Computational Analysis of Tsunami Wave Behaviour for Three
Historical Tsunami Events using T-Impulse Model
SYED MOHAMED E.1, 3216(/9$1&0.2
1Department of Computer Science & Engineering,
B. S. Abdur Rahman Crescent Institute of Science and Technology,
Chennai,
INDIA
2Curtin University,
Dubai,
UAE
Abstract: - Natural catastrophes pose a serious threat to both human life and the environment because they are
unpredictable. One of the most devastating natural disasters is a tsunami, and forecasting models are essential
to preventing catastrophic damage to the environment and people along the coast. In the Impulse model, the
generation of a tsunami depends on the impulse force generated during the event. Understanding tsunamis
begins with simulating the tsunami generation process. This process involves simulating both the motion of
the seafloor and the subsequent motion of the water above for tsunamis caused by underwater earthquakes.
This modeling strategy can mimic all three stages of a tsunami: generation, propagation, and run-up. Three
separate earthquake tsunami events—the 1755 Lisbon earthquake, the 1964 Alaska earthquake, the 2004
Sumatra earthquake are each investigated in this research. To demonstrate its relevance to current events and
various ocean locations, the results of these events are compared and confirmed with the observed data.
Analyzing the parameters used in this modeling study and identifying the parameter that has the most
influence will demonstrate their significance in tsunami generation. The seabed displacement profile, seawater
deformation, changes in tsunami characteristics during propagation, the tsunami's travel time, earliest arrival
time, the tsunami wave height at the coast, and inundation distance are the anticipated findings from this
study. The major objective of this study is to obtain the maximum and most accurate result possible using the
fewest parameters possible.
Key-Words: - Impulse modelling, Tsunami wave, Fault slip variation, Fault boundary, Tsunami travel time,
Fault boundary, 1755 Lisbon tsunami, 1964 Alaska tsunami, 2004 Sumatra tsunami.
Received: March 13, 2023. Revised: November 27, 2023. Accepted: December 7, 2023. Published: December 31, 2023.
1 Introduction
More than 70% of the Earth's surface is covered by
water, and underwater disruptions resulting from
earthquakes, landslips, volcanic eruptions, or
meteorite impacts can lead to tsunamis, posing
significant risks to human life and the
environment, [1]. The behavior of tsunami waves
can be predicted using tsunami wave modeling,
which is crucial for taking precautions to protect
lives from severe harm.
Although tsunamis are a common natural
occurrence worldwide, they most frequently
happen in the Pacific Ocean due to seismic and
volcanic activity associated with tectonic plate
boundaries in the Pacific Ring of Fire. The earliest
known tsunami occurred around 479 BC when a
Persian army advancing on the Greek town of
Potidaea was wiped out, [2]. While thousands of
tsunamis have been documented throughout
history, the 2004 Sumatra-Andaman tsunami,
which affected more than 15 nations, is considered
the deadliest tsunami ever.
In this analysis, we considered three historical
tsunami events covering three oceanic regions
(Atlantic Ocean, Indian Ocean, Pacific Ocean) and
three continents (Asia, Europe, North America,).
We focused on historical earthquake-generated
tsunami events: the 1755 Lisbon tsunami, [3],
1964 Alaska tsunami, [4], [5], 2004 Sumatra
tsunami, [6]. Figure 1 displays the bathymetry
profile of the world's oceans.
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Fig. 1: Bathymetry elevation profile in the
worldwide (NOAA)
In this study, the impulse model was employed
to evaluate all three stages of the tsunami. The
generation phase was simulated using seismic
information on the impulse force produced during
the earthquake. The tsunami propagation phase
was constructed with the aid of the Boussinesq
approximation and solitary wave theory, [7].
During this phase, the complete spectrum of
tsunami characteristic changes was evaluated
along the wave propagation path. The link between
the direction of propagating waves and the
topography of the beach was used to design the
final run-up phase.
The modeling provides the tsunami's earliest
arrival time based on the close distance of the
source and destination locations. These results are
attained due to factors such as tsunami wave
propagation characteristics, seabed displacement,
wave height at the coast, tsunami travel duration,
and the tsunami's earliest arrival time, all
influencing how a tsunami behaves.
The 1964 Alaska earthquake, with a moment
magnitude of Mw = 9.2, surpassed all previous
records for size, [8], [9]. Early calculations placed
the rupture's length, parallel to the Alaska-Aleutian
trench's strike, between 600 and 800 km, [10], [11]
and its rupture velocity, [12], [13], between 3 and
3.5 km/s. The rupture extended from Prince
William Sound to the Kenai Peninsula and beyond
Kodiak Island.
The Indian Ocean tsunami on December 26,
2004, is considered the worst tsunami in history,
causing damage and impacting more than 15
nations bordering the Indian Ocean, [14]. The
Sumatra-Andaman earthquake, with a magnitude
larger than 9.3, occurred when the Indian Oceanic
plate was being subducted beneath the Burma plate
and a portion of the Sunda plate, [15].
In the 2004 Sumatra tsunami, MOST
calculations indicated a maximum slip height
between 5m and 10m, and a close-up of the
estimated wave heights in the Bay of Bengal
showed a tsunami wave with a height of 70 cm and
greater than 2m recorded on the coast of the Bay
of Bengal, [16].
Python programming is used to create
graphical representations of working tsunami wave
models. It is used to calculate the rate at which a
tsunami wave spreads for three historical Tsunami
events under three different ocean types’ wave
circumstances.
This paper's first portion examines the several
methods currently in use for modeling the rate at
which tsunami waves propagate.
The fundamentals of impulse model
mathematical formulation are covered in section 2.
Section 3 presents the analysis of historical
tsunami events of the homogeneous ocean
modules are examined and the outcomes of their
simulations results.
The paper is concluded in Section 4.
2 Impulse Model Mathematical
Formulation
There are three main phases in the evolution of
earthquake-induced tsunami waves: generation,
propagation, and run-up. The impulse model
employed in this study comprehensively computes
all three stages of tsunami waves.
2.1 Tsunami Generation
The impulse model is utilized to simulate a
tsunami triggered by an underwater earthquake.
During an earthquake, the seafloor experiences
movement, leading to a significant displacement of
the water above the sea. This displacement is
attributed to an impulse force resulting from the
release of a considerable quantity of earthquake
energy. Assuming the seafloor is initially at rest,
with the velocity of the seabed in the x, y, and z
directions (u, v, and w) being zero at time t=0, the
seabed begins to shift due to the impulse force
until it reaches a time known as the rising time
required for seabed displacement.
Various forces, including the body force by the
fault and the hydrostatic pressure force by
saltwater, oppose the seabed's displacement. An
impulse force (F) is exerted on the seabed to
displace it. The motion of the shifting seabed can
be derived using Newton's third law of motion.
The formula for calculating the impulsive force
(FI) created to shift the seabed is as follows: The
body force by the fault and hydrostatic pressure
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force by saltwater are the forces opposing the
seabed from displacement, an impulse force (F) is
exerted on the seabed to displace it. The motion of
the shifting seabed can be derived with the use of
Newton's third law of motion. The formula for
calculating the impulsive force (FI) created to shift
the seabed is as follows:
  (1)
For the purpose of moving the seabed, the
rising time (t1) is computed using,

