Transcript Slide 1

Directivity of tsunami generated by
subduction zone sources
Andrei G. Marchuk
The Institute of Computational Mathematics and Mathematical Geophysics,
Siberian Branch of the Russian Academy of Sciences, Novosibirsk, RUSSIA
[email protected]
Tsunami sources location around the Pacific
The Pacific ocean bottom relief and the earthquake epicenters location
Location of some historical tsunami sources in the Kuril-Kamchatka subduction zone
The model bottom relief and location of tsunami source
The process of tsunami waves refraction above an uneven bottom was studied
using the wave-ray approximation.
Some exact analytical solutions for wave-ray shapes:
• bottom slope – segment of cycloid (Marchuk, 1980)
• parabolic bottom – arc of circle
In general case tsunami wave rays can be determine using differential
equations of wave ray


dx
p
 2  ,
dt n ( x )


dp

1
  ln n( x ) , ( n( x ) 
 ) (1)
gH ( x )
dt
with initial conditions
0 0

0 
x t 0  x , p t 0  n( x ) 
(2)
Wave-ray traces of tsunamis generated by the round source
Maximum wave height in all grid-points of the 1800x1800 computational area.
Round source. Deep trench.
Maximum wave height at all grid-points of the 1800x1800 computational area.
Round source. Constant depth
(a)
(b)
Tsunami time series at the central horizontal axis. Round source.
Trench (a) and constant depth (b).
Configuration of the ellipsoidal tsunami source.
Maximum wave height in all grid-points of the 1800x1800 computational area.
Ellipsoidal source. Constant depth
Maximum wave height in all grid-points of the 1800x1800 computational area.
Ellipsoidal source. Deep trench.
(a)
(b)
Tsunami time series at the central horizontal axis. Ellipsiodal source.
Trench (a) and constant depth (b).
Wave-ray chart for the eastern Hawaii
The Alaska-Aleutian subduction zone and tsunami source
location.(200x60 km, initial elevation 200 cm).
Maximum tsunami wave height around the Hawaiian islands (Source 4).
Conclusions
1. The slope of the deep water trench works like an optical
lens for tsunami waves. Due to the wave refraction above
the bottom slope the greater part of tsunami energy will be
concentrated in the shoreward and the seaward directions.
2. If the source boundary expands closer to the deep trench
axis, then the initially circled front line of the leading
tsunami wave will be formed into almost a flat shape after
passing a trench.
3. Some potentially dangerous for Hawaii locations of
tsunami source were determined.
Thank you!