ORIGINAL ARTICLE

Visualization of tsunami waves with Amira package

Erik O. D. Sevre Æ Dave A. Yuen Æ Yingchun Liu

Received: 3 April 2008 / Revised: 3 May 2008 / Accepted: 11 May 2008 / Published online: 27 June 2008

� Springer-Verlag 2008

Abstract In recent years numerical investigations of

tsunami wave propagation have been spurred by the mag-

nitude 9.3 earthquake along the Andaman–Sumatra fault in

December, 2004. Visualization of tsunami waves being

modeled can yield a much better physical understanding

about the manner of wave propagation over realistic sea-

floor bathymetries. In this paper we will review the basic

physics of tsunami wave propagation and illustrate how

these waves can be visualized with the Amira visualization

package. We have employed both the linear and nonlinear

versions of the shallow-water wave equation. We will give

various examples illustrating how the files can be loaded by

Amira, how the wave-heights of the tsunami waves can be

portrayed and viewed with illumination from light sources

and how movies can be used to facilitate physical under-

standing and give important information in the initial

stages of wave generation from interaction with the

ambient geological surroundings. We will show examples

of tsunami waves being modeled in the South China Sea,

Yellow Sea and southwest Pacific Ocean near the Solomon

Islands. Visualization should be a part of any training

program for teaching the public about the potential danger

arising from tsunami waves. We propose that interactive

visualization with a web-portal would be useful for

understanding more complex tsunami wave behavior from

solving the 3-D Navier–Stokes equation in the near field.

Introduction

Our awareness of the impending danger posed by tsunami

waves has been heightened by the Sumatran mega-

earthquake in 26 December 2004 and also by the series of

strong earthquakes in this area since that time, especially

in 2007. The great potential danger posed by tsunamis on

the economies along the sea coasts around the Pacific

basin was brought clearly to the fore by the widespread

destruction caused by the horrendously wide swath of

tsunami waves hitting many sites in the Indian Ocean.

Next to earthquakes and cyclones, tsunamis are one of the

most fearful natural hazards because, they occur unex-

pectedly in the worst times. Tsunamis are different from

other types of disasters, such as hurricanes, tornadoes,

floods, and volcanic eruptions, which have precursory

phenomena and hence can be monitored. These fast

waves of great destructive potential give no warning

except that the disturbance that causes them can be

detected by a seismograph. However, tsunami waves

travel about 30 times slower than seismic waves. There-

fore, enough warning is indeed possible for places

sufficiently far away from the earthquake. Before the

arrival of the first wave, the populace may have one to

several hours of warning, but that much time may not be

enough, if they are not properly educated or warned. But

the recent earthquake at the Solomon Islands (see below

in ‘‘Visualization results’’) shows that nearby earthquakes

can give the local populace hardly any warning. Tsunami

waves are not to be mistaken with wind-driven waves or

tidal waves and, in general, have a very long horizontal

extent, at least exceeding 100 km. In Fig. 1 we show an

example from a famous Japanese painting in the nine-

teenth century of a towering tsunami wave, coming up

ashore.

E. O. D. Sevre (&) � D. A. Yuen � Y. Liu

Department of Geology and Geophysics and University

of Minnesota Supercomputing Institute,

University of Minnesota, Minneapolis, MN 5545, USA

e-mail: esevre@i7.msi.umn.edu

123

Vis Geosci (2008) 13:85–96

DOI 10.1007/s10069-008-0011-1

The Sumatran event has given a lot of impetus to the study

of tsunamis. The last several years have seen an enormous

blossoming of interest, funding and developed capability in

the study of tsunamis. There has been a great spurt in tsunami

workshops and training courses. Numerical simulations of

tsunami waves have been given a new lease of life from these

new research activities. In order for more people to share in

the knowledge of tsunami waves and to understand the

meaning of numerical simulations, we need to develop better

visualization tools for portraying the computed solutions.

