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

2. Tsunami sources location around the Pacific

3. The Pacific ocean bottom relief and the earthquake epicenters location

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

5. The model bottom relief and location of tsunami source

6. 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) ,

7. Wave-ray traces of tsunamis generated by the round source

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

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

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

11. Configuration of the ellipsoidal tsunami source.

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

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

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

15. Wave-ray chart for the eastern Hawaii

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

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

22. 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.

23. Thank you!