The seismogram U = Source * Propagation * Site.
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Transcript of The seismogram U = Source * Propagation * Site.
![Page 1: The seismogram U = Source * Propagation * Site.](https://reader031.fdocuments.us/reader031/viewer/2022020308/5697c02c1a28abf838cd912b/html5/thumbnails/1.jpg)
The seismogramThe seismogram U = Source * Propagation * Site U = Source * Propagation * Site
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POINT SOURCE APPROXIMATIONPOINT SOURCE APPROXIMATION
Distance rWavelengthFault dimensionL
€
un(r x ,t) = Mpq ∗Gnp, q
€
r >> λ
λ >> L
€
r >> L
Far field terms dominates because r is relatively largeFar field terms dominates because r is relatively large
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NUCLEATION POINT POSITION
depth
surface
fault
EXTENDED SOURCEFAULT PARAMETERS
dip
N
Strike
wid
th W
length L
Hanging wallfoot wall
Fault azimuth
Fault dip
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EXTENDED SOURCEFAULT PARAMETERS
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surface
EXTENDED SOURCE PARAMETERIZATION
An extended source is represented by the distribution of point sources at the each grid point
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surface
fault
Rupture velocity (vr)
EXTENDED SOURCEFAULT PARAMETERS: Rupture Velocity
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surface
fault
d rakey
),( tyD
t
yDmax
rv
d
EXTENDED SOURCEFAULT PARAMETERS: Slip
€
tr =ξ
vr
€
ξvr
+ Tr
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barriersbarriers
asperitiesasperities
COMPLEX SOURCE PHENOMENAAsperities and barriers
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Depth
Into the
earth
Surface of the earth
Distance along the fault plane 100 km
KINEMATICS EXTENDED SOURCESlip on an earthquake fault
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 2.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 4.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 6.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 8.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 10.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 12.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 14.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 16.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 18.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 20.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 22.0
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KINEMATICS EXTENDED SOURCESlip on an earthquake fault: second 24.0
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Rupture on a Fault
Total slip during the 1992 Landers earthquake
KINEMATICS EXTENDED SOURCEFinal dislocation on the fault
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• Rupture velocity is few km/s. By default, seismologist uses 3 km/s
• The maximum duration d of the rupture is :
• The slip amplitude on the fault scales with the length.
• Slip velocity is around 1 m/s
€
T =L
vr
EXTENDED SOURCEFAULT PARAMETERS: Slip Velocity
surface
fault
Rupture velocity (vr)
L
)(tD
t
Tr = rise time
maxD
D(t).
t
maxD
tr
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CAVEAT: Using Appropriate Source Time Functions
SOURCE TIME FUNCTIONS:
The slip velocity history on each point on the fault is determined by the shape of the a priori assumed source time function.
Examples of single-window STF’s:
Examples of multi-window STF’s:time
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Kinematic relations:
N.B. This parameterization allow us to constrain the time of positive slip acceleration, i.e. time of Vpeak
Finite duration
Fast initial acceleration
Asymmetric shape
Large peak value
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Focal Mechanism
Focal Sphere around the source
A. Kelly, USGS
azimuth
S. Stein and M. Wysession
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Displacement Field from a double coupleDisplacement Field from a double couple x1
x2
x3
x1
x2
x3
x2
x1
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NODAL PLANE AND POLARITIESNODAL PLANE AND POLARITIES
+ -
- +
x3
x1
x2
dilatationcompression
x3
x2
x1
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The focal mechanism
• Polarities of first arrivals
+
-
-
+
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FOCAL MECHANISM
DISPLACEMENT DISLOCATION
+ -
-+
Dilatationcompression
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Focal Mechanism & Radiation pattern
b) Polarities of first P wave arrival• Stereographic projection
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Focal Mechanims & Radiation pattern
Calculation1) From polarities of first arrivals P-
waves
2) From waveform modeling through moment tensor
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Radiation pattern
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Radiation pattern
Far Field
Onde P
Onde S
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Radiation pattern
Far Field
Nodal Planes
S
P
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directive
antidirective
Non directive
COMPLEX SOURCE PHENOMENA
Directivity
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Hirasawa (1965)
COMPLEX SOURCE PHENOMENA
Directivity effect on radiation
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Fraunhofer ApproximationFraunhofer Approximation
€
r =r x −
r ξ = ro 1+
ξ 2
ro2
−2
r ξ ⋅ ˆ γ ( )
ro
= ro −r ξ ⋅ ˆ γ ( ) +
1
2
ξ 2
ro
−
r ξ ⋅ ˆ γ ( )
2
2ro
€
r ≈ ro −r ξ ⋅ ˆ γ ( )
The error in this approximation is
€
∂r =1
2
1
ro
ξ 2
−r ξ ⋅ ˆ γ ( )
2 ⎡ ⎣ ⎢
⎤ ⎦ ⎥<<
λ
4
€
L2 <<1
2λro
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