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