crest workshop in 2007 an integrated simulation...
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An Integrated Simulation of Seismic Wave and Tsunami Propagation
Takashi Furumura & Tatsuhiko Saito (ERI. Univ. Tokyo)
CREST Workshop in 2007
古村孝志 ・ 齊藤竜彦 (東大地震研)
Kuril Trench
Japa
n Tr
ench
Izu-
Oga
sawa
ra T
renc
h
Nankai Trough
Hokkaido
Honshu
20062007
Kuril Trench
Japa
n Tr
ench
Izu-
Oga
sawa
ra T
renc
hNankai Trough
Hokkaido
Honshu
Kyushu
North American Plate
InterplateIntraplate
Characteristics of two Tsunami Events in Kuril Islands
Large M8 earthquakes occurred in Kuril Trenchin 2006 and 2007; the former is an interplate event and the other is an intraplate event
After Yamanaka (2006; 2007)
h=6000-7000m
20062007
200 km
60 km
25 km
120 km
[Event 1] 2006 Nov. 15
[Event 2] 2007 Jan. 13
[Event 1] 2006 Nov. 15[Event 2] 2007 Jan. 13
Tsunami Database (JMA, 1999-)for 4000 Event* Source Depth (h=0,5,10km..)* Magnitude (M6,7,8,…)
100,000 stories
JMA Tsunami Alert System
After JMA
Japan Meteorological Agency (JMA) made a number of tsunami simulation and made a tsunami height database for possible events occurring around Japan.
66 areas4000 events
[1st Event] 2006 Nov. 15 ( Mj7.9; Mw8.2)
[2nd Event] 2007 Jan 13 (Mj8.2; Mw8.2)
Large Tsunami (>3m)Tsunami (>2m)Warning (<0.5m)
Tsunami Alert
60min60min
After JMA (2006;2007)
Warning (<0.5m)
Tsunami (>2m)
Warning (<0.5m)
Tsunami (>2m)
JMA Tsunami Alert
After JMA (2007)
Tide gage record shows larger tsunami from the 1st (2006) event and very weak tsunami from the 2nd (2007) event.
Over EstimationMistake Alert !
Under Estimation
Observed Tsunami
[Event 1] 2006 Nov. 15
[Event 2] 2007 Jan. 13
Hachinohe: 53cm
Hachinohe: 17cm
Observation:
Tsunami Simulation
(1) Deformation of seafloor posed by earthquake is calculated using program of Okada (1985) assuming homogeneous, half-space.
(2) Elevation of sealevel (initial tsunami) is assumed to besame as seafloor deformation x
ght
M∂η∂−=
∂∂
ygh
tN
∂η∂−=
∂∂
yN
xM
t ∂∂−
∂∂−=
∂η∂
∫η
−
=h
udzM
∫η
−
=h
vdzN
Linear long-wave equation
Equation of continuity
η: sea-level fluctuation
h: depth of sea floor
(3) Propagation of tsunami is calculated by using alinear, long-wave theory.
We made tsunami simulation for using a conventionaltsunami generation/propagation model assuming:
Tsunami Simulation
A parallel tsunami simulation code (Saito and Furumura, 2007) is used which took 30 min using 16CPU of AMD Opteron.
[Event 1] 2006 Nov. 15 [Event 2] 2007 Jan. 13
0 20 40 60 80 100 120 140 160 180-40
-30
-20
-10
0
10
20
30
0 20 40 60 80 100 120 140 160 180-60
-40
-20
0
20
40
Time [min.]
Time [min.]
Hei
ght [
mm
]H
eigh
t [m
m]
Tide Gauge.
Calculation
BPF: 100 – 10,000s
Simulation ResultsSimulation results are compared with the tide gauge data at offshore Tokachi. It is indicating under and overestimation of tsunami for 1st and 2nd events, respectively, – similar to JMA alert.
20cm
5cm
20cm
30cm
Over Estimation
Under Estimation
Tide Gauge.
Calculation
Tide Gauge Data: after JAMSTEC
[Event 1] 2006 Nov. 15
[Event 2] 2007 Jan. 13
Tsunami Simulation
(1) Deformation of seafloor posed by earthquake is evaluated using program of Okada (1985) assuming homogeneous, half-space.
(2) Elevation of sealevel (initial condition of tsunami) isassumed to be same as seafloor deformation
Conventional Assumptions:
(3) Propagation of tsunami is simulated by using alinear, long-wave theory.
