Transcript Intrinsic Attenuation

Seismic Attenuation
---from seismic wave travel
times to amplitudes
Haijiang Zhang
Courtesy of many different sources
Haberland et al., GRL 2003
EARTHQUAKE MAGNITUDE
Earliest measure of earthquake
size
Dimensionless number
measured various ways,
including
ML local magnitude
mb body wave magnitude
Ms surface wave magnitude
Mw moment magnitude
Easy to measure
No direct tie to physics of
faulting
Attnuation Mechanisms:
(1) Geometrical spreading: wavefront spreading out while energy per unit
area becomes less.
(2) Multipathing: waves seek alternative paths to the receiver. Some are
dispersed and some are bundled, thereby affecting amplitudes.
(3) Scattering: A way to partition energy of supposedly main arrivals into
boundary or corner diffracted, scattered energy.
Key: very wavelength dependent.
(4) intrinsic attenuation: due to anelasticity
the real earth materials are always “lossy”, leading to reduced wave
amplitudes, or intrinsic attenuation.
Mechanisms to lose energy:
(1) Movements along mineral dislocations
(2) Shear heating at grain boundaries
These are called “internal friction”.
……
4
Analogous to light behavoirs…
Geometric spreading: light moves
outward from lamp in expanding
spherical wave fronts. By conservation
of energy, the energy in a unit area of
the growing wave front decreases as r-2,
where r is the radius of the sphere or
distance from the lamp.
GEOMETRIC SPREADING:
SURFACE WAVES
Expect minimum at =90º, and maxima at 0º and 180º
From geometric
spreading alone, expect
minimum at =90º, and
maxima at 0º and 180º
Also have effects of
anelasticity
GEOMETRIC SPREADING: BODY WAVES
For body waves, consider a spherical wavefront moving away from a deep
earthquake. Energy is conserved on the expanding spherical wavefront
whose area is 4 π r 2, where r is the radius of the wavefront.
Thus the energy per unit wave front decays as 1 / r2, and the amplitude
decreases as 1 / r
MULTIPATHING
Seismic waves are focused and defocused by variations in velocity.
Effect of Multipathing
Idea of Ray Tubes in body waves
Angle dependent: ray bundle
expands or contracts due to
velocity structure. Also: amplitude
varies with takeoff angle
Ray tube size affects amplitudes,
10
smaller area means larger amplitude
Scattering:
Scattering occurs when there are velocity heterogeneities in
the medium with wavelengths on the order of  of the wave.
A simulation of 100 randomly-perturbed scatterers…
Snieder et al., Science, 2002
Moving the scatterers (here, 1/40th of the distance shown,
so the perturbation is visible) mostly changes the shapes
and amplitudes of the waveforms…
Waveforms
measured in a
granite sample
at temperatures
of 45°C (blue)
and 50°C (red).
Snieder et al., Science, 2002
Changing the matrix velocity, by contrast, introduces a shift
(delay or advance) that increases with coda time.
Scattering:
Interesting aside:
Coda energy in the
Earth tends to
attenuate much more
rapidly than on the
Moon!
This is partly because
lunar regolith is
highly fractured by
impacts, but mostly
because it contains
no fluids (and
consequently much
less intrinsic
attenuation!)
Intrinsic Attenuation:
Intrinsic attenuation, or anelasticity,
Spring constant k
describes the process by which elastic energy
in the Earth is converted to heat when the
seismic wave induces unrecoverable
deformation.
To examine this, let’s consider a spring:
For an idealized spring,
i 0 tt 0 
 2u
m 2  ku  0 has solution ut Ae
t
k
with oscillation frequency 0 
u
m
More realistically though, internal friction in the
spring will damp the system resulting in
where  is a damping
 2u
u 
m 2  m 
 ku  0
factor and Q  0/
t
t
is called the quality factor.
Mass
m
Intrinsic Attenuation:
This system has a solution with real and
imaginary parts; the actual displacement is the
real part and takes the form:
Reut A0e
 0t
2Q
Spring constant k

cos t
i.e., a harmonic oscillator with an exponential
decay of amplitude. Here, A0 is the initial
displacement (at time t = 0) and

Important to note:
  0 1
1
4Q 2
• High frequencies attenuate more than low
• Harmonic frequency is changed by attenuation
• Higher Q 
results in less change to frequency
and less intrinsic attenuation for given time
u
Mass
m
Generally,
loss of
amplitude due
to intrinsic
attenuation is
much greater
than that due
to partitioning,
spreading and
the other
amplitude
effects we
have
discussed
Definition of the quality factor
E