Good visualization will help a broader audience to learn

better about the tsunami phenomena. We will use the Amira

package (http://www.amiravis.com) as a vehicle for dem-

onstrating the usefulness and importance of visualization,

which goes hand in hand with numerical simulations. This

facile tool Amira has been used by our group in many areas of

science, ranging from mammograms (Arodz et al. 2005),

mantle convection (Erlebacher et al. 2002; Wang et al. 2007)

to postglacial rebound (Hanyk et al. 2007). The main purpose

of this paper is to communicate to an interested audience the

need for the use of visualization in tsunami studies, both in

research efforts and in educational training. We will begin by

going over the basic physics of tsunami waves as caused by

earthquakes. Then we will discuss the numerical solutions of

the wave equations with the shallow-water wave (SWW)

equations and stress the need to visualize the motions of the

wave height, of the order of meters to 10 m, which is a small

quantity relative to the width of the ocean basin. Then we will

go over the rudiments of visualization of the wave-height

with the Amira package and focus on certain techniques we

have employed, such as height exaggeration and the illu-

mination of the wave by a light source. Then we will present

some results from visualization of tsunami waves simulated

over the western Pacific Ocean, and the seas adjacent to the

Chinese coast. We will also present results on wave propa-

gation near the Solomon Islands, where we show the

influences of local geological structures on the fate of sub-

sequent tsunami waves. In the final section we discuss the

future of visualization on tsunami wave studies, especially

with added complexity in the type of more complicated

hydro dynamical equations in the near field and real-time

visualization of tsunami waves as part of a warning system.

Basic physical principles of tsunami waves

Before describing the visualization of tsunami waves, we

will give a brief summary of how tsunamis are generated

by earthquakes and how tsunami waves propagate across

the sea. The reader is referred to Geist (1999), Satake

(2007) and Gisler (2008) for a more thorough review of

tsunami physics and numerical modeling techniques. In

brief, tsunami waves are generated by earthquakes by

means of transfer of large-scale elastic deformation asso-

ciated with earthquake rupturing process to increase of the

potential energy in the water column of the ocean (Fig. 2).

Most of the time, the initial tsunami amplitude waves

are very similar to the static, coseismic vertical displace-

ment produced by the earthquake. In tsunami modeling

(Imamura et al. 1995) one commonly calculates the elastic

coseismic displacement field from elastic dislocation the-

ory (e.g. Okada 1985) with a single Volterra (uniform slip)

dislocation. Geist and Dmowska (1999) showed the fun-

damental importance that distributed time-dependent slip

has on tsunami wave generation. We note that because

variations in slip are not accounted for, these simple dis-

location models may underestimate coseismic vertical

displacement that dictates the initial tsunami amplitude.

After the initial excitation due to the initial seafloor

displacement, the tsunami waves propagate outward from

the earthquake source region and follow the inviscid SWW

equation, since the tsunami wavelength (around hundreds

of kilometers) is usually much greater than the ocean

depths. For water depths greater than about 100–500 m

(Shuto 1991; Liu et al. 2007), we can approximate the

SWW equations by the linear long-wave equations:

oz

otþ oM

oxþ oN

oy¼ 0

oM

otþ gD

oz

ox¼ 0

oN

otþ gD

oz

oy¼ 0;

ð1Þ

where the first equation represents the conservation of mass

and the next two equations govern the conservation of

momentum. The instantaneous height of the ocean is given

by z(x, y, t), a small perturbative quantity. The horizontal

coordinates of the ocean are given by x and y and t is the

elapsed time, M and N are the discharge mass fluxes in the

Fig. 1 This is a famous portrayal of the multi-scale nature of tsunami

waves (The Great Wave of Kanagawa) drawn by the Japanese painter

K. Hokusai in the early nineteenth century

86 Vis Geosci (2008) 13:85–96

123

horizontal plane along the x and y axes, g is the

gravitational acceleration, h(x, y) is the undisturbed depth

of the ocean, and the total water depth

D ¼ hðx; yÞ þ zðx; y; tÞ: ð2Þ

It is important to emphasize here that the real advantage

of the shallow water equation is that z is small quantity and

hence a perturbation variable, which allows it to be

computed accurately.

