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

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

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

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Page 1: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

M.A. Nosov, S.V. KolesovFaculty of Physics

M.V.Lomonosov Moscow State University, Russia

Page 2: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

Page 3: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

%801940

1547[WinITDB, 2007]:

Page 4: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

Page 5: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

INITIAL CONDITIONS or “roundabout manoeuvre”

1. Earthquake focal mechanism:

Fault plane orientation and depth

Burgers vector2. Slip distribution

[http://earthquake.usgs.gov/]

Central Kuril Islands, 15.11.2006

Page 6: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

3. Permanent vertical bottom deformations:

the Yoshimitsu Okada analytical formulae

numerical models

Central Kuril Islands, 15.11.2006

INITIAL CONDITIONS or “roundabout manoeuvre”

4. Long wave theory

Page 7: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

Page 8: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

The “roundabout manoeuvre” means

Initial Elevation = Vertical Bottom Deformation

???There are a few reasons why…

Page 9: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Dynamic bottom deformation (Mw=8)

[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

Page 10: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

permanent bottom

deformationduration ~10-100 s

Dynamic bottom deformation (Mw=8)

[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

Page 11: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Period of bottom oscillations

Page 12: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

g/H

Time-scales for tsunami generation

gH/Lg/H Tsunami generation is an instant process if

g/HT

L is the horizontal size of tsunami source;H is the ocean depthg is the acceleration due to gravityc is the sound velocity in water

instantHowever, if

c/H4T ocean behaves as a compressible medium

finite duration

Page 13: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

g/H

L is the horizontal size of tsunami source;H is the ocean depthg is the acceleration due to gravityc is the sound velocity in water

instant

c/H4

Compressib

le ocea

n

finite duration

traditional assumptions (i.e. instant & incompressible)

are valid

Time-scales for tsunami generation

gH/Lg/H Tsunami generation is an instant process if

g/HT However, if

c/H4T ocean behaves as a compressible medium

Page 14: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

1.Elastic oscillations do not propagate upslope

2.Elastic oscillations and gravitational waves are not coupled (in linear case)

Linear = Incompressible!

Page 15: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Initial Elevation = Vertical Bottom Deformation???

Page 16: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

222

0

2

2is

is3

nmk

)t,y,x()inyimxptexp(dydxdt)n,m,p(

where

p)kHtanh(gk)kHcosh(

)n,m,p()inyimxptexp(pdndmdp

i8

1)t,y,x(

“Smoothing”: min~H

exponentially decreasing function kHcosh

1

g/H~Tmin

Page 17: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Initial Elevation = Vertical Bottom Deformation

Due to “smoothing”

Page 18: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Permanent bottom deformations

vertical horizontal

Central Kuril Islands, 15.11.2006

Page 19: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Normal to bottom

Bottom deformation vector

zyx ,,)t,y,x(

zyx n,n,n)t,y,x(n

Sloping bottom and 3-component bottom deformation:contribution to tsunami

Page 20: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

zzyyxxn nnn),n(

traditionally under

consideration

traditionally neglected

Sloping bottom and 3-component bottom deformation:contribution to tsunami

n

0n x 0n y 1n z

Page 21: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

F)t,z,y,x(v

t

F

g

1t,y,x

).y,x(Hz),n,(tn

F

0z,z

Fg

t

F

0F

0z

2

2

Linear potential theory (3D model)

)t,y,x(1) Dynamic bottom deformation (DBD)

Tsunami generation problem: Incompressible = Linear

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.

Page 22: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

n,n

F̂n,

tn

F

:)y,x(Hzbottomat

FdtF̂where,0F̂0F

g/H

durationntdisplacemebottomis,dt

0

0

0

Simple way out for practice Instant generation

If you can’t have the best make the best of

what you have

)(0

Page 23: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

0z0 0 0z

0z0

2

2

2

2

2

2

2

z

F̂dt

z

Fdtw

:elevation

initial

0F̂*z

g/H*t

H/z*z,/t*t

:variablesonalnondimensiz

F̂g

t

z

Fg

t

F

:0zsurfacewaterat

g/H

Page 24: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

elevationinitialz

)y,x(Hz,n,n

0z,0F̂

0F̂

0

0

Simple way out for practice Instant generation

Permanent bottom deformations (all 3 components!)

Not only vertical but also horizontal bottom deformation is taken into account

“Smoothing”, i.e. removing of shortwave components which are not peculiar to real tsunamis

Page 25: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

0t

),()0,,( 0

R

gH

t

R

gH

t

0n

Linear shallow water theory

Initial conditions: Boundary conditions:

cosgHcosR

1gH

cosR

1

t 2222

2

at shoreline

at external boundary

Initial elevation

Page 26: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

15.11.2006

Initial Elevation=Vertical Bottom Deformation

Page 27: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

15.11.2006

Smoothing: Initial Elevation from Laplace Problem

Page 28: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

13.01.2007

Initial Elevation=Vertical Bottom Deformation

Page 29: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Smoothing: Initial Elevation from Laplace Problem

13.01.2007

Page 30: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

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

approach

0.1

1

10

0.1 1 10Runup heights, m (Laplace XYZ)

Run

up h

eigh

ts, m

(pu

re Z

)

0.1

1

10

0.1 1 10Runup heights, m (Laplace XYZ)

Run

up h

eigh

ts, m

(pu

re Z

)

15.11.2006 13.01.2007

Page 31: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Conclusions: 1. Optimal method for the specification of initial conditions in the tsunami problem is suggested and proved;

2. The initial elevation is determined from 3D problem in the framework of linear potential theory;

3. Both horizontal and vertical components of the bottom deformation and bathymetry in the vicinity of the source is taken into account;

4. Short wave components which are not peculiar to gravitational waves generated by bottom motions are removed from tsunami spectrum.

Page 32: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

Thank you for your

attention!

Page 33: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS
Page 34: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

15 Nov 2006 13 Jan 2007Volume, km3

9.06.1 6.1

-6.4-5.2 -5.2

-8

-6

-4

-2

0

2

4

6

8

10

Laplace,XYZ

Laplace, Z Pure, Z Laplace,XYZ

Laplace, Z Pure, Z

Page 35: OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF SEISMOTECTONIC TSUNAMIS

15 Nov 2006 13 Jan 2007Energy, 1014J

1.00 0.84 0.971.23 1.36

2.36

0

1

2

3

Laplace,XYZ

Laplace, Z Pure, Z Laplace,XYZ

Laplace, Z Pure, Z