/180) ≈17.3, and for 7 -12, 17 + 70 × tan(20 × π/180) × sin(90 × π/180) ≈ 42.5
should be written in the ﬁle as ‘Fault depth’ instead of 5.0 and 17.0. Every
parameters of 12 lines are written and saved with arbitrary ﬁle name for thebatch input.

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

29

Figure 3.4: Sea level changes owing to the 2018 Palu tsunami, Sulawesi,
Indonesia (5 min interval)
Fig. 3.7 shows the evolution of the Hokkaido scenario tsunami generated
by the model of Table 3.1 . The tsunami, generated by the fault displacements over a wide area, radically propagates and reach to the Paciﬁc coasts
after 10 – 20 minutes. The ﬁrst wave of tsunami arrives at most coasts of
Hokkaido and Tohoku after 30 minutes, and formations of edge waves are
conﬁrmed after 50 minutes.
Fig. 3.8 presents the computed surface elevations (not by ELIMO) reported by the government of Hokkaido. We ﬁnd the analogous features oftsunami elevations to Fig. 3.7.
I this way, ELIMO can simulate arbitrary tsunami generated by any
model without any limitation of number of segments.

30

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

Figure 3.5: Fault segments of the scenario tsunami of Hokkaido oﬀ earthquake.

Fault 1
Fault 2
Fault 3
Fault 4
Fault 5
Fault 6
Fault 7
Fault 8Fault 9Fault 10
Fault 11
Fault 12longitude(o )147.5584
146.8476
146.1445
145.4488
144.7606
144.1726
147.0946
146.3802145.6735
144.9746
144.1716
143.5836

latitude(o )42.413542.070341.7226
41.3704
41.0140
40.5693
42.942142.596242.2457
41.890741.460841.0132

length
(km)
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0

width
(km)
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0
70.0

slip length
(m)
35.0
35.0
35.0
35.0
35.0
35.0
30.0
30.0
30.0
30.0
30.0
30.0

strike
(o )
235
235
235
235
225
225
235
235
235
235
225
225

dip
(o )
10
10
10
10
10
10
20
20
20
20
20
20

rake
(o )
90
90
90
90
90
90
90
90
90
90
90
90

depth (fault top)
( km)
5.0
5.0
5.0
5.0
5.0
5.0
17.0
17.0
17.0
17.0
17.0
17.0

Table 3.1: Fault parameters for the segments of the scenario tsunami of
Hokkaido oﬀ earthquake (corresponding to Fig. 2.9).

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

31

Figure 3.6: Parameter text ﬁle for the ﬁle input.

Figure 3.7: The surface elevations along Hokkaido coasts by Hokkaido scenario tsunami, computed by ELIMO (10 minutes intervals).

CHAPTER 3. EXAMIPLES OF COMPUTATIONS

32

Figure 3.8: The surface elevations along Hokkaido coasts by Hokkaido scenario tsunami, reported by the local government of Hokkaido.

Conculding Remarks
Large earthquakes exceeding M8 are expected in near future, such as Tokai,
Nankai trough and Nemuro-oﬀ earthquakes. Multiple approaches for reducing tsunami disaster and minimizing damage expected for such earthquake
should be considered in a rush. We hope ELIMO that enables general users
to perform the tsunami computation supports developments of these approaches and improve education for disaster prevention.
June, 2023
ELIMO development teamYasunori Watanabe (Hokkaido University)

Acknowledgment

Development of ELIMO is partially supported by research grant, River
Center of Hokkaido.

33

Bibliography[1] Orlanski, I. (1976): A simple boundary condition for unbounded hyperbolic ﬂows, J. Comp. Phys., Vol.21, pp.251-269.
[2] Goto H., Okayasu A. and Watanabe Y. (2013), Computational Wave
Dynamics, World Scientiﬁc, ISBN: 978-981-4449-70-0.
[3] Cruz E., Yokoki H., Isobe M. and Watanabe A. (1993)，Annual journalof coastal engineering, JSCE, 40, pp. 46 –50.
[4] Watanabe Y., .Mitobe Y., Saruwatari A., Yamada T., Niida Y., (2012)
Evolution of the 2011 Tohoku earthquake tsunami on the Paciﬁc coastof Hokkaido, Coastal Engineering Journal, 54 (1), 1250002[5] Okada Y. (1985): Surface deformation due to shear and tensile faults
in a half-space, Bull. Seism. Soc. Am., Vol. 75, pp.1135 - 1154.
[6] Tanioka Y. and Satake K. (1996): Tsunami generation by horizontal
displacement of ocean bottom, Geophysical Research Letters, Vol. 23,
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[7] Hiroyasu Kawai, Makoto Stoh, Koji Kawakuchi and Katsumi Seki,Characteristics of the 2011 Tohoku tsunami waveform aquired aroud
Japan by NOWPHASE equipments, Coastal Engineering Journal,
55(3), 2013.
[8] Watts, P., Grilli, S.T., M.ASCE, Tappin D.R., Fryer G.J., Tsunami
generation by submarine mass failure. II: Predictive equations and cases
studies, J. Waterway, Port, Coastal and Ocean Engineering, 131:6, 298– 310, 2005
[9] Nakata K., Katsumata A., Muhari A., Submarine landslide source models consistent with multiple tsunami records of the 2018 Palu tsunami,
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34