We have also considered the non-linear SWW equation

because of shallow water region in the East China Sea and

Yellow Sea. Taking into account the effects of the bottom

friction due to sediments, the non-linear SWW equations

are given by three equations in the same manner as the

linear SWW equations and are expressed by:

oz

otþ oM

oxþ oN

oy¼ 0

oM

otþ o

ox

M2

D

� �o

oy

MN

D

� �þ gD

oz

oxþ sx

q¼ 0

oM

otþ o

ox

MN

D

� �þ o

oy

N2

D

� �þ gD

oz

oyþ sx

q¼ 0;

ð3Þ

where q is the density of water and f is the bottom frictional

coefficient. sx and sy are the shear stress components along

x and y directions. The bottom friction is given in terms of

the shear stresses at the bottom and are expressed in terms

of nonlinear terms in M and N, the mass fluxes, and the

Manning coefficient, which depends locally on the sedi-

mentary conditions at the sea bottom (e.g. Titov and

Synolakis 1998). The three variables of interest in the

shallow-water equations are z(x, y, t), the instantaneous

height of the seafloor, and the two horizontal velocity

components u(x, y, t) and v(x, y, t). We will employ the

height z as the principal variable in the visualization. The

wave motions will be portrayed by the movements of

the crests and troughs in the wave height z, which are

advected horizontally by u and v. Figure 3 shows a schematic

diagram portraying the relationship of z and the seafloor.

The wave fronts depicting z(x, y, t) are propagated by

the horizontal velocity components u(x, y, t) and v(x, y, t).

They are all part of the shallow-water equation system.

This scenario is shown in Fig. 4.

The usage of time-series at a given receiver is com-

monly used to record the time history of tsunami waves at a

particular locale. Figure 5 shows the time series of tsunami

waves arriving at a coastal area close to Shanghai (top

panel) and out in the East China Sea at the center of the

Ryukyu Trough (bottom panel). The source of the waves

Fig. 2 Illustration of

seismogenic tsunami process,

we note that z, called the wave-

height, is the vertical distance

between the usual water level

and the highest level of the

wave. This length-scale is

extremely small compared

to the distance of the ocean

basin (Adapted from

http://universe-review.ca/

F09-earth.htm)

Fig. 3 A 2-D schematic profile

of tsunami wave height z and

the seafloor bathymetry

delineated by H(x,y)

Vis Geosci (2008) 13:85–96 87

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comes from and hypothetical earthquake in the Ryukyu

area near the center of the Ryukyu Trough.

We can observe that at shallow depths there are large

differences between the linear and nonlinear SWW equa-

tions. At greater depths the two approximations give

similar results (see also Liu et al. 2007).

Introduction to the Amira package

In this section we will go over the rudiments in using the

Amira package specifically for tsunami problems. Other

discussions of the use of Amira can be found in Wang et al.

(2007) and Hanyk et al. (2007). The Amira package has

been around since 1999 and has been used for many types

of problems, in particular in the bio-medical field (see also

Arodz et al. 2005).

Amira is an interactive tool used for visualization in a

3-D environment. Many platforms are available, ranging

from PC’s to Apple products. We choose Amira to look at

tsunami data because of how easy it is to manipulate the

data and visualization environment for time series of both

2-D and 3-D data. The learning curve is very gentle with

Amira, menus are easy to follow, tools are simple to use,

and changes happen immediately without any need to wait

for rendering. We are quickly moving our perspective

between a variety of regions in a data set, as seen in the

figure below. It is easy to quickly generate these images

because of how freely the camera is able to navigate the

scene. It is important to have a tool that allows for quick

and simple tuning of the data. We take advantage of the

ability to quickly manipulate settings and see immediate

results in the visualized data.

We looked at an earthquake off of the south-western

coast of Solomon Islands, and noticed that the island

structures blocked the tsunami waves from penetrating the

islands and penetrating into the central Pacific Ocean. To

look at how the tsunami would propagate without the

Solomon Islands blocking, we lowered the topography by

500 m. With a 500 m hole the tsunami wave was obstructed

as it tried to penetrate the island chain, so a 3,000 m

depression was created. With a 3,000 m hole the Solomon

Islands appeared to have a minimal blocking effect. For the

depressions we used Etopo2 (http://www.ngdc.noaa.gov/

mgg/fliers/01mgg04.html) bathymetric data and altered the

topography field to create a 500 and 3,000 m holes,

respectively in the island chain. (see also Fig. 15 below,

where a comparison is conducted on the remarkable

influence of this hole on the subsequent tsunami wave

propagation).

