1. OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS
M.A. Nosov, S.V. Kolesov
Faculty of Physics
M.V.Lomonosov Moscow State University, Russia

2. OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

3. OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS
[WinITDB, 2007]:

4. OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

5. INITIAL CONDITIONS or “roundabout manoeuvre”
1. Earthquake focal mechanism:
Fault plane orientation and depth
Burgers vector
2. Slip distribution
Central Kuril Islands, [

6. INITIAL CONDITIONS or “roundabout manoeuvre”
3. Permanent vertical bottom deformations:
the Yoshimitsu Okada analytical formulae
numerical models
4. Long wave theory
Central Kuril Islands,

7. OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

8. OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS
The “roundabout manoeuvre” means
Initial Elevation = Vertical Bottom Deformation
???
There are a few reasons why…

9. Dynamic bottom deformation (Mw=8)
[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

10. Dynamic bottom deformation (Mw=8)
permanent bottom deformation
duration ~ s
[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

11. Period of bottom oscillations

12. Time-scales for tsunami generation
L is the horizontal size of tsunami source;
H is the ocean depth
g is the acceleration due to gravity
c is the sound velocity in water
Tsunami generation is an instant process if
finite duration
However, if
instant
ocean behaves as a compressible medium

13. Time-scales for tsunami generation instant
L is the horizontal size of tsunami source;
H is the ocean depth
g is the acceleration due to gravity
c is the sound velocity in water
traditional assumptions
(i.e. instant & incompressible) are valid
Tsunami generation is an instant process if
finite duration
instant
However, if
Compressible ocean
ocean behaves as a compressible medium

14. Linear = Incompressible!
Elastic oscillations do not propagate upslope
Elastic oscillations and gravitational waves are not coupled (in linear case)
Linear = Incompressible!

15. Initial Elevation = Vertical Bottom Deformation
???

16. “Smoothing”: min~H
exponentially decreasing function

17. Initial Elevation = Vertical Bottom Deformation
Due to “smoothing”

18. Permanent bottom deformations
vertical
horizontal
Central Kuril Islands,

19. Sloping bottom and 3-component bottom deformation:
contribution to tsunami
Normal to bottom
Bottom deformation vector

20. Sloping bottom and 3-component bottom deformation:
contribution to tsunami
traditionally neglected
traditionally under consideration

21. Linear potential theory (3D model)
Tsunami generation problem: Incompressible = Linear
Linear potential theory (3D model)
1) Dynamic bottom deformation (DBD)
Not instant!
2) Phase dispersion is taken into account
Disadvantages:
1) Inapplicable under near-shore conditions due to nonlinearity, bottom friction etc.;
2) Numerical solution requires huge computational capability;
3) Problem with reliable DBD data.

22. If you can’t have the best make the best of what you have
Simple way out for practice
Instant generation
If you can’t have the best make the best of what you have

24. Simple way out for practice
Instant generation
Not only vertical but also horizontal bottom deformation is taken into account
Permanent bottom deformations (all 3 components!)
“Smoothing”, i.e. removing of shortwave components which are not peculiar to real tsunamis

25. Linear shallow water theory
Initial conditions:
Boundary conditions:
at shoreline
at external boundary
Initial elevation

26. Initial Elevation=Vertical Bottom Deformation
Initial Elevation=Vertical Bottom Deformation

27. Smoothing: Initial Elevation from Laplace Problem
Smoothing: Initial Elevation from Laplace Problem

28. Initial Elevation=Vertical Bottom Deformation
Initial Elevation=Vertical Bottom Deformation

29. Smoothing: Initial Elevation from Laplace Problem
Smoothing: Initial Elevation from Laplace Problem

30. Comparison of runup heights calculated using traditional (pure Z) and optimal (Laplace XYZ) approach

31. Conclusions:
Optimal method for the specification of initial conditions in the tsunami problem is suggested and proved;
The initial elevation is determined from 3D problem in the framework of linear potential theory;
Both horizontal and vertical components of the bottom deformation and bathymetry in the vicinity of the source is taken into account;
Short wave components which are not peculiar to gravitational waves generated by bottom motions are removed from tsunami spectrum.

32. Thank you for your attention!

34. 15 Nov 2006
13 Jan 2007

35. 15 Nov 2006
13 Jan 2007