Deep Sea(6000-8000m)
Small FaultHeterogeneity
Accurate Tsunami SimulationーChallenge
1. FDM Simulation of Seismic Waves
- Equation of Motions in 3D- 3D Heterogeneous structure- Source Slip model
2. FDM Simulation of tsunami generation/propagation
-Navier-Stokkes Equations in 3D-Nonlinearity, Viscosity Friction, Dispersion, etc
Coupling (one way)
After IFREE/JAMSTEC
V (x,y,t)
V (x,y,t) or P (x,y,t)
Oceanic CrustAcretionary wedge
Oceanic Mantle
pzpypxp
p fzyx
U +∂
∂+
∂∂
+∂
∂=
σσσρ &&
⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂+
∂∂
+⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂+∂
∂+
∂∂=
pU
qU
zU
yU
xU qp
pqzyx
pq μδλσ
Equation of Motions:
Constitutive Equations (Stress-Strain)
FDM Simulation of Seismic Wave/Deformation of Seabed
Upper Crust
Lower Crust
Oceanic Mantle(Vp/Vs=1.73; σ=0.25)
Accretionary Prism (Vp/Vs=2.2; σ=0.37)
Oceanic Crust(Vp/Vs=1.8-1.9; σ=0.37-0.3)
(Vp/Vs=1.8-1.73;σ=0.3-0.25)
Fault Source- Low-angle reverse fault- W=30 km- Rupture Speed, Vr=3km/s
2D FDM Simulation- Staggered-grid,8th-order- 200km*100km (D=0.25km)- T=100sec- CPU, 10 min (Opteron 2.4GHz)
Vertical Deformation of Seafloor posed by earthquake is calculated by FDM using heterogeneous subduction zone structure
Seabed
50. 100. 150. 200.Distance [km]
50.
100.
0.
Dep
th [k
m]
(a) Plate Model (b) Plate + Accretionary Wedge
FDM Simulation of Seismic Wave/Deformation
Snapshots demonstrating wave propagation and deformation caused by earthquakeRed: Vertical, Green: Horizontal component and top panel illustrating deformation of seabed
Accretionary Wedge (Vp/Vs=2.2; σ=0.37)
Vertical Deformation of Seabed
Soft sediments in acretionary wedge cause very large deformation of seabed, which leads in large tsunami !
Oceanic Mantle
Upper Crust
Oceanic CrustFault
Lower Crust
Seabed
Vertical Deformation of Seabed
Fault
Seabed
(a) Half Space (Vp/Vs=1.73) (b) Plate Model (c) Plate + Accretionary Wedge
Fault:L=60km, D=4m
Half SpacePoission Solod (Vp/Vs=1.73)
Accretionary Wedge(Vp/Vs=2.0)
Crust
3D FDM simulation of seabed deformation
Oceanic MantleOceanic Crust
Mantle
Seafloor Deformation
up
down
FaultFault
(a) (b) (c)
★Large deformation occurs when earthquake fault cut soft acretionarywedge in the trench, which should causes large tsunami
★This is considered the cause of unusually large tsunami during shallowsubduction zone earthquakes such as 1896 Sanriku M8.5 earthquake (e.g. Fukao, 1979; Satake and Tanioka, 1999, etc. ) and may also be the case forthe 1st (2006) event ?
3D FDM Simulation – Summary-
[Event 1] 2006 Nov. 15 [Event 2] 2007 Jan. 13
Effect of Deep Sea
Sea Depth: 6000-8000m
The Long-wave, shallow water approximation used in the conventional tsunami simulation does not simulate tsunami propagation in deep(6000-8000m) sea ?
[Event 1] 2006 Nov. 15
[Event 2] 2007 Jan. 13
0=⋅∇ u
wyhv
xhu
th =
∂∂+
∂∂+
∂∂
0=nu
( ) guuuu −Δν+−∇=∇⋅+∂∂ p
tp: pressure, ν: kinematic viscosity coefficient, g: gravity vector
- Navier-Stokes Equation
- Mass continuity equation (incompressible flow)
Free surface at the top
Rigid boundary at the bottom
( ) 0,, == hzyxpPressure at the top
u = (u, v, w) : velocity vector
h (x,y): height of the top surface
Full 3D FDM Simulation of Tsunami
- Boundary Conditions
- 3D FDM simulation of NSSOLA-SURF in 3D
(e.g. Hirt et al. 1975, LLNL)
Direct tsunami simulation without approximations
Numerical simulation of tsunami generation:(1) Shallow (1000m) water
(b) Small Fault (W/L=10km/5km)(a) Large Fault (W/L=20km/40km)
h=1000mD0=4mTr=5s
Sea level- Top view Sea level-Top view
Vertical Deformation of Seafloor
Deep Sea (h=6000m)D0=5mW=20km, 60km
Numerical simulation of tsunami generation: (2) Deep (6000m) water
(b) Small Fault (W/L=10km/5km)(a) Large Fault (W/L=20km/40km) Sea level Sea level
Vertical Deformation of Seafloor
Thick water column cannot push up sea level very efficiently, and so the Initial tsunami height is much lower than the vertical deformation of seabed
Horizontal ViewHorizontal View(b) Narrow Tsunami (W=20km)(a) Wide Tsunami (W=60km)
Deep Sea (h=6000m)D0=5mW=20km, 60km
6000mDistance: 500km
Simulation of tsunami propagation: (2) Deep (6000m) water
Attenuation of tsunami height due to dispersion is very significant as propagating in deep sea especially for narrow tsunami
Tsunami
Flow
Tsunami
Flow
3m
Simulation of tsunami propagation: (1) Shallow (1000m) water
Shallow Sea (h=1000m)D0=5mW=20km, 60km
(a) Narrow Tsunami (W=20km)(b) Wide Tsunami (W=60km)Slice View Slice View
Dispersion of tsunami is not sot strong in case for shallow water.
