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
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
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
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