(2)
Seabed movement is calculated using the
below equations and these are applicable in the
following conditions are, the time is ,
the horizontal boundary condition in ‘x’ direction
is  .









󰇣

󰇤

(3)
From Equation (1) to (3), the symbols represent
the following:
M: Magnitude of the earthquake
μ: Shear modulus of the earth's crust at the
point of generation
Af: Area of the fault
Mo: Seismic moment
Sf: Fault slip factor
ms: Seabed mass
FI: Impulse force
Subscripts 's' and 'w' represent the seabed and
seawater, respectively. Symbols include:
m: Mass
ρ: Mass density
V: Volume of the displaced seabed
A: Area
dw: Average depth of the water
FIx: Horizontal impulse force
FIz: Vertical impulse force
Fg: Body force
FH: Hydrostatic pressure force
u, w: Horizontal and vertical velocities in
x and z directions
g: Gravity acceleration
Consider a fluid domain in three dimensions
that is unbounded in the x, y of horizontal and
bounded in z of vertical direction. The domain's
initial conditions are (i) fluid equilibrium, (ii)
seawater velocity (u = v = w = 0 in x, y, and z
directions), and (iii) z = = 0 at the free surface and
z = -h near the seafloor. To mimic the creation of
tsunami waves more effectively, the momentum
change of the seabed is equated to that of the
saltwater above it. The governing equations are
applicable in the following conditions are,
  ,  .



  (4)
The velocity of seawater due to the seabed and
beginning seawater elevation is estimated by
deriving the following equation, Because the
average water depth is used in this generation
region, the velocity doesn't depend on the space
dU/ds = 0, U(u, v). The following equations are
derived from equation (4) to account for the
additional impulse force caused by the bottom
moment when determining the velocity of
seawater in the x, y, and z directions:

 
 
 


 (5)

 󰇛󰇜

 


 (6)
Equation (5) above is used to get the seawater
velocity in the direction of elevation of displaced
water in the x and y directions, and equation (6) is
used to determine the seawater velocity in the z
direction. The calculation for seawater subsidence
goes the other way from elevation. To calculate the
sinking of seawater, the vertical velocity is
multiplied by the gravitational force.
2.2 Tsunami Propagation
After the tsunami was generated, the wave began
to spread from a source point in all directions. The
tsunami wave travels over very long distances
without significantly reducing its energy. This
tsunami wave propagation modelling makes use of
the solitary wave theory and the Boussinesq wave
approximation. This includes the dispersion
relationship because the tsunami wave modelling
takes into account the changing bathymetry.
The domain boundary is expressed as Ω = R2
[-d + ξ(x, y, t), η(x, y, t)] because the bottom
boundary shifts after an earthquake depending on
the type of fault. Where, η is the vertical elevation
of the sea surface and ξ is the height of the sea bed
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deformation. The seafloor is rigid, and
impermeable; the flow is irrotational; the fluid is
ideal; surface tension is disregarded; the pressure
at the free surface is constant; the wave height is
minimal in relation to the wave length; and the
potential flow theory is applicable. The vertical
boundary condition is changes to,
 󰇛󰇜 󰇛󰇜.

 
 


 
 


 


 
 


