Transcript Слайд 1 - Tsunami Laboratory, Novosibirsk, Russia.
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
OPTIMAL INITIAL CONDITIONS FOR SIMULATION OF
SEISMOTECTONIC TSUNAMIS [WinITDB, 2007]:
1547 80 % 1940
OPTIMAL
INITIAL CONDITIONS
FOR SIMULATION OF
SEISMOTECTONIC TSUNAMIS
INITIAL CONDITIONS or “roundabout manoeuvre” 1. Earthquake focal mechanism:
Fault plane orientation and depth
Burgers vector 2. Slip distribution
Central Kuril Islands, 15.11.2006
[http://earthquake.usgs.gov/]
INITIAL CONDITIONS or “roundabout manoeuvre” 3. Permanent vertical bottom deformations:
the Yoshimitsu Okada analytical formulae
numerical models 4. Long wave theory
Central Kuril Islands, 15.11.2006
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 (M w =8)
[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]
Dynamic bottom deformation (M w =8) permanent bottom deformation duration ~10-100 s
[Andrey Babeyko, PhD, GeoForschungsZentrum, Potsdam]
Period of bottom oscillations
Time-scales for tsunami generation
H / g L / gH
Tsunami generation is an instant process if
T H / g
However, if
T 4 H / c
ocean behaves as a compressible medium 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
finite duration
H / g
instant
Time-scales for tsunami generation
H / g L / gH
Tsunami generation is an instant process if
T H / g
However, if
T 4 H / c
ocean behaves as a compressible medium L
is the horizontal size of tsunami source;
H traditional assumptions
is the acceleration due to gravity
c
is the sound velocity in water
are valid finite duration
H / g 4 H / c
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 ???
“Smoothing”:
min ~H
T min ~ H / g 1 ( x , y , t )
exponentially decreasing function
cosh 1 8 3 i s s i i dp dm dn p 2 exp( cosh( pt kH ) imx gk iny tanh( ) ( p , kH ) p m 2 , n ) where ( p , m , n ) 0 dt dx dy exp( pt imx k 2 m 2 n 2 iny ) ( x , y , t )
Initial Elevation = Vertical Bottom Deformation Due to “smoothing”
Permanent bottom deformations vertical horizontal
Central Kuril Islands, 15.11.2006
Sloping bottom and 3-component bottom deformation: contribution to tsunami
( x , y , t ) n ( x , x , y , z y , t ) n x , n y , n z
Normal to bottom Bottom deformation vector
Sloping bottom and 3-component bottom deformation:
n ( n ,
contribution to tsunami
n x 0 n y 0 ) n x x n y y n n z z 1 z
traditionally neglected
n
traditionally under consideration
Tsunami generation problem: Incompressible = Linear
t 2 F n F 2 F x v ( x , , y , y , t 0
Linear potential theory (3D model)
t z , g t ( ) , F z n , ), 1 g F t F z z z 0 0 ( x , y , t )
Not instant!
2) Phase dispersion is taken into account
H ( x , y ).
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.
Simple way out for practice
0 dt , is bottom
best make the best of
nt
Instant generation
duration
what you have
H / g F 0 at bottom 0 , z H ( x , y ) : where 0 0 ( ) Fdt F n t , n 0 , n
at water surface z 0 : 2 F t 2 g F z 2 Fˆ t 2 g Fˆ z nondimensi t * t / , onal variables z * z / H : 2 Fˆ t * 2 2 Fˆ H / g z * Fˆ 0 initial elevation : H / g 0 0 w z 0 dt 0 F z z 0 dt Fˆ z z 0
Simple way out for practice Instant generation
0
n
0
0 ,
z z
0
Not only vertical but also Permanent bottom deformations horizontal bottom deformation (all 3 components!) is taken into account
0
,
n
, z
H ( x , y )
“Smoothing”, i.e. removing of shortwave components which are not peculiar to real tsunamis
initial elevation
Linear shallow water theory
2 t 2 R 2 1 cos 2 gH R 2 1 cos gH cos
Initial conditions:
( , , 0 ) 0 ( , ) t 0
Initial elevation Boundary conditions:
n 0
at shoreline
t t gH R gH R
at external boundary
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
13.01.2007
Smoothing: Initial Elevation from Laplace Problem
10
Comparison of runup heights calculated using traditional (pure Z) and optimal (Laplace XYZ) approach 15.11.2006
13.01.2007
10 1 1 0.1
0.1
1 Runup heights, m (Laplace XYZ) 10 0.1
0.1
1 Runup heights, m (Laplace XYZ) 10
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.
15 Nov 2006 13 Jan 2007 Volume, km 3 10 8 6 -2 -4 -6 -8 4 2 0 9.0
6.1
6.1
-6.4
-5.2
-5.2
Laplace, XYZ Laplace, Z Pure, Z Laplace, XYZ Laplace, Z Pure, Z
3 15 Nov 2006 Energy, 10 14 J 13 Jan 2007 2 2.36
1 1.23
1.36
1.00
0.84
0.97
0 Laplace, XYZ Laplace, Z Pure, Z Laplace, XYZ Laplace, Z Pure, Z