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2012/02/15 APEC - Tsukuba International Conference VI
Strong velocity gradient related to the 2011 Tohoku Earthquake
using travel time data from active seismicity detected by the dense
seismic network
○Makoto MatsubaraNational Research Institute for Earth
Science and Disaster Prevention (NIED)
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Outline Seismic observation (NIED Hi-net)
Seismicity and velocity structure related with the Tohoku earthquake
Problem for mathematics
APEC - Tsukuba International Conference VI2012/02/15
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Seismic observation(NIED Hi-net)
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Hi-net (High-sensitivity seismograph Network)
2012/02/15 APEC - Tsukuba International Conference VI
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Seismic stations before and after 1995 event
APEC - Tsukuba International Conference VI2012/02/15
Inhomogeneous distribution
All the data are concentrated to JMA and a unified processing was
started on October 1997
- before Kobe Eq. - - after Kobe Eq. -
JMA: 188 stns.UNIV: 274 stns.NIED: 89 stns.Total: 551 stns.
(as of Jan 1995)
NIEDHi-net:782 stns.
(as of Jan 2010)
APEC - Tsukuba International Conference VI2012/02/15
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Kyushu U.
Kochi U.DPRI
Nagoya U.
ERI
Tohoku U.
Hirosaki U.
Hokkaido U.
AISTJAMSTEC
Kagoshima U.Contribution to JMA unified hypocenter catalog
7 %
5 %
NIEDHi-net57 %
22 %JMA
(March, 2009)APEC - Tsukuba International Conference VI2012/02/15
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About 200 JMA stations and 800 NIED Hi-net stations are used. APEC - Tsukuba International Conference VI2012/02/15
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Seismic waveformof the Tohoku earthquake
APEC - Tsukuba International Conference VI2012/02/15
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14:00 15:00Waveform for the Tohoku earthquake
APEC - Tsukuba International Conference VI2012/02/15
North
South
March 11, 2011
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APEC - Tsukuba International Conference VI2012/02/15
March 11 March 120:00
4:00
8:00
12:00
16:00
20:00
0:00
4:00
8:00
12:00
16:00
20:00
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Shake mapand damage of seismic stations
APEC - Tsukuba International Conference VI2012/02/15
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Shake map and damage of seismic stations
APEC - Tsukuba International Conference VI2012/02/15
Shizugawa (18 m)
Sendai (2 m)
Large acceleration
Small acceleration
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APEC - Tsukuba International Conference VI2012/02/15
Acceleration waveform
Many seismic wave emitted from different place at different time
Shizugawa
Sendai
Time[s]
Waveforms at stations along the coast
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Aftershock seismicity
APEC - Tsukuba International Conference VI2012/02/15
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Hypocenters of aftershocks in one week
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Aftershock alongthe plate boundary
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Hypocenter of aftershock in one week
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Induced seismicityafter the Tohoku earthquake
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APEC - Tsukuba International Conference VI2012/02/15
2/11 - 3/10 3/11 - 4/10Seismicity before and after the Tohoku event
Aftershocksof March 9event (M7.3)
Activated seismicityIn volcanic zone
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Seismic velocity structure
APEC - Tsukuba International Conference VI2012/02/15
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Seismic velocity structurewithin the Pacific plate
Two low-velocity zones
Landward remarkable low-velocity zone
High-velocity zone on the seaward side
Matsubara and Obara (2011)
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APEC - Tsukuba International Conference VI2012/02/15
Seismic velocity structurewithin the Pacific plate
Initial rupture point consistent with the boundary of the low-/high-velocity zones
Matsubara and Obara (2011)
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APEC - Tsukuba International Conference VI2012/02/15
Comparison with coseismic slip region
Large slip on the east side of the initial rupture point
Slip region extends 100 km on the west side of the initial rupture point
(Yagi, 2011)
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APEC - Tsukuba International Conference VI2012/02/15
(Yagi, 2011)
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APEC - Tsukuba International Conference VI2012/02/15
Western edge of the slip region consistent with the low-velocity zone
( 八木 , 2011)
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Strong-energy-radiated region on the west side of the initial rupture point