 
 (7)
Since the tsunami wave has a long period and
the pressure at the free surface is nil, the wave
height (H) is smaller than the wavelength (L).
Using equation (6) to obtain the pressure changes
at the bottom during the earthquake event, vertical
acceleration is omitted for the long wave
approximation, i.e. Du/Dt = 0, and the force acting
on the seawater owing to the displacement of the
seabed is applied. The below equation's negative
sign denotes a pressure that is greater than the
normal pressure as measured at the bottom and
acting in an upward vertical direction. The
development of tsunamis can be seen in the rising
pressure. An early warning system for tsunamis
uses a bottom pressure recorder to help determine
the bottom pressure when a tsunami is coming.
󰇛󰇜󰇣󰇛 󰇜󰇛󰇜
 󰇤(8)
3 Analysis of Historical Tsunami
Events
The following information is needed for this
Impulse modelling study. These information
pertains to earthquake, tsunami, and ocean
bathymetry. The General Bathymetric Chart of the
Oceans (GEBCO), the National Oceanic and
Atmospheric Administration (NOAA), and the
United States Geological Survey provided the data
on bathymetry, earthquake, and tsunami events,
respectively. Here, the origin is assumed to be the
earthquake epicenter. The distance from the
epicenter is indicated by the length in latitude and
longitude.
The fault boundary line is mathematically
determined using the curve fitting approach, which
aids in discretizing the fault line into intervals
based on rupture velocity. The sea surface
deformation can be calculated by using the
estimated seabed deformation in both the
horizontal and vertical directions provided by the
impulse force. The rise in water level on the ocean
side, which spreads as a far-off tsunami, and the
decline in water level on the shoreside which
propagates as a close-by tsunami, are both
examples of this sea surface deformation. Seabed
movement causes the sea surface to be raised in
the direction of overriding; the height of the
elevation is a function of the water depth at the
fault location and the impulsive force brought on
by the seabed movement.
When a tsunami first rises, it resembles an N-
type wave and is characterized by uplift on the
ocean side (Distant tsunami) and downward dips
on the beach side (local tsunami). The vertical
velocity will be zero if the water is displaced to its
maximum height. Here, it is assumed that the point
of maximal water displacement marks the
beginning of the tsunami's spread in directions
orthogonal to that of the rupture. As a result, an
equal amount of the potential energy of the
displaced water is transferred, which is the energy
that will cause the tsunami wave to propagate
further. Assumes the fluid moves in all eight
directions from the commencement point as a
result of the energy being distributed in a circular
pattern.
Once the tsunami starts, it disrupts the entire
ocean's depth, and this wave propagates alone (in
shallow water, a wave's wavelength is greater
than the depth of the water). The water depth along
the path of the tsunami wave propagation affects
the wave properties (wave height, amplitude, and
wavelength) for shallow-water waves. There are
no obstructions in the tsunami wave's path in this
wave propagation zone. As a result, it is regarded
as a homogenous situation with a variable ocean
floor. Every node calculates the wave properties
and the interval spacing of 500 m. assuming the
tsunami wave propagated as a solitary wave and
was driven by the energy of displaced water
transferred to the water molecules. Using the linear
frequency dispersion relationship, the wavelength
and wave period may be calculated. The depth of
the sea determines the height of a tsunami wave.
The increasing water depth causes the tsunami
wave height to decrease towards the ocean. But at
the coast, tsunami wave height increases with the
reducing water depth.
In this paper, the generation and propagation
phases of tsunami were analyzed in detail. The
following results are anticipated from the impulse
modelling:
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(i) Data on seabed deformation;
(ii) Properties of deep-ocean tsunami waves;
(iii) Tsunami wave characteristics at the shore;
(iv) Travel duration of the tsunami wave to reach
the destination; and
(v) Tsunami wave's earliest arrival time.
In this study, the three ocean basins where
earthquake tsunamis occur most frequently—the
Pacific Ocean, Atlantic Ocean, and Indian
Ocean—are used to test the applicability of the
Impulse modelling method. In order for the
tsunamis to affect as many nations as possible
across the three continents of Asia, Europe, and
North America, tsunami wave propagation
analyses were conducted. In this paper, the
following historical tsunami events are analyzed:
1. 1755 Lisbon tsunami
2. 1964 Alaska tsunami
3. 2004 Sumatra tsunami
Table 1. Symbols used in this paper, [17]
Sl.
No.
Symbols
Names
1
Lon
Longitude
2
Lat
Latitude
3
LR
Rupture length
4
TR
Rupture time
5
dS
Slip variation along the fault
6
Ho
Tsunami wave height in the deep
ocean
7
C
Wave celerity
8
L
Wave length
9
T
Wave period
10
D
Distance b/n source and destination
11
ETH
Estimated tsunami height at coast
12
ETT
Estimated tsunami travel time
13
EAT
Estimated arrival time of tsunami
14
OTH
Observed tsunami wave height at
coast
15
OTT
Observed tsunami travel time
16
ΔH
Difference b/n observed and
estimated tsunami height at coast
17
ΔT
Difference b/n observed and
estimated tsunami travel time
Table 1 shows the symbols and names of
T-impulse model for tsunami wave.
3.1 1755 Lisbon Earthquake
The Great Lisbon earthquake struck Portugal, the
Iberian Peninsula, and Northwest Africa on
November 1 at approximately 9:40 local time.
