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March 4, 2008 1 John Anderson: GE/CEE 479/679: Lecture 13
Earthquake EngineeringGE / CEE - 479/679
Topic 13. Wave Propagation 2
John G. Anderson
Professor of Geophysics
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March 4, 2008 2 John Anderson: GE/CEE 479/679: Lecture 13
Combining in F=ma
• In this equation, Xi is a body force acting on the point, if any.
•
( ) iii
i Xuxt
uρμ
θμλρ +∇+
∂
∂+=
∂
∂ 22
2
23
2
22
2
21
22
x
u
x
u
x
uu
∂∂
+∂∂
+∂∂
=∇
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March 4, 2008 3 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 4 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 5 John Anderson: GE/CEE 479/679: Lecture 13
The Free Surface
• S-waves can have two polarizations:– SH - wave motion is parallel to
the surface. Causes only horizontal shaking.
– SV - wave motion is oriented to cause vertical motion on the surface.
• Amplitudes are approximately doubled
SH
SV
Motion in and out of the plane of this figure - hard to draw.
Motion perpendicular to the direction of propagation causes vertical motion of the free surface.
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March 4, 2008 6 John Anderson: GE/CEE 479/679: Lecture 13
Two Media in Contact
• This way of drawing is consistent with horizontal layers in the Earth.
• Lower velocities near the surface imply wave propagation direction is bent towards the vertical as the waves near the surface.
111 ,, βμρ
222 ,, βμρ
i1
i2
2
2
1
1 sinsin
ββii
=
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March 4, 2008 7 John Anderson: GE/CEE 479/679: Lecture 13
Two Media in Contact• For an incoming SV
wave, the situation gets even more complex.
• In this case, both P- and SV-waves are transmitted and reflected from the boundary.
• The P- and SV-waves are coupled by the deformation of the boundary.
1111 ,,, αβμρ
1222 ,,, αβμρ
i1
i2 i2
Incoming SVReflected SV
Transmitted SV
Transmitted P
Reflected Pj2
j1
Generalized Snell’s Law
2
2
1
1
2
2
1
1 sinsinsinsin
ααββjjii
===
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March 4, 2008 8 John Anderson: GE/CEE 479/679: Lecture 13
Realistic Earth Model
• Eventually, as the velocity increases with depth, rays are bent back towards the surface.
• Waves cannot penetrate into layers where β is too large.
111 ,, βμρ
222 ,, βμρ
i1
i2
2
2
1
1 sinsin
ββii
=
βi
psin
=
p is the “ray parameter. It is constant along the ray
β increases
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March 4, 2008 9 John Anderson: GE/CEE 479/679: Lecture 13
Body Waves: Discussion
• The travel time curves of body waves can be inverted to find the velocity structure of the path.
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March 4, 2008 10 John Anderson: GE/CEE 479/679: Lecture 13
Seismic Refraction
• Because velocity increases with depth, rays are bent back towards the surface.
• Apparent velocity at the array of sensors is the same as the velocity of the refracted ray along the top of the refracting layer.
• Records from a profile of sensors radial from an explosion can thus be inverted to find velocity with depth.
111 ,, βμρ
222 ,, βμρ
i1
i2
2
2
1
1 sinsin
ββii
=
βi
psin
=
p is constant along the ray
β increases
* ΔΔΔΔΔΔΔΔΔΔΔΔ
Refracted wave
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March 4, 2008 11 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 12 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 13 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 14 John Anderson: GE/CEE 479/679: Lecture 13
Realistic Earth Model
• Due to Snell’s law, energy gets trapped near the surface.
• This trapped energy organizes into surface waves.
111 ,, βμρ
222 ,, βμρ
i1
i2
2
2
1
1 sinsin
ββii
=
β increases
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March 4, 2008 15 John Anderson: GE/CEE 479/679: Lecture 13
Four types of seismic wavesBody WavesP Waves Compressional, Primary
S Waves Shear, Secondary
Surface WavesLove Waves
Rayleigh Waves
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March 4, 2008 16 John Anderson: GE/CEE 479/679: Lecture 13
Surface Waves
• Love waves: trapped SH energy.
