・ rays snell ’ s law structure of the earth ・ seismic waves near-field terms (static...
TRANSCRIPT
![Page 1: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/1.jpg)
・ 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
II.1 Theoretical Seismology 2: Wave Propagation
![Page 2: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/2.jpg)
Seismic waves
Faulting
![Page 3: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/3.jpg)
Homogeneous Earth
![Page 4: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/4.jpg)
Structure in the Earth
Crust-MantleCore-Mantle
440 km660 km
![Page 5: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/5.jpg)
Snell’s LawFermat’s Principle
1
2 sin 1 / sin 2 = n21
Air
Water
Rays
![Page 6: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/6.jpg)
1
2
1 < 2
Ray Paths in a Layered Medium
1
2
1 > 2
S lower
Faster
Faster
Slower
![Page 7: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/7.jpg)
1
2
3
Ray Paths in a Layered Medium
1/1
1/2
1/3
Distance
Time
![Page 8: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/8.jpg)
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
Moho
![Page 9: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/9.jpg)
![Page 10: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/10.jpg)
![Page 11: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/11.jpg)
Forward Branch
Backward Branch
![Page 12: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/12.jpg)
Forward Branch
Backward Branch
Forward Branch
Shadow Zone
![Page 13: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/13.jpg)
Forward Branch
Backward Branch
Forward Branch
Shadow Zone
PcP
・ 1912 Gutenberg observed shadow zone 105o to 143o
・ 1939 Jeffreys fixed depth of core at 2898 km (using PcP)
ForwardBranch
BackwardBranch
ForwardBranch
PPcP
PKP
Shadow Zone
![Page 14: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/14.jpg)
PcP
Core Reflections
![Page 15: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/15.jpg)
![Page 16: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/16.jpg)
Aspects of Waves not Explained by Ray Theory
・ Different types of waves (P, S) ・ Surface Waves ・ Static Displacements ・ Frequency content
Seismic Waves
![Page 17: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/17.jpg)
Wave Equation
21
2
21
12 1
t
u
cx
u
1-D wave equation c = propagation speed
Slinky: constant velocity wave propagation, no mass transfer, different from circulation eq.
![Page 18: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/18.jpg)
1-D Wave Equation
21
2
21
12 1
t
u
cx
u
LW 3.2.1
2
T T = wave period = angular frequency
)]/(sin[),( cxtAtxu Solution
![Page 19: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/19.jpg)
Wave Period and Wavelength
wavelength 300 km
Velocity 6 km/s
Velocity = Wavelength / Period
x
t
wavelength
period
Space
Time
period 50 sfrequency = 1/period= 0.02 hz
![Page 20: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/20.jpg)
Body waves ( P ・ S )
0.01 to 50 sec 50 m to 500 km
Surface waves 10 to 350 sec 30 to 1000 km
Free Oscillations 350 to 3600 sec 1000 to 10000 km
Static Displacements
-
Period Wavelength
![Page 21: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/21.jpg)
)()()2(2
2
uuft
u
3-D Wave Equation with Source
source spatial 2nd derivative
Solution
dtM
rAtxu
r
r
N )(1
4
1),(
/
/ 04 )(
1
4
1)(
1
4
1022022
rtM
rA
rtM
rA ISIP
)(1
4
1)(
1
4
10303
rtM
rA
rtM
rA FSFP
Near-field Terms (Static Displacements)
Far-field Terms (P, S Waves)
![Page 22: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/22.jpg)
Near-field terms
・ Static displacements
・ Only significant close to the fault
・ Source of tsunamis
r/ r/
t →
r/ r/
![Page 23: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/23.jpg)
Static Displacements
Bei-Fung Bridge near Fung-Yan city, 1999 Chi-Chi, Taiwan earthquake
![Page 24: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/24.jpg)
Static displacements
Co-seismic deformationof 2003 Tokachi-okiEarthquake (M8.0)
![Page 25: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/25.jpg)
Generation of Tsunami from Near-field Term
![Page 26: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/26.jpg)
Far-field Terms
・ Propagating Waves
・ No net displacement
・ P waves
・ S waves
)(1
4
1)(
1
4
10303
rtM
rA
rtM
rA FSFP
![Page 27: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/27.jpg)
Surface Waves
S
Shearer, Fig. 8.1
Period (sec)
Love
RayleighG
roup
Velo
city
(km
/sec)
![Page 28: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/28.jpg)
January 26, 2001 Gujarat, India Earthquake (Mw7.7)
Recorded in Japan at a distance of 57o (6300 km)
Love Waves
vertical
radial
transverse
Rayleigh Waves
![Page 29: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/29.jpg)
Normal Modes Normal Modes
(Daishinji, Fukui Prefecture)(Daishinji, Fukui Prefecture)Free Oscillations of the Earth 1960 Chile Earthquake
Useful for studies of ・ Interior of the Earth ・ Largest earthquakes
(Stein and Gellar 1978)
![Page 30: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/30.jpg)
Toroidal and Spheroidal Modes
ToroidalSpheroidal
Dahlen and Tromp Fig. 8.5, 8.17
![Page 31: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/31.jpg)
Natural Vibrations of the Earth
Shearer Ch.8.6Shearer Ch.8.6Lay and Wallace, Ch. 4.6Lay and Wallace, Ch. 4.6
![Page 32: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/32.jpg)
Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
Free Oscillations l=1 m=1
![Page 33: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/33.jpg)
Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
Free Oscillations l=1 m=2
![Page 34: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/34.jpg)
Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
Free Oscillations l=1 m=3
![Page 35: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/35.jpg)
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
![Page 36: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/36.jpg)
![Page 37: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/37.jpg)
Why are observed seismograms so messy ?
![Page 38: ・ Rays Snell ’ s Law Structure of the Earth ・ Seismic Waves Near-Field Terms (Static Displacements) Far-Field Terms (P, S, Surface waves) ・ Normal modes](https://reader030.vdocuments.pub/reader030/viewer/2022032606/56649ea05503460f94ba3e21/html5/thumbnails/38.jpg)
Structure: Free Surface
Earth is a not homogenous whole-space
Free surface causes many complications - surface waves - reflections (pP, sP, sS)