Everything close by was nearly completely
destroyed by the earthquake's aftermath, including
subsequent flames and a wave. Seismologists
believe the Lisbon earthquake had a magnitude of
7.7 or higher and had its epicenter in the Atlantic
Ocean around 200 km west-southwest of tip St.
Vincent, a tip in the Algarve region, and about 290
km southwest of Lisbon. It was the city's third
known large-scale earthquake in chronological
order (after those of 1321 and 1531).
Approximately 12,000 people are thought to have
died in Lisbon, making it one of the worst
earthquakes in recorded history.
Fig. 2: Modelling study area of the 1755 Lisbon
Earthquake
Figure 2 shows the modelling study area of the
1755 Lisbon earthquake, the line indicates the
plate boundary between the Eurasian plate and
African plate, the red mark indicates the Lisbon
earthquake epicenter, and rectangular region
shows tsunami generation zone. The earthquake's
epicenter is located at 37.00 0N and 10.00 0W. The
rupture proceeded with a speed of 1.7 km/s
westward and took 3 1/2 to 6 minutes to go 360
km rupture length.
Table 2. Earthquake information data for the 1755
Lisbon earthquake tsunami (U.S. Geological
Survey)
Parameters
Values
Date
1/11/1755
Initiation time
09:30:00 UTC
Source
Lisbon, Portugal
Epicentre
10.000W, 37.000N
Magnitude
8.5
Focal depth
8 km
Fault length
360 km
Fault width
80 km
Dip angle
40°
Rupture duration
3 ½ to 6 minutes
Table 2 shows information about the
earthquake that caused a tsunami wave on
November 1, 1755 in Lisbon, Portugal collected
from the U. S. geological survey. Table 3 shows
the estimated values of tsunami-generating
parameters in the 1755, Lisbon tsunami. The
slip of the fault is estimated by Kannamori
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calculations to be 81.938 m for a dip value of 40o.
Near the epicenter 52.67 m maximum vertical
displacement of the fault was calculated.
On the south side, it is determined that the
maximum height of the seafloor increase and the
horizontal displacement are 52.67 m and 62.76 m,
respectively. The propagated tsunami waves were
travel in the Atlantic Ocean region.
Table 3. 1755 Lisbon earthquake – Estimated
values of tsunami generating parameter
Sl.
No.
Parameters
Values
Units
1
Earthquake energy
3.55E+17
J
2
Seismic Moment
7.08E+21
Nm
3
Impulse force
4.33E+15
N
4
Slip
52.66884
M
Figure 3 shows the fault boundary coordinates
of Lisbon earthquake fit to the curve to discretize
the fault line in the interval spacing 1.7 km
depending on the rupture velocity (v = fault
length/rupture duration or 360/211.75 = 1.7) to
find the earthquake fault zone where the tsunami
waves are generated. Using the discretization helps
to find the fault slip variation along the fault
boundary line that indicates in Figure 4 for the
1755, Lisbon earthquake.
Fig. 3: 1755 Lisbon earthquake fault boundary line
with curve fitting
Fig. 4: Fault slip variation along the Lisbon
earthquake fault boundary line
The Lisbon Earthquake (1/11/1755) was
initiated at the time of 09 hours 30 minutes UTC.
The rupture begins at the epicenter (10.00 0W,
37.00 0N). Rupture propagate westward in the fault
boundary, It took 211.75 seconds to reach the
rupture length of 359.9 km. The total time for
rupture is estimated as 211.75 seconds or 3
minutes 31 seconds, and the slip variation near the
epicenter is a maximum of 52.67 m and it varies
along the fault between 3 m and 52.67 m (U. S.
Geological Survey) that given in Table 4.
Table 4. The seabed deformation along the fault
boundary line of 1755 Lisbon Earthquake
Nodes
Lat (oN)
Lon(oW)
LR,
km
TR, s
dS, m
1
36.305
10.200
39.99
23.52
46.81
2
36.453
10.603
79.33
46.67
41.06
3
36.584
11.008
117.9
69.38
35.41
4
36.696
11.413
155.8
91.67
29.86
5
36.788
11.819
193.1
113.6
24.41
6
36.858
12.225
229.9
135.2
19.03
7
36.910
12.632
266.3
156.6
13.69
8
36.944
13.038
302.6
178.0
8.394
9
36.96
13.445
338.7
199.2
3.108
Table 5 depicts the destination that is selected
for this modelling to analyze the behavior of
tsunami waves. The deep ocean tsunami wave
characteristics caused by the Lisbon earthquake in
1755 are shown in Table 6. In the deep ocean, a
tsunami's wave height is estimated to be between
0.4 and 1.13m, its propagation speed is calculated
to be between 84 and 195 km per second, its
wavelength is calculated to be between 70 and
1050 km, and its period is calculated to be between
14 minutes and 1 hour 30 minutes.
-13.0 -12.5 -12.0 -11.5 -11.0 -10.5
35.6
35.8
36.0
36.2
36.4
36.6
36.8
Latitude (N)
Longitude (W)
3.000
8.500
14.00
19.50
25.00
30.50
36.00
41.50
47.00
Slip, m
Slip variation along the fault line of 1755 Lisbon Earthquake
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Table 5. Selected destination for this modeling
Sl. No.
Location
1
Portugal-Azores
2
Penzance, England
3
Mounts Bay, England
4
Gibraltor, Spain
5
Hayle, England
Table 6. Characteristics of the first tsunami wave
to arrive at the destinations in the 1755 Lisbon
tsunami
Locati
on
Lat
(oN)
Lon
(oW)
Ho, m
C,
km/s
T,
hh/mm/
ss
1
38.72
27.22
1.14
187.4
0.52.49
2
50.117
5.55
0.81
103.6
0.19.08
3
50.033
5.417
0.66
84.97
0.14.12
4
36.15
5.35
0.47
195.9
1.30.04
5
50.167
5.417
0.73
93.71
0.16.30
Table 7 shows the results of the first tsunami
wave to reach the defined destination by using the
Impulse modelling for 1755, Lisbon earthquake
tsunami. From the historical data, the tsunami
wave height at the coast of locations given in the
table is obtained. By comparing the results of
historical observed data with the estimated data
shows the Impulse modelling study can be applied
to real-time tsunami events to determine the
tsunami wave behavior.
Table 7. The initial tsunami wave's outcomes at the
coastline of the destinations in the 1755 Lisbon
tsunami