Fig. 5 Comparison of water heights in time-series with linear and nonlinear models for various water depths in eastern China sea region. (Only

the results of the first 4.1 h are plotted to avoid visual congestion)

Fig. 4 Tsunami wave with the two horizontal velocity components,

u and v. The red vector shows the direction of the wave front heading

toward the beach. The horizontal axes are given by x and y(Background is adapted from http://susilo.typepad.com/nurani/

images/quake3.jpg)

88 Vis Geosci (2008) 13:85–96

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To check that we have created a hole correctly in the

appropriate location, we then employed Amira to look at

the topography data. Amira allowed us to quickly switch

between angles and check that the depression lay in fact in

the correct location for allowing the tsunami wave to go by

the Solomon Islands (Fig. 6).

Visualization of data begins with loading of the data.

When the data is loaded, we can quickly look at it using an

orthoslice that has a default grayscale colormap based on

the minimum and maximum values of the data set. To have

a better understanding of the data, it is important to create a

customized colormap that highlights important features in

the data. Colormaps are easy to create and customize using

the colormap editor (pictured below). Adding a colormap

will increase the level of detail we can see in the data. By

visualizing data as a height field, we can scale the height

field by adding depth as an auxiliary variable and inspire an

even greater understanding of the data being visualized.

Amira also has a handful of default colormaps available

for the new user to use. These colormaps are basic, and

some tweaking is often required to generate an ideal col-

ormap for a given data set. Once a colormap is loaded, one

can access the colormap editor (Fig. 7) to tweak the col-

ormap to your needs.

To take visualization one step further than basic col-

ormaps, Amira allows the user to make use of height fields.

The best way to see the advantages of a good colormap and

height field is to look at a gray scale image, then add a

customized colormap, then give the image a little depth by

using a height field. The combination of a height field and a

colormap creates a realistic and natural image that is easily

interpreted by the human eye. It is like creating a terrain for

the viewer to fly through (Fig. 8).

For visualization it is vital to have a good light source to

illuminate the data to highlight regions of interest, in this

case, the South China Sea off the coast of Viet Nam. Amira

provides an interface where the light source is an object

that the user is able to manipulate with the mouse. We

usually use a spotlight to highlight regions of interest in the

data sets. A well placed light source will highlight data

features, while a poor light source can drown out items of

interest by creating awful glare. By having a light source at

a low angle the glare is reduced, while enhancing contrast

Fig. 6 Multiple views of Etopo1 seafloor data (NGDC).This figure

shows Etopo1 data that has been rendered by Amira. All four images

were rendered in less than a couple minutes because Amira allows for

quick manipulation of the camera and data. a Shows the view from

within a trench off the coast near Gizo island, one the major islands in

the Solomon Islands, the artificial hole is not visible from this view.

b Shows the scene from above, a depression that removes part of the

Solomon islands is visible from this angle. c This angle is looking

down the trench, and we can see the depression levels the ocean floor

and removes the wall of the trench. d Shows the scene from afar,

allowing for a global view of the topography

Fig. 7 Colormap in Amira. This colormap is a basic colormap

provided by Amira, but the user is able to modify any of the 256

control points to further customize the colormap to satisfy their

desires. In fact, the colormap can be set up to incorperate any number

of control points

Vis Geosci (2008) 13:85–96 89

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in the image by increasing illumination on a single side of

objects in the scene (Fig. 9).

Amira is easy to work with because it is easy to work

with multiple files. The menus in Amira allow you to load a

single file or a time series of data, consisting of multiple

files representing data over time. The time series is easy to

load and allows users to access special menus and options

specific for a time series. With a TimeSeries object a user

can load many frames of a run, and set up the visualization

environment for the first item in the series, then select

various elements of the series to watch how the

visualization changes through the series. Using the Mov-

ieMaker object, the user can render a frame for each item in

the time series, using the same parameters, which vastly

simplifies the movie making process (Fig. 10).