APEC - Tsukuba International Conference VI2012/02/15
Comparison with strong energy emission region
(Honda et al., 2011)
Consistentwith the high-velocity zone
betweentwo low-velocity zones
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Strong-energy-radiated region extending south-southwestward
Slightly-strong-energy-radiated region on the east side of the initial rupture point
APEC - Tsukuba International Conference VI2012/02/15
Comparison with strong energy emission region
(Honda et al., 2011)
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(Honda et al., 2011)
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Strong-energy-radiated region on the west side of the initial rupture point
Consistentwith the high-velocity zone
betweentwo low-velocity zones
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APEC - Tsukuba International Conference VI2012/02/15
Seamount ?Low-velocity zone near the initial rupture point
Subducted seamount off Ibaraki and Fukushima
(Yamasaki and Okamura, 1989)
Subducted seamount estimated from the configuration of seafloor
(Hudnut, 2011)
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(Hudnut, 2011)Matsubara and Obara (2011)
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Matsubara and Obara (2011)
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(Hudnut, 2011)Matsubara and Obara (2011)
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Matsubara and Obara (2011)
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Continuous low-velocity and low-Vp/Vs zone
Possibility of existence of subducted seamount
Matsubara and Obara (2011)
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APEC - Tsukuba International Conference VI2012/02/15
Low-velocity zone as a fluctuation within the high-velocity zone
Action as the initial rupture point
Large slip region
Matsubara and Obara (2011)
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APEC - Tsukuba International Conference VI2012/02/15
Seismic velocity structure within the Pacific plate and coseismic slip region
Two low-V zone off Tohoku region
Hypocenter consistent with the boundary of the high-/low-V zone
High-V zone between the low-V zones consistent with the strong-energy-radiated region
Coseismic slip region consistent with high-V zone on the east side of the landward low-V zone
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APEC - Tsukuba International Conference VI2012/02/15
Initial rupture within the fluctuated structure to huge coseismic slip
Low-V and low-Vp/Vs zone as the fluctuation within the high-V zone
Subducted seamount as a fluctuation within the heterogeneous structure acting as a initial rupture point
Rupture over whole high-V zone (asperity) lead to huge earthquake?
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Determination of hypocenter
APEC - Tsukuba International Conference VI2012/02/15
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Seismic wave (Body wave) P-wave
PrimaryCompressional
S-waveSecondaryTransverse
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Traditional method to determine hypocenter No GPS satellite
Difficulty in detection of accurate exact time.
Relatively easy to measure time between the arrival times of P- and S-waves
Use of differential time between the arrival times of P- and S-waves (S-P time)
APEC - Tsukuba International Conference VI2012/02/15
S-P time[sec]
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Empirical method to estimatethe distance to hypocenter
Typical crustal seismic velocityP-wave: 6.0 km/sS-wave: 3.5 km/s
In the case of 8 km hypocentral distance:P-wave arrives in 1.33 s.S-wave arrives in 2.28 s.S-P time → about 0.95 s = 2.28 - 1.33.
Distance between hypocenter and seismic station is approximately 8x[S-P time(s)] km.
APEC - Tsukuba International Conference VI2012/02/15
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Empirical method to estimatethe distance to hypocenter
Distance between hypocenter and seismic station is approximately 8x[S-P time(s)] km.
Measure S-P time at least three stations or more.
Estimation of hypocenter with compasses.
APEC - Tsukuba International Conference VI2012/02/15
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Traditional method to determine hypocenter
APEC - Tsukuba International Conference VI2012/02/15
Station A
Station BStation C
Epicenter (E)
Radius=8×[ S− P time at each station ]
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Traditional method to determine hypocenter
APEC - Tsukuba International Conference VI2012/02/15
Station A
Station BStation C
Epicenter (E)
Depth (D)
Hypocenter
Station AEpicenter (E)
Pythagorean theorem
Radius=8×[ S− P time at each station ]
𝑅𝐴=8×[S−P time at Station A ]
𝐷=√𝑅𝐴2 −AE2
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Calculation of ray path, seismic velocity, and traveltime
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Fermat’s PrincipleLight follows the path of least time.Seismic wave also does.