Location
D, km
ETH,
m
ETT,
hh/mm/ss
EAT,
hh/mm/ss
1
1512
1.972
2.49.13
12.19.52
2
1576.8
2.876
2.14.31
11.44.31
3
1571.9
2.352
2.13.25
11.43.25
4
417.80
1.951
1.20.05
10.50.05
5
1585.9
1.740
2.28.11
11.58.11
The link between the historical and estimated
tsunami wave height at each location from the
1755 Lisbon earthquake is shown in Table 8.
The table shows that there is a very tiny,
potentially inconsequential, discrepancy between
historical and estimated tsunami wave heights near
the shore, which can be corrected in the future.
The average percentage of accuracy of estimated
values is obtained as 86.38%.
Table 8. Relationship between the historical
(NOAA) and estimated 1755 Lisbon earthquake-
tsunami wave height at the destinations
Location
OTH,
m
ETH,
m
ΔH,
m
Accuracy
(%)
1
2
1.9722
0.028
98.61
2
2.44
2.8761
0.436
82.127
3
1.8
2.3528
0.553
76.5046
4
2.1
1.9518
0.148
92.9429
5
2.13
1.7406
0.389
81.7183
Figure 5 presents a comparison graph between
the historical and estimated tsunami wave heights
for the Lisbon tsunami of 1755, reaching different
destinations. Numerical numbers on the graph
correspond to the locations indicated in the table.
Historical tsunami wave height information along
the coast is derived from NOAA data. The graph
aims to illustrate the effectiveness of the Impulse
model in predicting the behavior of the tsunami
wave during the actual occurrence.
Fig. 5: Comparison graph between the historical
and estimated tsunami wave height at the
destinations due to the 1755-Lisbon
Earthquake-tsunami
3.2 1964 Alaska Earthquake
The 9.2-magnitude Prince William Sound
earthquake on March 28, 1964, now the second-
largest earthquake ever recorded, was the
easternmost megathrust earthquake. The
earthquake ruptured along a fault line
approximately 800 miles (1,300 km) long. The
event's rupture length extended approximately 700
km from Prince William Sound in the northeast to
the southern tip of Kodiak Island in the southwest.
This seismic activity occurred in the area
where the North American plate subducts beneath
the Pacific plate, giving rise to the Aleutian Islands
and the deep offshore Aleutian Trench through
subduction. Additionally, this megathrust
earthquake triggered a destructive tsunami,
causing damage along the Gulf of Alaska, the US
West Coast, and in Hawaii.
1 2 3 4 5
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
2
2.44
1.8
2.1 2.13
1.9722
2.8761
2.3528
1.9518
1.7406
Tsunami wave height at coast (m)
Location
Observed Tsunami height
Estimated Tsunami height
Tsunami wave height comparison for 1755, Lisbon Earthquake tsunami
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Fig. 6: Modelling study area of the 1964
Earthquake
Figure 6 shows the modelling study area of the
1964 Alaska earthquake, the line indicates the
Aleutian arc which is a plate boundary between the
North America plate and Pacific plate, the yellow
mark indicates the Alaska earthquake epicenter,
and rectangular region shows tsunami generation
zone. The earthquake's epicenter is located at
61.017 0N and 147.648 0W. The rupture proceeded
with a speed of 1.4 - 2 km/s in the southwest
direction and took 6 minutes 51 seconds to go
699.6 km rupture length.
Table 9. Earthquake information data for the 1964
Alaska earthquake tsunami (U.S. Geological
Survey)
Sl. No.
Parameters
Values
1
Date
28/3/1964
2
Initiation time
3:36:14 UTC
3
Source
Alaska
4
Epicenter
61.017oN, 147.648oW
5
Magnitude
9.2
6
Focal depth
33 km
7
Fault length
700 km
8
Dip angle
6 12o
9
Rupture velocity
1.4 – 2 km/s
Table 9 shows information about the
earthquake that caused a tsunami wave on March
28, 1964 in Alaska collected from the U. S.
geological survey.
Table 10 shows the estimated values of
tsunami-generating parameters in the 1964, Alaska
tsunami. The slip of the fault is estimated by
Kannamori calculations to be 114.62 m for a dip
value of 9o. Near the epicenter 17.93 m maximum
vertical displacement of the fault was calculated.
The rupture propagated towards the westward
direction, the South Pacific plate is subducted
under the North American plate. It is determined
that the maximum height of the seafloor increase
and the horizontal displacement are 17.93 m and
113.21 m, respectively. The propagated tsunami
waves were traveling in the Atlantic Ocean region.
Table 10. 1964 Alaska earthquake – Estimated
values of tsunami generating parameter
Sl. No.
Parameters
Values
Units
1
Earthquake energy
3.98E+18
J
2
Seismic Moment
7.94E+22
Nm
3
Impulse force
3.47E+16
N
4
Slip
17.93
m
Figure 7 shows the fault boundary coordinates
of Alaska earthquake fit to the curve to discretize
the fault line in the interval spacing of 1.7 km
depending on the rupture velocity to find the
earthquake fault zone where the tsunami waves are
generated. Using the discretization helps to find
the fault slip variation along the fault boundary
line that indicates in Figure 8 for the 1964, Alaska
earthquake.
Fig. 7: 1964 Alaska earthquake fault boundary line
with curve fitting
Fig. 8: Fault slip variation along the Alaska
earthquake fault boundary line
The Alaska Earthquake (28/3/1964) was
initiated at the time of 03 hours 36 minutes 14
seconds UTC. The rupture begins at the epicenter
-155 -154 -153 -152 -151 -150 -149
53
54
55
56
57
Latitude (N)
Longitude (W)
0.2000
2.063
3.925
5.788
7.650
9.513
11.38
13.24
15.10
Slip (m)
Slip variation along the faultline during 1964, Alaska Earthquake
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(147.648 0W, 61.017 0N). Rupture propagate
westward in the fault boundary, It took 411.47
seconds to reach the rupture length of 699.59 km.
The total time for rupture is estimated as 411.47
seconds or 6 minutes 51 seconds, and the slip
variation near the epicenter is a maximum of 17.93
