1
Lecture 2
Locations
51
P
S
Love
Rayleigh
Seismic waves
52
Waves on a seismogram (110˚)
2
53
Expansion of early arrivals
54
Example earthquake
55
Ray paths through multilayeredstructure
3
56
Transmitted & reflected wavesP & SV
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Transmitted & reflected wavesSH
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Site effects: Ground displacementfor 1989 Loma Prieta earthquake
4
Derivation of p, the rayparameter
p is the horizontal slowness of a wave.It is the reciprocal of velocity.
60
Snell’s law for sphericalEarth
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Snell’s law for sphericalEarth
5
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Snell’s law for sphericalEarth
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Snell’s law for sphericalEarth
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Snell’s law for sphericalEarth
6
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Ray path geometry in sphericalEarth
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Partial derivatives in terms of p
!
"T
"h= #
(r2
v(r )2# p
2)1/ 2
r
"T
"$= #
r sin i cosz
v(r )
"T
"%= p sin z sin$
Variations intravel timewithhypocentraldepth
Variations inlatitude
Variationswith longitude
r = radius of Earth
i = take-off angle
z = azimuth
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Inversion modelling
7
68
Positioning with GPS
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Ray paths for increase in velocitywith depth
70
Seismogram & ray paths
8
71
Ray paths for increasing velocity
72
Shadow zones for decreasingvelocity
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Triplication effects for increasingvelocity
High amplitudeswhere raysconcentrated
Low amplitudeswhere rayssparse
9
74
Focusing of P waves at the antipode
Rial, J.A., Geophys. J. R. astr. Soc. (1978) 55, 737-743
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Paths of various body wave phases
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Body wave phase nomenclature
10
77
Seismogram & core reflections
ScS2
ScS3
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Ray paths for core phases
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Ray paths for major core phases
11
80
PKP arrival time data & precursors
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SPdKS phase
82
Earth models used in seismology
12
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Jeffreys-Bullen & IASP91 Earthmodels
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Upper mantle velocity models
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Lowermost mantle velocity models
13
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Jeffreys-Bullen Earth model“regions”
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Travel time data and IASP91 modelcurves
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IASP91 travel time curves forsurface & deep earthquakes
14
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Whole-mantlevelocity models
fromtomography
Surface waves & normal modes
91
Rayleigh waves: particle motion
15
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Rayleigh wave displacements vs.depth
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Rayleigh wave group velocity,Walvis ridge
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Rayleigh wave phase velocity vs.oceanic plate age
16
95
6-hr record section
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2004Sumatra
earthquakewaveforms
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Equivalence of surface waves &normal modes
17
98
Spheroidal modes
0S2 = “footballmode”Period = 3233 s(54 min)
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Displacement associated withtorsional mode
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Torsional modes
18
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The “breathing mode”
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Amplitude spectrum, modes, 35 hrs