To rescue someone in the water, you would run along the beach until you are almost closest point on the shore, rather than swimming directly to the person.
Ray path
APEC - Tsukuba International Conference VI2012/02/15
Beach
Running: Faster
Sea
Swimming: Slower
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The deeper zone, the higher velocity, generally Deeper zone is compressed by loading above that
and becomes harder than the shallower zone.
Soft material: low velocity → slow Hard material: high velocity → fast
The deeper zone, the faster seismic velocity
Ray passes through deeper high-velocity zone to reach as fast as possible.
Sometimes, there is low-velocity zone in the deeper zone owing to the geological material
APEC - Tsukuba International Conference VI2012/02/15
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Example of ray pathin homogeneous layer structure
Ray shoots out upward if the seismic station exists near the hypocenter.
APEC - Tsukuba International Conference VI2012/02/15
Station
HypocenterFastest
Low-velocity layer
High-velocity layer
Very-high-velocity layer
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Example of ray path
Ray shoots out downward if the station is far from the hypocenter since the deeper layer has high-velocity.
APEC - Tsukuba International Conference VI2012/02/15
Fastest
Station
HypocenterLow-velocity layer
High-velocity layer
Very-high-velocity layer
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Example of ray path
Ray shoots out downward and pass though deeper layer if the station is far away from the hypocenter since the deeper layers have high-velocities.
APEC - Tsukuba International Conference VI2012/02/15
Station
Hypocenter
Fastest
Low-velocity layer
High-velocity layer
Very-high-velocity layer
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At what distance does the head wave arrive earlier?
APEC - Tsukuba International Conference VI2012/02/15
Station
Hypocenter5 km/s layer
6 km/s layer
Station
Hypocenter
D: Hypocenter distance
D < ? km D > ? km
Snell’s law Refracted waveHead wave
Direct waveFaster
Faster
𝑣1
𝑣2
𝑖
𝑗
sin 𝑖sin 𝑗=
𝑣1𝑣2
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Hypocenter
5 km/s layer
6 km/s layer
Station
6
5 18
15
√11
3√112√11
sin 𝑖= sin 𝑖sin 𝑗=
𝑣1𝑣2
=56
√ (2√11)2+ (5+𝑥+15 )2
At what distance does the head wave arrive earlier?
APEC - Tsukuba International Conference VI2012/02/15
Known:Velocity of each layer: 5 and 6 km/sThickness of the first layer: about 10 kmDepth of hypocenter: 6.6 km
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At what distance does the head wave arrive earlier?
APEC - Tsukuba International Conference VI2012/02/15
√ (2√11)2+(5+𝑥+15 )2
5 >6+185 +
𝑥6
Traveltime for direct wave
Hypocenter
5 km/s layer
6 km/s layer
Station
6
5 18
15
√11
3√112√11
sin 𝑖= sin 𝑖sin 𝑗=
𝑣1𝑣2
=56
√ (2√11)2+ (5+𝑥+15 )2
Traveltime for head wave
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Traveltime curve Many kinds of waves
How long it takes to reach seismic station for each kind of wave.
Assumption of event at earth surface
APEC - Tsukuba International Conference VI2012/02/15
Tim
e (m
inut
es)
Distance (degrees)(USGS)
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Estimation of seismic velocity structurein case of layer structure
Plot traveltime and distance at many seismic stations to draw travel time curve
Estimate the seismic velocity and thickness of each layer.
APEC - Tsukuba International Conference VI2012/02/15
Tim
e (s
ec)
Distance (km)
0 50 100
10
20
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Estimation of seismic velocity structurein case of layer structure
Seismic velocity is estimated from slope of the line.
APEC - Tsukuba International Conference VI2012/02/15
Tim
e (s
ec)
Distance (km)
0 50 100
10
20
5 km/s
6 km/s
7 km/s
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Estimation of seismic velocity structurein case of layer structure
Seismic velocity is estimated from slope of the line.