m and it varies along the fault between 0.2 m and
17.93 m (U. S. Geological Survey) given in Table
11.
Table 11. The seabed deformation along the fault
boundary line of 1964 Alaska Earthquake
Nodes
Lat
(oN)
Lon
(oW)
LR, km
TR, s
dS, m
1
57.353
148.231
110.70
65.12
15.10
2
56.703
149.367
200.89
118.17
12.78
3
56.226
150.477
283.89
166.99
10.66
4
55.801
151.565
366.08
215.34
8.55
5
55.358
152.628
449.99
264.70
6.40
6
54.883
153.663
534.99
314.70
4.23
7
54.414
154.677
617.15
363.03
2.12
8
54.043
155.688
691.67
406.86
0.21
Table 12 depicts the destination that is selected
for this modelling to analyze the behavior of
tsunami waves. The deep ocean tsunami wave
characteristics resulting from the Alaska
earthquake in 1964 are presented in Table 10. In
deep ocean conditions, the estimated tsunami wave
height ranges from 0.42 to 48 meters, the
calculated propagation speed ranges between 22
and 218 kilometers per second, the wavelength is
estimated to be between 218 and 225 kilometers,
and the wave period is calculated to be between 10
and 15 minutes.
Table 12. Selected destination for this modelling
Sl.
No.
Location
1
Cape St Elias
2
Cape Chiniak
3
Kodiak Island
4
Old Harbor Kodiak
5
Cape Yakataga
6
Yakutat
Table 13. Characteristics of the first tsunami wave
to arrive at the destinations in the 1964 Alaska
tsunami, [17], [18], [19]
Location
Lat
(oN)
Lon
(oW)
C,
km/s
L, km
T,
hh/mm/ss
1
59.8
144.6
218.7
142.41
0.10.51
2
57.621
152.1
224.4
157.44
0.11.41
3
57.718
152.5
223.7
175.10
0.13.02
4
57.201
153.3
222.9
196.83
0.14.42
5
60.07
142.4
219.2
143.34
0.10.53
6
59.55
139.7
219.2
143.47
0.10.54
Table 13 depicts the distance and time reached
the first tsunami wave arrived in the destinations
using Latitude and Longitude in the 1964 Alaska
tsunami.
Table 14. The initial tsunami wave's outcomes
at the coastline of the destinations in the 1964
Alaska tsunami
Location
D, km
ETH,
m
ETT,
hour
EAT,
hh/mm/ss
1
283.4886
1.4
0.62
4.13.16
2
164.574
9.57
0.55
4.09.16
3
184.2267
6.3
0.723
4.19.37
4
157.6422
7.4
0.74
4.20.26
5
383.8488
3.89
0.83
4.26.08
6
472.7035
1.5
1.17
4.53.34
Table 14 shows the results of the first tsunami
wave to reach the defined destination by using the
Impulse modelling for 1964, Alaska earthquake
tsunami. From the historical data, the tsunami
wave height at the coast of locations given in the
table is obtained. By comparing the results of
historical observed data with the estimated data
shows the Impulse modelling study can be applied
to real-time tsunami events to determine the
tsunami wave behavior.
The connection between historical and
estimated tsunami travel times to reach specified
locations from the 1964 Alaska earthquake
tsunami is illustrated in Table 12. The table
indicates a minimal, potentially inconsequential,
discrepancy between historical and estimated
tsunami wave heights near the shore, which could
be addressed in future corrections. The average
percentage accuracy of estimated values is
calculated as 88.87%.
Table 15. Relationship between the historical
(NOAA) and estimated 1964 Alaska earthquake-
tsunami wave travel time to reach destinations
Location
OTT
(hours)
ETT
(hours)
ΔT,
mm/ss
Accuracy
(%)
1
0.7
0.62
4.48
88.5714
2
0.5
0.55
3.00
90
3
0.8
0.723
4.37
89.3499
4
0.8
0.74
3.36
92.5
5
0.7
0.83
7.48
81.4286
6
1.4
1.28
7.12
91.4286
Figure 9 presents a comparison graph between
the historical and estimated tsunami travel times
for the Alaska tsunami of 1964 to reach various
destinations. Numerical numbers on the graph
correspond to the locations indicated in the table.
Historical tsunami wave height information along
the coast is derived from NOAA data. The graph
aims to illustrate the effectiveness of the Impulse
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models in predicting the behavior of the tsunami
wave during the actual occurrence.
Fig. 9: Comparison graph between the historical
and estimated tsunami wave travel time to reach
the destinations due to the 1964-Alaska
earthquake-tsunami
3.3 2004 Sumatra Andaman Earthquake
The seafloor on the underlying Burma plate
ruptured in a northward direction during the
Sumatra-Andaman earthquake of 2004, elevating
seaward into the trench and subsiding landward
towards the shoreline. The rupture extended from
northwest Sumatra north to the Andaman Islands.
The earthquake's epicenter is approximately 110 to
130 meters from the fault boundary at 3.316°N and
95.854°E. The rupture travelled a distance of 1200
kilometers in 8 to 10 minutes at a pace of 2.5 km/s
towards the north.
Fig. 10: Modelling study area of the 2004
Sumatra-Andaman Earthquake
Figure 10 depicts the modeling study area of
the 2004 Off West Coast of Sumatra earthquake.
The red line indicates the plate boundary between
the Burma plate and the Indian plate, the red mark
signifies the Sumatra earthquake epicenter, and the
rectangular region outlines the tsunami generation
zone or earthquake fault zone. The earthquake's
epicenter is situated at 3.3160°N and 95.8540°E.
The rupture advanced at a speed of 2.5 km/s in the
Northward direction and took 7 minutes and 59
seconds to cover a rupture length of 1199.87 km.
Table 16 shows information about the
earthquake that caused a tsunami wave on
December 26, 2004 in the Off West Coast of
Sumatra collected from the U. S. geological
survey.
Table 16. The seabed deformation along the fault
boundary line of 2004 Sumatra Earthquake
Sl.
No.
Parameters
Values
1
Date
26/12/2004
2
Initiation time
00:58:53.4 UTC
3
Source
Off West Coast of
Sumatra
4
Epicentre
3.316oN, 95.854oE
5
Magnitude
9.15
6
Focal depth
30 km
7
Fault length
1200 km
8
Dip angle
8o
9
Rupture velocity
2.5 km/s
Table 17 shows the estimated values of
tsunami-generating parameters in the 2004
Sumatra, Indian Ocean tsunami. The slip of the