This figure shows how the MovieMaker in Amira works.

You need to setup your options for were to output the

movie files, how to output the files. For making high

quality movies we usually output at 640 9 480 resolutions,

and then we render to a series of lossless PNG files to

ensure maximum quality for encoding. Using this process

the images are rendered by Amira then another application

is used to combine the movies into a movie file. To keep

the movies accessible to a variety of users, we usually

encode in several formats. Quicktime movies are generally

the highest resolution and most compatible, but are also

very large (Fig. 11).

Using this technique in Amira, we were able to make

rapidly a couple movies for analyzing tsunami wave

propagation. The two movies that have been uploaded are

looking at a tsunami originating in the Okinawa Trough.

Please look at the two websites below. The first movie is

looking at the scene from the north and watching as the

wave propagates through the Yellow Sea. The second

movie is watching the wave propagation from a low angle

near Taiwan to see when the tsunami reaches Taiwan and

the mainland (Fig. 12).

First movie’s website: http://www.msi.umn.edu/

*esevre/tsunami/jan2008/temp/final-pics/movies/yellowsea1.

mov

Second movie’s website: http://www.msi.umn.edu/

*esevre/tsunami/jan2008/temp/final-pics/movies/yellowsea2.

mov.

Visualization results

Our research has looked mainly at tsunamis originating

near Southeast Asia. We have been looking at tsunami

effects on three different regions: the South China Sea, the

Fig. 8 The impact of combining a color map and height field on

transforming 2-D datasets. This figure shows how a good colormap

and height field enhance the data set. a Shows the data with a simple

linear colormap. b Shows the data after a customize colormap has

been created and aplied to enhance features of interest. c shows how

the height field further enhances the image by creating more depth

and a more natural landscape

Fig. 9 Using light sources in Amira. These figures show how Amira

treats the light source as an object in the scene that can be

manipulated by the user. a Shows the light source high above the

scene of the South China Sea. In (b) we have lowered the light source

for more drastic angles in the scene

90 Vis Geosci (2008) 13:85–96

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Yellow Sea, and the Solomon Islands. Tsunami waves,

originating in the Okinawa trough, then propagate towards

the Yellow Sea, Taiwan, and Southeastern China. Below is

a map of the southeastern China region.

The subduction zones, Manila subduction site and

Ryukyu subducting trench, between the Philippines Sea

plate and the Eurasian Plate are regions of strong stress

concentration in the East Asian plate. The Manila trench

and Okinawa trough represent probably the most dangerous

seismogenic tsunami sources that could seriously impact

the coastal area of China (Liu et al. 2008).

South China Sea

For the South China Sea runs we used visualization to

analyze the effectiveness of the grid size used for the run. If

the grid is too coarse, it will work fine for linear SWW runs

but nonlinear SWW runs resulted in poorer results that

Fig. 10 Loading files and

creating movies on Amira This

figure shows Amira in action for

creating tsunami visualizations.

a Shows how time series of data

can easily be loaded by

selecting the desired files format

directory. b Shows how the

movie maker can be set up to

use the loaded time series for

producing a series of images, or

a movie file of the numerical

simulation

Vis Geosci (2008) 13:85–96 91

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were immediately evident from the visualization. In the

figures below we can see how a coarse grid provides a

smoother but a more realistic wave image.

Nonlinear simulations of the shallow water equation

requires a sufficient grid resolution. While a course grid

suffices to simulate linear solutions, the same grid size

results in a chaotic and jagged solution (Fig. 13a).

Increasing the grid size results in a more natural and a

smoother solution (Fig. 13b) of the nonlinear SWW solu-

tion. Visualization with Amira allowed for a quick

identification of these numerically induced irregularities in

the solution for a run using a grid size that was not fine

enough.

We use visualization as a means of comparing results

from linear and nonlinear simulations.

