2.4 Seismic Waves
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2
2.4.1 Plane waves
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2.4.3 Spherical waves
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Appendix
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Characteristics of P
 A compressional wave, deforms rocks
g y by
y change
g of volume and consists
largely
of alternating pulses of contraction and
expansion acting in the direction of wave
travel.
• Compressional waves are the first waves to
be recorded by a seismometer, so they are
called P (for “primary”) waves.
P-wave: Longitudinal wave (縱波)
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Characteristics S waves
 The second kind of body waves is a
shear
h
wave.
• Shear waves deform materials by change
of shape,
• Because shear waves are slower than P
waves and reach a seismometer some time
after P waves arrives, they are called S (for
“secondary”) waves.
S-wave: Transverse wave
SV motions on the vertical plane parallel to the propagation direction
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• Compressional (P) waves can pass
through solids
solids, liquid
liquid, or gases
gases.
• P waves move more rapidly than other
seismic waves:
– 6 km/s is typical for the crust.
– 8 km/s is typical for the uppermost mantle.
 Shear (S) waves consist of an alternating
series of side-wise movements.
• Shear waves can travel only within solid
matter.
• The speed of a S wave is ~ 1/ 3 times that of a
P wave. A typical speed for a S wave in the
crust is 3.5 km/s, 5 km/s in the uppermost
mantle.
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• Seismic anisotropy - the dependence of seismic wave
speed on direction of polarization.
• Large-scale horizontal flow  Lattice preferred
orientation (LPO) of anisotropic mineral (e.g.
(e g Olivine)
 Vsh > Vsv
http://garnero.asu.edu/resources/animations/splits.html
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2.4.5 Energy in a plane wave
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Low velocity = Large amplitude
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2.5 Snell’s Law
Snell’s Law is a formula used to describe the
relationship between the angles of incidence and
refraction, when referring to light or other waves,
passing
p
g through
g a boundary
y between two different
isotropic media, such as air and glass
1. Solution of wave equation
2. Fermat’s principle
3 Huygens
3.
Huygens’ principle
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Use x,y,z for ease of intuition.
Let’s consider plane waves propagating in the x-z plane.
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Ray path
Which medium is faster?
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2.5.5 Critical angle
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2.5.7 Ray parameter and slowness
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Why is the horizontal slowness (p) the same for P and S waves,
waves
but the vertical slowness different?
Because we have horizontal boundaries!
2.5.8 Waveguides
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SOFAR (SOund Fixing And Range)
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Data
 Hydroacoustic Data
(1) International Monitoring
System (IMS)
hydrophone triad stations
in Indian Ocean
DG
- H08S : South Diego
Garcia (DG) array
(-7.6°, 72.5°)
- H01W : Cape Leeuwin
(CL) array
( 34 9°, 114.1
(-34.9
114 1°))
CL
Sukyung Yun
Results
NEIC catalogue (1973~2006)
Sukyung Yun
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Tsunami의
Tsunami
의 전파
해저의 지형 (깊이)가 가장 중요한 요소로 작용
Titov et al., (2005)
2.5.9 Fermat’s principle and geometric ray theory
Fermat’s principle: The ray paths between two points are those for which the
travel time is an extremum, a minimum or maximum, with respect to the nearby
possible path
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2.5.10 Huygens’ principle and diffraction
Huygens’ principle: Each point on a wavefront is considered to be a Huygens’ source
that give rise to another circular wave front
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i
i
j
sin i 
V1dt
V dt
V dt V dt
, sin j  2  AC  1  2
sin i sin j
AC
AC
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1. Longer wavelengths  broader lobes
2 An obstacle (slit) is less than a half
2.
wavelength wide, waves are insensitive
to the details of its structure
3. The slit is very wide, diffraction occurs
only at the slit’s edges.
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There has to be a
continuity
i i off motion
i
along the boundary (e.g.,
the P waves leaving the
boundary have to have
the same frequency as
the S waves arriving at
the boundary).
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