fault is estimated by Kannamori calculations to be
61.88 m for a dip value of 8o. Near the epicenter
8.61 m maximum vertical displacement of the fault
was calculated. The rupture propagated towards
the northward direction, the Indian plate in west
side is subducted under the Burma plate in east
side. It is determined that the maximum height of
the seafloor increase and the horizontal
displacement are 8.61 m and 61.88 m,
respectively. The propagated tsunami waves were
traveling in the Atlantic Ocean region.
Table 17. 2004 Sumatra earthquake – Estimated
values of tsunami generating parameter
Figure 11 illustrates the fault boundary
coordinates of the Sumatra earthquake, fitted to a
curve and discretized at interval spacings of 2.5
km. This discretization is based on the rupture
velocity and is crucial for identifying the
earthquake fault zone where tsunami waves are
generated. The process of discretization aids in
determining the fault slip variation along the fault
1 2 3 4 5 6
0.4
0.6
0.8
1.0
1.2
1.4
0.7
0.5
0.8 0.8
0.7
1.4
0.62
0.55
0.723 0.74
0.83
1.28
Travel time comparison for 1964 Alaska Earthquake tsunami
Travel time (hours)
Locations
Observed TT
Estimated TT
Sl.
No.
Parameters
Values
Units
1
Earthquake energy
3.35E+18
J
2
Seismic Moment
6.68E+22
Nm
3
Impulse force
5.41E+16
N
4
Slip
8.612
m
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boundary line, as indicated in Figure 12 for the
2004 Sumatra earthquake.
Fig. 11: 2004 Sumatra earthquake fault boundary
line with curve fitting
Fig. 12: Fault slip variation along the Sumatra
earthquake fault boundary line
The Off West Coast of Sumatra Earthquake on
December 26, 2004, was initiated at 58 minutes
53.4 seconds UTC. The rupture commenced at the
epicenter (95.8540E, 3.3160N) and propagated
northward along the fault boundary. It took 479.94
seconds to reach a rupture length of 1199.87 km.
The total time for rupture is estimated to be 479.4
seconds or 7 minutes and 59 seconds. The slip
variation near the epicenter is a maximum of 8.61
m, and it varies along the fault between 0.4 m and
8.61 m, as reported by the U.S. Geological Survey
(shown in Table 15).
Table 18. The seabed deformation along the fault
boundary line of 2004 Sumatra Earthquake
Nodes
Lat (oN)
Lon(oW)
LR, km
TR, s
dS, m
1
3.853
93.773
143.57
57.43
7.582
2
4.930
93.132
279.04
111.6
6.610
3
6.007
92.623
408.73
163.4
5.679
4
7.084
92.227
534.32
213.7
4.778
5
8.161
91.938
657.01
262.8
3.897
6
9.238
91.753
777.81
311.12
3.030
7
10.31
91.679
897.87
359.15
2.168
8
11.39
91.733
1018.8
407.54
1.300
9
12.47
91.938
1143.3
457.34
0.407
Table 19 depicts the destination that is selected
for this modelling to analyze the behavior of
tsunami waves. The deep ocean tsunami wave
characteristics caused by the Sumatra earthquake
in 1964 are shown in Table 20. In the deep ocean,
a tsunami's wave height is estimated to be between
0.3 and 3.17 metress, its propagation speed is
calculated to be between 150 and 190 kilometres
per second, its wavelength is calculated to be
between 300and 450 kilometres, and its period is
calculated to be between 16 minutes and 1 hour 57
minutes.
Table 19. Selected destination for this modeling
Sl. No.
Location
1
Portblair,AndamanIsland
2
Marina, Chennai
3
Silver beach, Cuddalore
4
Velankanni
5
Nagapattinam
6
Karaikal, Puducherry
7
Appikonda beach, Vizag
8
Paradeep, Orissa
9
Cocos island, Australia
Table 20. Characteristics of the first tsunami
wave to arrive at the destinations in the 2004,
Sumatra tsunami
Location
Lat
(oN)
Lon
(oW)
C, km/s
L, km
T,
hh/mm/
ss
1
11.675
92.761
159.102
306.91
0.32.09
2
13.083
80.3
179.034
436.44
0.40.37
3
11.739
79.786
181.086
422.67
0.38.54
4
10.681
79.853
181.729
376.66
0.34.32
5
10.784
79.850
184.389
337.10
0.30.28
6
10.918
79.853
183.019
340.73
0.31.01
7
17.567
83.171
147.873
15748
5.35.01
8
20.26
86.7
147.141
15516
5.17.30
9
-12.12
96.883
84.901
32.77
0.06.25
Table 21 displays the results of the time for the
first tsunami wave to reach the defined destination
using the Impulse modeling for the 2004 Sumatra
earthquake tsunami. Historical data provides the
observed tsunami wave height at the coast of
locations given in the table.
Comparing the results of historical observed
data with the estimated data shows that the
Impulse modeling study can be applied to real-
time tsunami events to determine the tsunami wave
behavior.
92.0 92.5 93.0 93.5
4
6
8
10
12
Latitude (N)
Longitude (E)
0.4000
1.362
2.325
3.287
4.250
5.213
6.175
7.137
8.100
Slip (m)
Slip Variation along fault boundary line of 2004, Sumatra
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Table 21. The initial tsunami wave's outcomes
at the coastline of the destinations in the 2004
Sumatra tsunami
Location
D, km
ETH,
m
ETT,
hour
EAT,
(UTC)
hh/mm/ss,
1
103.8795
2.3
0.35
1.19.53
2
1287.243
2.18
2.48
3.27.41
3
1328.997
6.17
2.35
3.19.53
4
1316.846
3.85
2.57
3.33.05
5
1317.385
12.47
2.47
3.27.05
6
1317.424
5.16
2.36
3.20.29
7
1114.084
1.9
2.513
3.29.39
8
979.0124
1.572
2.47
3.27.05
9
1744.476
0.7
2.3386
3.19.11
The connection between historical and
estimated tsunami travel times to reach defined
locations from the 2004 Sumatra earthquake
tsunami is illustrated in Table 18. The table
indicates a very slight, potentially inconsequential
discrepancy between historical and estimated
tsunami wave heights near the shore, which can be
addressed in the future. The average percentage
accuracy of estimated values is calculated as
93.48%.
Table 22. Relationship between the historical
(NOAA) and estimated 2004 Sumatra earthquake-
tsunami wave travel time to reach destinations-
[18], [19], [20]
Location
OTT
(hours)
ETT
(hours)
ΔT,
mm/ss
Accuracy
(%)
1
0.25
0.35
6.00
60
2
2.567
2.48
5.13
96.6108
3
2.31
2.35
2.24
98.2979
4
2.51
2.57
3.36