Estimate thickness of each layer from traveltimes.
APEC - Tsukuba International Conference VI2012/02/15
Tim
e (s
ec)
Distance (km)
0 50 100
10
20
5 km/s
6 km/s
7 km/s
(50 km, 10 s)
(110 km, 20 s)
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Estimation of seismic velocity structurein case of layer structure
APEC - Tsukuba International Conference VI2012/02/15
6h√11
×2
5+50− 5h
√116
=10=505
√11
sin 𝑖= sin 𝑖sin 𝑗=
𝑣1𝑣2
=56
6
5
h
ratio𝑖
𝑗𝑖
50 km
5 km/s layer
6 km/s layer
h=7.5 km
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Advanced method of inversion of seismic velocity
APEC - Tsukuba International Conference VI2012/02/15
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Seismic tomography Method of resolving internal structure in
the earth like CT scan
Fastzone
Slowzone
Averagevelocity
zone
Ray passing throughmainly slow zone→ Long time
Ray passing throughmainly fast zone→ Short time
Ray passing throughaverage zone
2012/02/15 APEC - Tsukuba International Conference VI
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Principle of seismic tomography Traveltime: Time of wave propagation from
hypocenter to seismic station
Residual = to – tcto: Observed traveltimetc: Calculated traveltime
Distance betweenthe earthquake
and seismic station [km]
Traveltime [s]Seismic velocity
[km/s]=
2012/02/15 APEC - Tsukuba International Conference VI
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Principle of seismic tomography Residual =
: Observed traveltime : Calculated traveltime
Positive residual: Actually more time to propagate Actual seismic velocity is slowerthan the assumed seismic velocity
2012/02/15 APEC - Tsukuba International Conference VI
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Principle of seismic tomography Residual =
: Observed traveltime : Calculated traveltime
Negative residual: Actually less time to propagate Actual seismic velocity is fasterthan the assumed seismic velocity
2012/02/15 APEC - Tsukuba International Conference VI
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Process of seismic tomography Residual :
Difference between observed and calculated traveltimes
Homogeneousmedia
Calculation of residuals Distribution of residualson ray paths
2012/02/15 APEC - Tsukuba International Conference VI
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Process of seismic tomography
Homogeneousmedia
Estimationof low velocity zone
Estimationof high velocity zone
Calculation of residuals Distribution of residualson ray paths
2012/02/15 APEC - Tsukuba International Conference VI
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Observation equation
(Time to proceed 1 km)
[s/km] [km] [s]
Lengthof ray path
at a grid nodeFor each ray
(Matrix)
Slownessat a grid node
(Vector)Unknown
Traveltimefor eachRay path
(Vector)
X =
2012/02/15 APEC - Tsukuba International Conference VI
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Observation equationN
umbe
r of r
ay p
aths
Number of unknown parameters
Length of ray pathat a grid node
Slo
wne
ssat
a g
rid n
ode
X =
trave
ltim
e of
eac
h ra
y pa
th
We can solvewith calculation
of inverse matrix
BUT
Too huge matrix
2012/02/15 APEC - Tsukuba International Conference VI
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Tsunami arrival
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Tsunami velocity Tsunami velocity
: Gravitational acceleration: Depth of water (sea)
Depth: 1000 m → 99 m/s 350 km/h Depth: 3000 m → 171 m/s 617 km/h Depth: 5000 m → 221 m/s 800 km/h
APEC - Tsukuba International Conference VI2012/02/15
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Estimation of arrival time of tsunami Pacific ocean: Average depth 4000 m Tsunami velocity 200 m/s 700 km/h
Distance between Japan and Chile across Pacific ocean: 17000 km
APEC - Tsukuba International Conference VI2012/02/15
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Estimation of arrival time of tsunami Known
Distance to hypocenterDepth of the water (sea)
We can estimate the arrival time of tsunami
We can study both arithmetic and disaster prevention.
APEC - Tsukuba International Conference VI2012/02/15
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Thank you for your attention!
APEC - Tsukuba International Conference VI2012/02/15