This figure compares the results of a nonlinear run using

a coarse (a) and fine (b) grid size from the same view angle

and time step. On the coarse grid we can see that there are

far more elements have a singular and jagged character,

while the fine grid delivers a smoother solution.

Eastern China Sea

The images below show a tsunami wave 200 min after the

earthquake rupturing event.

This figure shows waves arriving at China (left) as

they pass by Taiwan (right). (a) Is looking down giving

a more global sense of the wave propagation, (b) is a

low angle view showing how the waves will approach

the eastern Chinese coast. The hypothetical epicenter of

eastern China sea is located at Okinawa trough trench,

near the center of the image A. The geographical loca-

tion of the earthquake is at 26.0N, 125.56E. The wave is

heading for eastern Chinese main land coastal area and

northern of Taiwan island bordering eastern China Sea.

In imagine B, Taiwan Island is the right being crossed

by the waves. We note that in Fig. 14a and b we are

looking at the same place and at the same time. Only the

camera angle is varying variable. This gives one an idea

of the importance played by different angles. Both the

local and global views are presented by these vantage

points.

Solomon Islands, April first, 2007 earthquake

and the attendant tsunami

Here we want to show how not only is the island blocking,

but that the wall like structure of the trench is what deflects

Fig. 11 The topography and geophysical background of South China

Sea and the adjacent region

Fig. 12 Sequence of tsunami shots propagating across the South

China Sea. This figure shows two shots of the South China Sea

differing by a few hours. The early shot (a) shows how the initial

wave formation looks, while the later shot (b) allows us to see how

the propagating waves interact with each other. The hypothetical

epicenter of South China Sea is located at Manila trench, western of

Philippine Islands. The geographical location of the epicenter is

14.5N, 119.0E. The tsunami wave is heading for eastern Chinese and

Vietnamese coastal area, marked by Hue and Danang bordering South

China Sea at the left

92 Vis Geosci (2008) 13:85–96

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the tsunami. A hole of 500 m still was considerable for

blocking tsunamis, but a 3,000 m hole allowed waves to

pass freely. For geological background the reader is urged

to consult these works (Taira et al. 2004; Fisher et al. 2007;

Mc Adoo et al. 2008) (Fig. 15).

Tsunami waves coming from the 1 April, earthquake

off the coast of the Solomon islands were prevented

from propagating into the central Pacific Ocean by the

Solomon Islands. Our simulations have shown that the

Solomon Islands block tsunami waves generated by

nearby earthquakes. We were curious whether digging a

hole in the Solomon Islands would result in a stronger

wave heading out to the northeast. Three simulations

were run, the first simulation looks at the wave propa-

gation with the island intact. The second and third

simulation look at a manufactured topography where a

500 and 3,000 m hole created in the island near the

epicenter of the earthquake. These simulations show that

the island blocks most of the effects of the tsunami wave

propagation. A 500 m hole allows the wave to propagate

somewhat but there is still a significant blocking effect.

While the 3,000 m hole allows most of the energy to

propagate beyond the Solomon Islands to the northeast,

toward the Hawaiian Islands.

This figure shows convincingly how the geological

topography of the Solomon islands serve to block tsunami

waves originating in the southwestern trench of the

Fig. 13 Numerical influence

from varying grid sizes. (There

is a difference of a factor of 2

along each direction for these

grids or a factor of 4 in the total

number of grid points, the

original grid was 320 9 320

points). The bathymetry data of

a is Etopo2, that of b is Etopo1

Fig. 14 Two different views at

the same time of tsunami waves

passing nearby Taiwan

Fig. 15 The map of Solomon Islands and adjacent region underlain by

the Etopo1 bathymetry. The pink frame borders the computing area of

tsunami. Pink triangle marks the epicenter of the Solomon Island

tsunamogenic earthquake, which occurred on the night of 1 April 2007

Vis Geosci (2008) 13:85–96 93

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Solomon Islands. Looking at two different depths of holes

shows that a deep hole is necessary for the most powerful

waves to penetrate through the Solomon Islands and might

have caused havoc on Hawaiian Islands.

