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・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) PowerPoint Presentation
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Theoretical Seismology 2: Wave Propagation. ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes Free oscillations of the Earth. Faulting. Seismic waves.

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Presentation Transcript
slide1

Theoretical Seismology 2: Wave Propagation

・ Rays

Snell’s Law

Structure of the Earth

・ Seismic Waves

Near-Field Terms (Static Displacements)

Far-Field Terms (P, S, Surface waves)

・ Normal modes

Free oscillations of the Earth

slide2

Faulting

Seismic waves

slide4

Structure in the Earth

Crust-Mantle

Core-Mantle

440 km

660 km

slide5

Snell’s Law

Fermat’s Principle

Rays

q1

Air

Water

q2

sin q1 / sin q2 = n21

slide6

a1

q1

q2

a2

a1 > a2

Ray Paths in a Layered Medium

Faster

a1

q1

Slower

Slower

q2

Faster

a2

a1 < a2

slide7

Time

1/a3

1/a2

1/a1

Distance

Ray Paths in a Layered Medium

a1

a2

a3

slide8

Moho

Andrija Mohorovicic (1857-1936)

Found seismic discontinuity at

30 km depth in the Kupa Valley

(Croatia).

Mohorovicic discontinuity or ‘Moho’

Boundary between crust and mantle

slide11

Forward Branch

Backward Branch

slide12

Forward Branch

Shadow Zone

Forward Branch

Backward Branch

slide13

PcP

Shadow

Zone

・ 1912 Gutenberg observed shadow zone 105o to 143o

・ 1939 Jeffreys fixed depth of core at 2898 km

(using PcP)

Backward

Branch

Forward

Branch

PKP

Forward

Branch

PcP

Shadow

Zone

P

Forward Branch

Forward

Branch

Backward Branch

slide14

PcP

Core Reflections

slide16

Seismic Waves

Aspects of Waves not Explained by Ray Theory

・ Different types of waves (P, S)

・ Surface Waves

・ Static Displacements

・ Frequency content

slide17

Wave Equation

1-D wave equation

c = propagation speed

Slinky: constant velocity

wave propagation, no mass transfer, different from circulation eq.

slide18

1-D Wave Equation

Solution

T = wave period

w = angular frequency

LW 3.2.1

wave period and wavelength
Wave Period and Wavelength

Velocity 6 km/s

Space

x

wavelength 300 km

wavelength

Time

t

period 50 s

frequency = 1/period= 0.02 hz

period

Velocity = Wavelength / Period

slide20

Period

Wavelength

slide21

3-D Wave Equation with Source

source

spatial 2nd derivative

Near-field Terms (Static Displacements)

Solution

Far-field Terms (P, S Waves)

slide22

r/a

r/b

r/a r/b

Near-field terms

  • ・ Static displacements
  • ・ Only significant close to the fault
  • ・ Source of tsunamis

t →

slide23

Static Displacements

Bei-Fung Bridge near Fung-Yan city, 1999 Chi-Chi, Taiwan earthquake

slide24

Static displacements

Co-seismic deformation

of 2003 Tokachi-oki

Earthquake (M8.0)

slide26

Far-field Terms

  • ・ Propagating Waves
  • ・ No net displacement
  • ・ P waves
  • ・ S waves
slide28

Surface Waves

GroupVelocity (km/sec)

Love

Rayleigh

Period (sec)

S

Shearer, Fig. 8.1

slide29

January 26, 2001 Gujarat, India Earthquake (Mw7.7)

vertical

Rayleigh Waves

radial

transverse

Love Waves

Recorded in Japan at a distance of 57o (6300 km)

amplitude and intensity

A(t) = A0e -ω0t/2Q

Amplitude and Intensity

Seismic waves loose amplitude with distance traveled - attenuation

So the amplitude of the waves depends on distance from the earthquake. Therefore unlike magnitude intensity is not a single number.

slide31

Modified Mercalli Intensity

I Barely felt

II Felt by only few people

III Felt noticeably, standing autos rock slightly

IV Felt by many, windows and walls creak

V Felt by nearly everyone, some dished and windows broken

VI Felt by all, damaged plaster and chimneys

VII Damage to poorly constructed buildings

VIII Collapse of poorly constructed buildings,

slight damage to well built structures

IX Considerable damage to well constructed buildings,

buildings shifted off foundations

X Damage to well built wooden structures, some masonary

buildings destroyed, train rails bent, landslides

XI Few masonary structure remain standing, bridges

destroyed, ground fissures

XII Damage total

slide32

Normal Modes

(Stein and Gellar 1978)

Free Oscillations of the Earth

1960 Chile Earthquake

(Daishinji, Fukui Prefecture)

Useful for studies of

・ Interior of the Earth

・ Largest earthquakes

slide33

Toroidal and Spheroidal Modes

Toroidal

Spheroidal

Dahlen and Tromp Fig. 8.5, 8.17

slide34

Natural Vibrations of the Earth

Shearer Ch.8.6

Lay and Wallace, Ch. 4.6

slide35

Free Oscillations l=1 m=1

Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

slide36

Free Oscillations l=1 m=2

Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

slide37

Free Oscillations l=1 m=3

Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html

slide38

Summary

Rays

Earth structure causes complicated ray paths

through the Earth (P, PKP, PcP)

Wave theory explains

・ P and S waves

・ Static displacements

・ Surface waves

Normal Modes

The Earth rings like a bell at long periods