Q  
2 E
1
Energy dissipated in
a cycle
Energy stored
 f 
A  A0 exp 
 Qt 
Putting everything together
Aij ( f )  Si ( f )I j ( f )Gij (R)Bij ( f ,R
Bij ( f )  exp( 
 fR
vQ
)
Intrinsic attenuation
(1) Movements along mineral dislocations
(2) Shear heating at grain boundaries
• Affected by temperature, pressure,
frequency, and medium properties
• Attenuation property is complementary to
velocity.
Haberland et al., GRL 2003
The key here is to correlate a decrease in Q with fluids in the crust and
mantle. The fluid layer again represents melting due to subduction.
Myers et al., 1995
23
(Romanowicz & Mitchell, 2007)
Nakajima et al., 2003, GRL
How to estimate Q
•Code wave
•Surface wave
•Body wave
•Amplitude data
•…….
Coda wave
attenuation
Kumar et al., 2005
Estimating Q from body wave
----- using t*
Aij ( f )  Si ( f )I j ( f )Gij (R)Bij ( f ,R)
é æ ö2 ù
f
ln[A( fi )] = ln(W0 )+ ln[S( fi )]- ln ê1+ ç ic ÷ ú + (-p fit*)
êë è f ø úû
Site Response
Attenuation Model
Amplitude Q
tomography
(Shunping Pei)
ABCE
• Amplitude of
horizontal component
• Period
2005 1 1
O=03 15 40.2
+/- 0.04s
LAT=26.92 N
+/- 0.30km
LONG=100.31 E +/- 0.33km
DEPTH= 10 km +/- 0.14km
STATIONS USED = 6, STAND DEV= 2.63s
ML=2.9/ 6,
EYA 0.9 202 Pg
03 15 56.4 0.7
Sg 03 16 07.6 -0.1
SMN
ML=3.0
0.6 0.20
SME
0.6 0.61
PZH 1.4 108 Pn
03 16 03.1 -2.3
Pg
03 16 05.0 0.9
Sg 03 16 19.4 -3.2
SMN
ML=2.9
0.6 0.17
SME
0.7 0.18
XAC 2.1 347 Pn
03 16 15.7 0.5
Pg
03 16 19.6 3.0
Sg 03 16 44.5 -0.4
SMN
ML=3.2
1.0 0.11
SME
1.0 0.23
TCG1 2.5 221 Pg
03 16 24.0 0.0
Sg 03 16 55.7 -2.2
SMN
ML=3.7
0.6 0.52
SME
0.5 0.42
KMI 2.8 128 Pg
03 16 28.9 -1.1
Sg 03 17 07.4 -1.1
SMN
ML=2.8
0.8 0.045
SME
0.7 0.047
ZOT 3.1 82 ePg 03 16 36.8 2.5
Sg 03 17 14.6 -1.5
SMN
ML=2.8
1.0 0.031
SME
1.0 0.038
Theory and Method
Station
Source
Crust
Upper mantle
Aij ( f )  O j ( f ) I i ( f ) Si ( f )Gij ( R) Bij ( f , R)
Aij ( f )  O j ( f ) I i ( f ) Si ( f )Gij ( R) Bij ( f , R)
Bij ( f )  exp(
Q  Q0 f

 fR
vQ
1
0
)  exp(cQ R)
c  f
1
/v
1
0
Yij  ln Aij ( f )  ln Gij ( R)  ai  b j  Q cR
ai  ln Si ( f )
b j  ln O0 ( f )
1
0
Yij  ln Aij ( f )  ln Gij ( R)  p * M L  ai  b j  Q cR
b j  ln O0 ( f )  p * M L
Yij  ai  b j   Q cRijk
1
0 k
k
ML Tomography in North China
ABCE of 1985 to 1995
(Annual Bulletin of Chinese Earthquakes)
1. Each event was recorded by at least 2 stations,
2. Residuals between -2.0 ~ 2.0 ,
3. Period T of the Sg wave maximum amplitude (A) is between 0.4~2.0s,
4. Epicentral distance is between 100km-800km.
5. Event depth is less than 20km.
10899 amplitude data
1732 events
91
stations
10899 Amplitude data
1732 Events (+)
91
Stations (▲)
Histogram of ML distribution
500
400
Count
300
200
100
0
2.5
3.0
3.5
4.0
4.5
Events Magnitude ML
5.0
5.5
Result
Earthquakes with M>7
Phillips et al., 2005
Q from the tomographic inversion of 1 Hz Lg amplitude ratios
Liu et al., 2004
Yij  ai  b j   Q cRijk
1
0 k
k
Yij  ai  b j   Q cRijk
1
0 k
k
Checkerboard Test
2°× 2°
Checkerboard Test
1.5°× 1.5°
Standard deviation 0.67
Standard deviation 0.41
Summary
• Crustal attenuation can be reconstructed by tomographic imaging
method using amplitude data.
• Attenuation levels are correlated with regional tectonic structure.
High attenuation often occurs in active tectonic areas with
significant faulting, while attenuation is low in the stable Ordos
Craton.
• The estimate of attenuation shows a close correlation with
topography.
Q0 is generally low in basins, whereas high Q0 mostly occurs in
mountains and uplift regions where crystalline basement appears
in the surface. It is possible that low Q0 in basins is caused by
fluid in the upper crust, and deep sediment in basins, while high
Q0 in the mountains and uplift regions results from the presence
of old, dense rocks there.
(Published in BSSA(2006))