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

57

Transmitted & reflected wavesSH

58

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

61

Snell’s law for sphericalEarth

5

62

Snell’s law for sphericalEarth

63

Snell’s law for sphericalEarth

64

Snell’s law for sphericalEarth

6

65

Ray path geometry in sphericalEarth

66

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

67

Inversion modelling

7

68

Positioning with GPS

69

Ray paths for increase in velocitywith depth

70

Seismogram & ray paths

8

71

Ray paths for increasing velocity

72

Shadow zones for decreasingvelocity

73

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

75

Paths of various body wave phases

76

Body wave phase nomenclature

10

77

Seismogram & core reflections

ScS2

ScS3

78

Ray paths for core phases

79

Ray paths for major core phases

11

80

PKP arrival time data & precursors

81

SPdKS phase

82

Earth models used in seismology

12

83

Jeffreys-Bullen & IASP91 Earthmodels

84

Upper mantle velocity models

85

Lowermost mantle velocity models

13

86

Jeffreys-Bullen Earth model“regions”

87

Travel time data and IASP91 modelcurves

88

IASP91 travel time curves forsurface & deep earthquakes

14

89

Whole-mantlevelocity models

fromtomography

Surface waves & normal modes

91

Rayleigh waves: particle motion

15

92

Rayleigh wave displacements vs.depth

93

Rayleigh wave group velocity,Walvis ridge

94

Rayleigh wave phase velocity vs.oceanic plate age

16

95

6-hr record section

96

2004Sumatra

earthquakewaveforms

97

Equivalence of surface waves &normal modes

17

98

Spheroidal modes

0S2 = “footballmode”Period = 3233 s(54 min)

99

Displacement associated withtorsional mode

100

Torsional modes

18

101

The “breathing mode”

102

Amplitude spectrum, modes, 35 hrs