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2.4 Seismic Waves

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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 largely by change of volume and consists g y y gof alternating pulses of contraction and expansion acting in the direction of wave travel.

• Compressional waves are the first waves toCompressional 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 hshear 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 liquid or gasesthrough solids, liquid, or 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 solidShear waves can travel only within solid

matter.• The speed of a S wave is 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.

~ 1/ 3

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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 Olivine)orientation (LPO) of anisotropic mineral (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 amplitudeLow velocity = Large amplitude

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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 through a boundary between two different

2.5 Snell’s Law

p g g yisotropic media, such as air and glass

1. Solution of wave equation

2. Fermat’s principle3 Huygens’ principle3. 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 wavesWhy is the horizontal slowness (p) the same for P and S 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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Hydroacoustic Data

(1) International Monitoring System (IMS) hydrophone triad stations

Data

DGin Indian Ocean

- H08S : South Diego Garcia (DG) array (-7.6°, 72.5°)

- H01W : Cape Leeuwin (CL) array ( 34 9° 114 1°)

DG

CL(-34.9 , 114.1 )

Sukyung Yun

Results

NEIC catalogue (1973~2006)

Sukyung Yun

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TsunamiTsunami의의 전파전파

해저의지형 (깊이)가가장중요한요소로작용

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

j

i

j

j

dtV

i

dtVAC

AC

dtVj

AC

dtVi

sinsinsin,sin 2121

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1. Longer wavelengths broader lobes2 An obstacle (slit) is less than a half2. An obstacle (slit) is less than a half

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 i i f icontinuity of motion

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).