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. [email protected] Tsunami sources location around the Pacific.

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Directivity of tsunami generated by subduction zone sources

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]


Directivity of tsunami generated by subduction zone sources

Tsunami sources location around the Pacific


Directivity of tsunami generated by subduction zone sources

The Pacific ocean bottom relief and the earthquake epicenters location


Directivity of tsunami generated by subduction zone sources

Location of some historical tsunami sources in the Kuril-Kamchatka subduction zone


Directivity of tsunami generated by subduction zone sources

The model bottom relief and location of tsunami source


Directivity of tsunami generated by subduction zone sources

  • 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)

,


Directivity of tsunami generated by subduction zone sources

Wave-ray traces of tsunamis generated by the round source


Directivity of tsunami generated by subduction zone sources

Maximum wave height in all grid-points of the 1800x1800 computational area. Round source. Deep trench.


Directivity of tsunami generated by subduction zone sources

Maximum wave height at all grid-points of the 1800x1800 computational area. Round source. Constant depth


Directivity of tsunami generated by subduction zone sources

(a)

(b)

Tsunami time series at the central horizontal axis. Round source. Trench (a) and constant depth (b).


Directivity of tsunami generated by subduction zone sources

Configuration of the ellipsoidal tsunami source.


Directivity of tsunami generated by subduction zone sources

Maximum wave height in all grid-points of the 1800x1800 computational area. Ellipsoidal source. Constant depth


Directivity of tsunami generated by subduction zone sources

Maximum wave height in all grid-points of the 1800x1800 computational area. Ellipsoidal source. Deep trench.


Directivity of tsunami generated by subduction zone sources

(a)

(b)

Tsunami time series at the central horizontal axis. Ellipsiodal source.

Trench (a) and constant depth (b).


Directivity of tsunami generated by subduction zone sources

Wave-ray chart for the eastern Hawaii


Directivity of tsunami generated by subduction zone sources

The Alaska-Aleutian subduction zone and tsunami source location.(200x60 km, initial elevation 200 cm).


Directivity of tsunami generated by subduction zone sources

Maximum tsunami wave height around the Hawaiian islands (Source 4).


Directivity of tsunami generated by subduction zone sources

Conclusions

  • 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.

  • 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.

  • Some potentially dangerous for Hawaii locations of tsunami source were determined.


Directivity of tsunami generated by subduction zone sources

Thank you!


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