Directivity of tsunami generated by subduction zone sources

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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
mag_at_omzg.sscc.ru
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Tsunami sources location around the Pacific
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The Pacific ocean bottom relief and the
earthquake epicenters location
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Location of some historical tsunami sources in
the Kuril-Kamchatka subduction zone
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The model bottom relief and location of tsunami
source
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• 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
,
(
)
(1)
,
with initial conditions
(2)
,
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Wave-ray traces of tsunamis generated by the
round source
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Maximum wave height in all grid-points of the
1800x1800 computational area. Round source. Deep
trench.
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Maximum wave height at all grid-points of the
1800x1800 computational area. Round source.
Constant depth
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(a)
(b)
Tsunami time series at the central horizontal
axis. Round source. Trench (a) and constant depth
(b).
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Configuration of the ellipsoidal tsunami source.
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Maximum wave height in all grid-points of the
1800x1800 computational area. Ellipsoidal source.
Constant depth
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Maximum wave height in all grid-points of the
1800x1800 computational area. Ellipsoidal source.
Deep trench.
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(a)
(b)
Tsunami time series at the central horizontal
axis. Ellipsiodal source. Trench (a) and
constant depth (b).
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Wave-ray chart for the eastern Hawaii
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The Alaska-Aleutian subduction zone and tsunami
source location.(200x60 km, initial elevation 200
cm).
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Maximum tsunami wave height around the Hawaiian
islands (Source 4).
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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.

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Thank you!