Tsunami
Flow
Tsunami
Flow
1000mDistance: 500km
3m
Sea Depth= 6000-7000m
Tsunami Simulation - Summary
[Event 1] 2006 Nov. 15[Event 2] 2007 Jan. 13
After Yamanaka (2006; 2007)
200 km
60 km
25 km
120 km
Deep: >6000mDeep: >6000mSea Depth
StrongWeakAttenuation by Dispersion
Not efficientEfficientPush up Sea surface
nomay beLarge Deformation in Acretionary Wedge
Small: 25km*120kmLarge: 200km*60kmFault Size (L*W)
[Event 2] 2007 Jan. 13Mw8.2
[Event 1] 2006 Nov. 15 Mw8.2
Weak TsunamiLarger Tsunami
Integrated Simulation for Earthquake and Tsunami
1. FDM Simulation of Seismic Waves
2. FDM Simulation of tsunami generation/propagation
One Way Coupling
Region: 800km*400km*100km(Dx=0.5km)
Time: 200s (Dt=0.005s)CPU Time: 2 hours (ES: 32 node)
Region: 800km*400km*100km(Dx=0.05km)
Time: 4000s (Dt=0.1s)CPU Time: 2 hours ?? (ES: 32 node)
Micro Scale Tsunami Simulation- Run up- Flood- etc
Oscillation Simulation of Buildings and Tanks
Deformation of seabead in 3DHeterogeneous media
Coupling
Saito and Furumura (2006)
Furumura et al. (2006)
(a) Plate Model (b) Plate + Accretionary Wedge
FDM Simulation of Seismic Wave/Deformation
Snapshots demonstrating wave propagation and deformation caused by earthquakeRed: Vertical, Green: Horizontal component and top panel illustrating deformation of seabed
Vertical Deformation of SeabedVertical Deformation of Seabed
Accretionary Wedge (Vp/Vs=2.2; σ=0.37)
Fault
Seabed
Oceanic Mantle
Upper Crust
Oceanic CrustFault
Lower Crust
Seabed
(a) Plate Model (b) Plate + Accretionary Wedge
FDM Simulation of Seismic Wave/Deformation
Snapshots demonstrating wave propagation and deformation caused by earthquakeRed: Vertical, Green: Horizontal component and top panel illustrating deformation of seabed
Accretionary Wedge (Vp/Vs=2.2; σ=0.37)
Vertical Deformation of Seabed
Soft sediments in acretionary wedge cause very large deformation of seabed, which leads in large tsunami !
Oceanic Mantle
Upper Crust
Oceanic CrustFault
Lower Crust
Seabed
Vertical Deformation of Seabed
Fault
Seabed
Two Large M8 Earthquakes in Kuril Islands
(1) 2006 Nov. 15, Mj7.9; Mw8.2 (2) 2007 Jan 13, Mj8.2; Mw8.2
JMA Tsunami Alert
1047.7日本海中部地震1983 (昭58)
2307.8北海道南西沖地震1993 (平5)
1428.5チリ地震1960 (昭35)
1,4438.0南海地震1946 (昭21)
1,2237.9東南海地震1944 (昭19)
3,0648.1昭和三陸地震1933 (昭8)
21,2598.5明治三陸地震1896 (明29)
死者数規模(M)地震名発生年
2006 Nov. 15 Event(Mw8.2)
2007 Jan 13 Event (Mw8.2)Kuril Trench
Japa
n Tr
ench
Izu-
Oga
sawa
ra T
renc
h
Nankai Trough
Hokkaido
Honshu
Shikoku
Kyushu