Geoscience Reference
In-Depth Information
Fig. 2.3
Plots or marigrams of
tsunami wave trains at various
tidal gauges in the Pacific region.
Based on Wiegel (
1970
)
Wake Island 9 March 1957
50
40
30
20
10
250
300
350
400
minutes
Unalaska 9 March 1957
3.5
Hilo 9 March 1957
1.0
3.0
0.5
2.5
0.0
-0.5
-1.0
2.0
1.5
18
21
24
3
6
15
18
21
24
GMT
GMT
Antofagasta, Chile 10 April 1957
Midway Island 9-10 March 1957
1.5
2.0
1.5
1.0
1.0
0.5
15
18
21
24
6
9
12
15
GMT
GMT
Shallow water begins when the depth of water is less than
half the wavelength. As oceans are rarely more than 5 km
deep, the majority of tsunami travel as shallow-water
waves. In this case, the trigonometric functions character-
izing sinusoidal waves disappear and the velocity of the
wave becomes a simple function of depth as follows:
2.3
Tsunami Wave Theory
The theory of waves, and especially tsunami waves, are
described in many basic references (Wiegel
1964
,
1970
;
Pelinovsky
1996
; Geist
1997
; Trenhaile
1997
; Komar
1998
). The simplest form describing any wave is that rep-
resented by a sine curve (Fig.
2.4
). These sinusoidal waves
and their features can be characterized mathematically by
linear, trigonometric functions known as Airy wave theory
(Komar
1998
). This theory can represent local tsunami
propagation in water depths greater than 50 m. In this the-
ory, the three ratios presented in Eq.
2.1
are much less than
one. This implies that wave height relative to wavelength is
very low—a feature characterizing tsunami in the open
ocean. The formulae describing sinusoidal waves vary
depending upon the wave being in deep or shallow water.
C
¼
g
ð
0
:
5
ð
2
:
2
Þ
where
C
m s
1
= wave speed
ð
Þ
g
9
:
81 m s
1
= gravitational acceleration
ð
Þ
The wavelength of a tsunami is also a simple function of
wave speed, C, and period, T, as follows:
L
¼
CT
ð
2
:
3
Þ