Summary and future perspectives

Since the 1960s scientific visualization has always been a

specialized form of computing at the edge of contemporary

technology. As the computing field has grown and matured,

more software has become available for visualization

technologies. In the last few years, visualization has

gradually grown from a tool employed by a few researchers

to understand their data into a facile tool and more people

are beginning to appreciate the importance of visualization

in computational geosciences, which has been stressed in

the report by Cohen (2005). In this paper we have shown

Fig. 16 The influence of the

local geological structure near

the epicenter on initial tsunami

wave propagation

Fig. 17 Schematic diagram of a viable set-up for real-time tsunami

visualization

94 Vis Geosci (2008) 13:85–96

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how the Amira visualization package (http://www.

amiravis.com) can help to improve our understanding of

the wave propagation of tsunami waves. When linked

together with Google Earth (http://earth.google.com), a

solid foundation can be built for disseminating the dangers

of tsunami waves and training of teachers in tsunami-prone

countries next to subduction zones, such as Thailand and

Indonesia.

With each level of increasing complexity, such as the

use Navier–Stokes equation (Mader 2004; Gisler 2008)

instead of the commonly used SWW equations(e.g. Satake

2007) and the generation of tsunami waves by volcanic

eruptions and landslides, there will be greater need for

more sophisticated forms of visualization, such as stereo

projection, which is also available with the Amira package.

The movie made by stereoscopic rendering by using two

focal points would portray realistically wave-breaking

events, which would be the solution to 3-D Navier–Stokes

equation. Global modeling of tsunami wave propagation

(Kowalik et al. 2005) with grid points exceeding 100

million points and a time step of 2 s will also put movie-

making in high demand. The phenomenon of run-up on the

coast (e.g. George and Leveque 2006) represents another

challenge in visualization, since we are dealing with a

bunch of nested grids with multiple scales, where the grid

configuration close to the beach is several times denser

than the previous grid system out in the ocean. We will

need to use of Web-portal for interactive visualization

(Damon et al. 2008) of 3-D compressible tsunami runs with

hundred million degrees of freedom. In this connection

tsunami modelers can also make use of the Australian

visualization tools Underworld (Goyette et al. 2008), which

was developed for geodynamics (Fig. 16).

Today many institutions around the world are working

to develop suites of codes for modeling wave generation,

propagation and inundation with the goal of producing and

broadcasting life-saving information in real time. We feel

that visualization should play a more prominent role in this

venture. In the final figure we show our idea of interactive

visualization, which is feasible with the technology already

developed in other areas of visualization endeavors in

mantle and stellar convection (Damon et al. 2008; Green-

sky et al. 2008). It is extremely important that visualization

and simulation should act in concert in real-time fore-

casting and warning, as depicted below in Fig. 17. The use

of a web-portal technology is crucial in this type of tsunami

response system with interactive visualization, because of

its outreaching capabilities.

Acknowledgments We thank fruitful discussions with Chuck

Zhang, Matt Knepley, Jim B S.G. Greensky, Steve Chen and Me-

gan Damon. This research was supported by ITR program and

Infrastructure program of EAR Division of National Science

Foundation.

References

Arodz T, Kurdziel M, Severe EOD, Yuen DA (2005) Pattern

recognition techniques for automatic detection of suspicious-

looking anomalies in mammograms. Comput Methods Programs

Biomed 79:135–149

Cohen RE (ed) (2005) High-performance computing requirements for

the computational solid-earth sciences, 102pp. http://www.

geo-prose.com/computational_SES.html

Damon MR, Kameyama MC, Knox M, Porter DH, Yuen DA, Severe

EOD (2008) Interactive visualization of 3-D mantle convection.

Vis Geosci (in press)

Erlebacher G, Yuen DA, Dubuffet FW (2002) Case study: visuali-

zation and analysis of high Rayleigh number 3-D convection in

the Earth’s mantle. In: Proceedings of IEEE Visualization, pp

529–532

Fisher MA, Geist EL, Sliter R, Wong FL, Reiss C, Mann DM (2007)

Preliminary analysis of the earthquake (Mw 8.1), tsunami of

April 1, 2007, in the Solomon Islands, Southwestern Pacific

Ocean. Sci Tsunami Hazards 26(1):1–20

Geist EL (1999) Local tsunamis and earthquake source parameters.

