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

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF

SEISMOTECTONIC TSUNAMIS

%801940

1547[WinITDB, 2007]:

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

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

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…

Dynamic bottom deformation (Mw=8)

[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

permanent bottom

deformationduration ~10-100 s

Dynamic bottom deformation (Mw=8)

[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]

Period of bottom oscillations

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

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

1.Elastic oscillations do not propagate upslope

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

Linear = Incompressible!

Initial Elevation = Vertical Bottom Deformation???

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

Initial Elevation = Vertical Bottom Deformation

Due to “smoothing”

Permanent bottom deformations

vertical horizontal

Central Kuril Islands, 15.11.2006

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

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

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.

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

0z0 0 0z

0z0

2

2

2

2

2

2

2

z

F̂dt

z

Fdtw

:elevation

initial

0F̂*z

F̂

g/H*t

F̂

H/z*z,/t*t

:variablesonalnondimensiz

F̂g

t

F̂

z

Fg

t

F

:0zsurfacewaterat

g/H

elevationinitialz

F̂

)y,x(Hz,n,n

F̂

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

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

15.11.2006

Initial Elevation=Vertical Bottom Deformation

15.11.2006

Smoothing: Initial Elevation from Laplace Problem

13.01.2007

Initial Elevation=Vertical Bottom Deformation

Smoothing: Initial Elevation from Laplace Problem

13.01.2007

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

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.

Thank you for your

attention!

15 Nov 2006 13 Jan 2007Volume, km3

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Laplace,XYZ

Laplace, Z Pure, Z Laplace,XYZ

Laplace, Z Pure, Z

15 Nov 2006 13 Jan 2007Energy, 1014J

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Laplace, Z Pure, Z Laplace,XYZ

Laplace, Z Pure, Z