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Seismology: Wave Propagation. Art McGarr Based on lectures by James Mori and Dave Boore . Contents. ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes

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seismology wave propagation

Seismology: Wave Propagation

Art McGarr

Based on lectures by James Mori and Dave Boore

contents
Contents

・ 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

wave propagation
Wave Propagation
  • As seismic waves travel through Earth, they interact with the internal structure of the planet and:
    • Refract – bend / change direction
    • Reflect – bounce off of a boundary (echo)
    • Disperse – spread out in time (seismogram gets longer)
    • Attenuate – decay of wave amplitude
    • Diffract – non-geometric “leaking” of wave energy
    • Scatter – multiple bouncing around
what is a wave
What is a Wave ?
  • A wave is a disturbance that transfers energy.
  • Waves are common in nature:
    • Light is a wave
    • Sound is a wave
  • Waves are periodic in both space and time (they have wavelengths and periods)
sound wave analogy
Sound Wave Analogy
  • Seismic waves represent acoustic (sound) energy and so are analogous to speech:

Speech

Earthquakes

  • Vocal cords vibrate
  • (2) Sound waves propagate
  • thru atmosphere
  • (3) Ears record these
  • vibrations
  • (4) Brain processes the
  • recordings
  • A locked fault segment fails (ruptures)
  • (2) Sound waves propagate thru the Earth
  • (3) Seismometers record these vibrations
  • (4) Seismologists process these recordings (seismograms)
slide6

Homogeneous Earth

If the Earth had constant velocity the wave paths would be very simple.

slide7

Structure in the Earth results in complicated paths

Lowrie, 1997, fig 3.69

Bolt, 2004, fig 6.3

slide8

q1

Air

Water

q2

sin q1 / sin q2 = n21

Snell’s Law

Fermat’s Principle

Rays

slide9

a1

q1

q2

a2

a1 > a2

Ray Paths in a Layered Medium

a = velocity of seismic energy in the layer

Faster

a1

q1

Slower

Slower

q2

Faster

a2

a1 < a2

slide10

Time

1/a3

1/a2

1/a1

Distance

Ray Paths in a Layered Medium

a1

a2

a3

slide11

The 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

The Moho

The Moho

Copywrite Tasa Graphic Arts

slide14

Forward Branch

شاخه در حال پيشروی

Receding Branch

شاخه در حال عقب نشينی

slide15

Forward Branch

شاخه در حال پيشروی

Shadow Zone

زون سايه

Forward Branch (PKPbc)

شاخه در حال پيشروی

Receding Branch (PKPab)

شاخه در حال عقب نشينی

slide16

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

slide17

PcP

Core Reflections

انعکاسات هسته

slide19

Seismic Waves

・ Different types of waves (Body, Surface)

・ Wave Equation

・ Static Displacements

・ Frequency content

seismic wave types
Seismic Wave Types

Seismic waves can be labeled by the paths they take in the Earth.

  • Body Waves:
    • P waves
    • S waves
  • Surface Waves:
    • (1) Love Waves
    • (2) Rayleigh Waves
slide22

Surface Waves

امواج سطحی

slide23

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

زلزله گجرات هند، 26 جنوری سال 2001 شدت 7.7

عمودی

vertical

Rayleigh Waves

امواج ری لی

P PP S SS

radial

دايروی

transverse

متقاطع

Love Waves

امواج لف

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

در فاصله 57 درجه (6300 کيلومتر) در جاپان ثبت گرديده است.

slide24

1-D Wave Equation

معادله موج يک بعدی

Solution:

c = propagation speed

c = سرعت پخش

This is the equation that explains the waves on a spring: constant velocity wave propagation, no mass transfer, different from circulation eq.

wave period and wavelength
Wave Period and Wavelengthپيريود يا دوران موج و طول موج

Velocity = Wavelength / Period

سرعت =طول موج تقيسم بر پيريود يا دوره

Space

فضاء

x

Velocity 6 km/s

سرعت 6 کيلومتر فی ثانيه

Wavelength

طول موج

period 50 s

Wavelength 300 km

Time

زمان

t

period 50 s

frequency = 1/period= 0.02 hz

Period

پيريود يا دوره

slide26

پيريود

Period

طول موج

Wavelength

multiple frequency signals
Multiple-Frequency Signals
  • Most signals are composites of waves with many different frequency components.
  • The range of frequency is sometimes called the “band” and we speak of bandwidth.
slide28

3-D Wave Equation with Source

معادله سه بعدی با منبع آن

Source

منبع

spatial 2nd derivative

مشتق دوم فضايي

Near-field Terms (Static Displacements)

مراحل نزديک به ساحه (بيجايي ستاتيک)

Solution

حل

Far-field Terms (P, S Waves)

مراحل ساحه دور امواج پی و اس

slide29

r/a

r/b

r/a r/b

Near-field terms

مراحل نزديک به ساحه

  • ・ Static displacements
  • بيجايی ستاتيک
  • ・ Only significant close to the fault
  • فقط زمانيکه به منبع نزديک باشد مهم است
  • ・ Source of tsunamis
  • منبع سونامی ها

t →

slide30

Static Displacements

بيجايی ستاتيک (ساکن)

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

پل بی فنگ نزديک شهرفنگ يان، زلزله منطقه چی چی تايوان سال 1999

slide31

Static displacements

بيجايی ستاتيک يا ساکن

Co-seismic deformation

of 2003 Tokachi-oki

Earthquake (M8.0)

تغيير شکل حاصله از زلزله تکاچی اوکی سال 2003 مقياس 8.0

slide32

Generation of Tsunami from Near-field Term

توليد سونامی از مرحله نزديک به ساحه

زلزله!

ترينچ

ساحه ذخيره سترين يا فشار

سونامی

EA

برگشت الاستيکی

PAC

slide33

Far-field Terms

مرحله دور از ساحه

  • ・ Propagating Waves
  • پخش امواج
  • ・ No net displacement
  • in an elastic medium
  • هيچ نوع بيجايی در جسم
  • الاستيکی صورت نمی گيرد
  • ・ P waves
  • امواج P
  • ・ S waves
  • S امواج
slide34

Normal Modes

Liberty Bell

(USA)

Useful for studies of

・ Interior of the Earth

・ Largest earthquakes

l=1 m=3

l=1 m=1

l=1 m=2

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

slide35

Toroidal and Spheroidal Modes

حالات تورويدل و کروی

Toroidal

تورويدل

Spheroidal

کروی

Dahlen and Tromp Fig. 8.5, 8.17

slide36

Natural Vibrations of the Earth

اهتزازات طبيعی زمين

Indexes describe spherical harmonics

اندکس های حالات مختلف کروی را تشريح می کند

بعضی از دوره های حالت نورمال مشاهده شده

حالتهای کروی

حالتهای تورويدل

Shearer Ch.8.6

Lay and Wallace, Ch. 4.6

slide37

Summary

خلاصه

Rays شعاعها

Velocity structure includes gradients, discontinuities

and LVZ’s, causing complicated ray paths

through the Earth (P, PKP, PcP)

ساختمان سرعت گريدينتها، انقطاعها و زونهای سرعت پايين را در

بر دارد که مسير شعاعها را در زمين مغلق ميسازد.

Wave theory explains

تيوری امواج چيز های ذيلرا تشريح می نمايد:

・ P and S waves

امواج پی و اس

・ Static displacements

بيجايی ستاتيک

・ Surface waves

امواج سطحی

Normal Modes

حالاتهای نورمال

The Earth rings like a bell at long periods

زمين مانند زنگ برای مدتهای طويل به صدا می آيد