In: Dmoska R, Saltzman B (eds) Tsunamigenic earthquakes and

their consequences, vol 39. Advances in Geophysics, pp 117–

209

Geist EL, Dmowska R (1999) Local tsunamis and distributed slip at

the source. Pure Appl Geophys 154:485–512

George DL, Leveque RJ (2006) Finite volume methods and adaptive

refinement for global tsunami propagation and local inundation.

Sci Tsunami Hazards 24:319–328

Gisler GR (2008) Tsunami simulations. Annu Rev Fluid Mech 40:71–

90

Goyette S, Takatsuka M, Clark S, Mueller RD, Rye P, Stegman DR

(2008) Increasing the usability and accessibility of geodynamic

modeling tools to the geosciences community: Underworld GUI.

Vis Geosci (in press)

Greensky JBSG, Czech W, Yuen DA, Knox M, Damon MR, Chen S,

Kameyama MC (2008) Ubiquitous interactive visualization of

3-D mantle convection via web application using Java and Ajax

framework. Vis Geosci (in press)

Hanyk L, Yuen DA, Matyska C, Velimsky J (2007) Visualization of

time-dependent dynamics of postglacial rebound. Vis Geosci.

doi:10.1007/s10069-007-0007-2

Horrillo J, Kowalik Z, Shigihara Y (2006) Wave dispersion study in

the Indian Ocean tsunami of December 26, 2004. Mar Geod

29:149–166

Imamura F, Gica E, Takahashi T, Shuto N (1995) Numerical

simulation of the 1992 Flores tsunami; interpretation of tsunami

phenomena in northeastern Flores Island and damage at Babi

Island. Pure Appl Geophys 144:555–568

Kowalik Z, Knight W, Logan T, Whitmore P (2005) Numerical

modeling of the global tsunami. Sci Tsunami Hazards 23:40–

56

Liu Y, Santos A, Wang SM, Shi Y, Liu H, Yuen DA (2007) Tsunami

hazards along the Chinese coast from potential earthquakes in

South China Sea. Phys Earth Planet Inter 163:233–244

Liu Y, Shi Y, Yuen DA, Severe EOD, Yuan X, Xing HL (2008)

Comparison of linear and nonlinear shallow wave water

equations applied to tsunami waves over the China Sea. Vis

Geosci. Springer, Berlin

Mader CL (2004) Numerical modeling of water waves, 2nd edn. CRC

Press, Boca Raton 274pp

Mc Adoo BG et al (2008) Solomon Islands tsunami, one year later,

E.O.S. Trans Am Geophys Union 89(18):169–170

Okada Y (1985) Surface deformation due to shear and tensile faults in

a half-space. Bull Seismol Soc Am 75:1135–1154

Vis Geosci (2008) 13:85–96 95

123

Satake K (2007) Tsunami, in treatise of Geophysics. In: Kanamori H

(ed) Earthquake Seismology, vol 4. Elsevier, Amsterdam, pp

484–508

Shuto N (1991) Numerical simulation of tsunamis—its present and

near-future. Nat Hazards 4:171–191

Taira A, Mann P, Rahardiawan R (2004) Incipient subduction of the

Ontong Java Plateau along the North Solomon trench. Tectono-

physics 389:247–266

Titov VV, Synolakis CE (1998) Numerical modeling of tidal wave

runup. J Waterways Port Coast Ocean Eng 124:157–171

Wang SM, Zhang S, Yuen DA (2007) Visualization of downwellings

in 3-D spherical mantle convection. Phys Earth Planet Inter

163:299–304

Yoneshima S, Mochizuki K, Araki E, Hino R, Shinohara M, Suyehiro K

(2005) Subduction of the Woodlark Basin at New Britain Trench,

Solomon Islands region. Tectonophysics 397(3–4):189–201

96 Vis Geosci (2008) 13:85–96

123