97.6096
5
2.516
2.47
2.45
98.1717
6
2.27
2.36
5.24
96.0352
7
2.6
2.513
5.13
96.6538
8
2.46
2.47
0.36
99.5935
9
2.3
2.3386
2.18
98.3494
Table 22 depicts the accuracy of the estimated
tsunami wave travel time of 2004-Sumatra
earthquake as compared to the Observed tsunami
travel time.
The comparison graph between the historical
and estimated tsunami travel times for the
Sumatra, Indian Ocean tsunami of 2004 to reach
various destinations is depicted in Figure 13.
Numerical numbers on the graph correspond to the
locations indicated in the table. NOAA data is
utilized for historical tsunami wave height
information along the coast. The outcomes
demonstrate the effectiveness of the Impulse
models in predicting the behavior of the tsunami
wave during the actual tsunami occurrence.
Fig. 13: Comparison graph between the historical
and estimated tsunami wave travel time to reach
the destinations due to the 2004, Sumatra
earthquake-tsunami
4 Conclusion
The Impulse modeling method, employed to
simulate the tsunami generation and propagation
phases, is utilized to analyze three significant
historical tsunami events: the 1755 Lisbon
tsunami, the 1964 Alaska tsunami, the 2004
Sumatra tsunami. The run-up phase of the tsunami
is not explored due to a lack of historical data in
this context. These three historical tsunamis,
occurring in various regions, cover six continents
(Asia, Europe, North America), three oceans (the
Pacific, Atlantic, and Indian Oceans), and
numerous nations, providing a comprehensive test
of the applicability and suitability of the impulse
modeling approach across diverse oceanic regions.
The study examines the tsunami wave
characteristics during the propagation phase using
Impulse modeling and observes that these
characteristics are solely dependent on the ocean's
depth, with earthquake parameter variations
having no impact on tsunami wave propagation
properties. The accuracy of the results is assessed
by comparing them with historical data obtained
from the U.S. Geological Survey and the National
Oceanic and Atmospheric Administration
(NOAA). The overall accuracy is determined to be
90.25%. The accuracy percentage is higher for
distant tsunamis and lower for local or near shore
tsunamis but remains within an acceptable range.
The Impulse modeling method proves
effective in forecasting tsunami wave behavior
across various oceanic regions, even with minimal
earthquake data. Reliable results are obtained in
homogeneous ocean conditions when there are no
obstructions in the path of the tsunami wave.
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.25
2.567
2.31
2.51 2.516
2.27
2.6
2.46
2.3
0.35
2.48
2.35
2.57 2.47 2.36
2.513 2.47
2.3386
Travel time (hours)
Locations
Observed TT
Estimated TT
Travel time comparison for 2004 Sumatra-Andaman Earthquake tsunami
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Volume 19, 2023
However, caution is advised when applying the
method in conditions with obstacles. Future
research aims to enhance the accuracy of Impulse
modeling across all ocean conditions.
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[1] Helene and M T Yamashita (2006),
Understanding the tsunami with a simple
model, European Journal of Physics,
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[2] Smid, T. C. (1970). Tsunamis in Greek
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[3] Pablo G. Silva a, Javier Elez b, Raúl Pérez-
López c, Jorge Luis Giner-Robles d, Pedro
V. Gómez-Diego a, Elvira Roquero e,
Miguel Ángel Rodríguez-Pascua c, Teresa
Bardají f (2023), The AD 1755 Lisbon
Earthquake-Tsunami: Seismic source
modelling from the analysis of ESI-07
environmental data, Quaternary
International, 651, 6-24.
[4] Chris Zweck a 1, Jeffrey T Freymueller a,
Steven C Cohen b (2002), The 1964 great
Alaska earthquake: present day and
cumulative postseismic deformation in the
western Kenai Peninsula, Physics of the
Earth and Planetary Interiors, 132,(1–3), 5-
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[5] Chris Zweck, Jeffrey T. Freymueller, Steven
C. Cohen (2002). Three-dimensional elastic
dislocation modeling of the postseismic
response to the 1964 Alaska earthquake.
Journal of Geophysical Research: Solid
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WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT
DOI: 10.37394/232015.2023.19.122
Syed Mohamed E., Pon Selvan C. M.
E-ISSN: 2224-3496
1369
Volume 19, 2023
Tsunami Database.- NOAA National
Centers for Environmental Information. doi:
10.7289/V5PN93H7
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gridded_bathymetry_data/ (Accessed Date:
February 16, 2024).
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Syed Mohamed has carried out the following:
Identified the parameters
Developed the theory and performed the
computations.
Verified the analytical methods
Conceived the original idea.
Developed the theoretical formalism,
performed the analytic calculations and
performed the numerical simulations
Carried out the statistical, mathematical,
computational techniques to analyze the
historical and study data.
Carried out the simulation and the
optimization.
Designed the model and the computational
framework and analysed the data
Carried out the implementation
Worked out almost all of the technical
details, and performed the numerical
calculations for the suggested experiment.
- Pon Selvam has carried out the following:
Encouraged
Helped suggestion given in the articles
Both authors contributed to the final version of the
manuscript
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.e
n_US
WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT
DOI: 10.37394/232015.2023.19.122
Syed Mohamed E., Pon Selvan C. M.
E-ISSN: 2224-3496
1370
Volume 19, 2023