• Rayleigh waves: combination of trapped P- and SV- energy.
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March 4, 2008 17 John Anderson: GE/CEE 479/679: Lecture 13
Surface Waves
• For surface waves, geometrical spreading is changed.– For body waves, spreading is ~1/r.– For surface waves, spreading is ~1/r0.5.
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March 4, 2008 18 John Anderson: GE/CEE 479/679: Lecture 13
Surface Waves: Discussion
• Body waves are not dispersed.• Surface waves are dispersed, meaning that
different frequencies travel at different speeds.• Typically, low frequencies travel faster. These
have a longer wavelength, and penetrate deeper into the Earth, where velocities are faster.
• Typically, Love waves travel faster than Rayleigh waves.
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March 4, 2008 19 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 20 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 21 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 22 John Anderson: GE/CEE 479/679: Lecture 13
Surface Waves
• Surface wave dispersion curves can be inverted to find the velocity structure of the path crossed by the surface waves.
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March 4, 2008 23 John Anderson: GE/CEE 479/679: Lecture 13
Surface Waves: Discussion• Particle motion in S-waves is normal to the direction of
propagation.
• This is also true of Love waves.
• However, Love waves would show changes in phase along the direction of propagation that would not appear in vertically propagating S waves.
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March 4, 2008 24 John Anderson: GE/CEE 479/679: Lecture 13
Surface Waves: Discussion
• Motion of Rayleigh waves is “retrograde elliptical”.
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March 4, 2008 25 John Anderson: GE/CEE 479/679: Lecture 13
Site Response
• What is site response
• What causes it
• What are it’s characteristics.
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March 4, 2008 26 John Anderson: GE/CEE 479/679: Lecture 13
Classic example of site effect : Mexico City
• Mexico City, Mexico
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March 4, 2008 27 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 28 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 29 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 30 John Anderson: GE/CEE 479/679: Lecture 13
Figure 2
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March 4, 2008 31 John Anderson: GE/CEE 479/679: Lecture 13
Physics of Site Response
• Layer over half space
• Multiple layers over half space
• Basins
• Topography
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March 4, 2008 32 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 33 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 34 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 35 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 36 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 37 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 38 John Anderson: GE/CEE 479/679: Lecture 13
Multiple flat layers
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March 4, 2008 39 John Anderson: GE/CEE 479/679: Lecture 13
Basins: major phenomena
• Amplification
• Energy trapped
• Conversion to surface waves at basin edge
• Longer duration
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March 4, 2008 40 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 41 John Anderson: GE/CEE 479/679: Lecture 13
• Basin edge
• Kobe, Japan earthquake disaster.
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March 4, 2008 42 John Anderson: GE/CEE 479/679: Lecture 13
Liu and Heaton, ~1980
Study of strong motion from the San Fernando earthquake.
Published in Bull. Seism. Soc. Am.
Demonstration of a basin effect.
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March 4, 2008 43 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 44 John Anderson: GE/CEE 479/679: Lecture 13
Site Characterization• Goal: characterize the average effect of geology on strong motion,
and use this to improve predictions.
• The shallow geology is an almost miniscule part of the total path from the earthquake to the station.
• However, it has a strong effect on the ground motions, because it is the closest to the station.
• Geophysical measurements, using wave propagation techniques, are used to measure near-surface site characteristics.
• Also need to know basin geometry, depth.
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March 4, 2008 45 John Anderson: GE/CEE 479/679: Lecture 13
Geotechnical Site Classification
• Many schemes to classify the site.
• Encroaching into the territory that Prof. Siddharthan will discuss later.
• But it’s good to introduce the subject from the viewpoint of the seismologist.
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March 4, 2008 46 John Anderson: GE/CEE 479/679: Lecture 13
Seed and Idriss (1982)
• 1. Rock sites• 2. Stiff soil sites (< 60 m deep)• 3. Deep cohesionless soil sites (> 75 m deep)• 4. Sites underlain by soft to medium stiff clays
Problem with this approach:Does not recognize that the spectral shape also depends on the earthquake magnitude.
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March 4, 2008 47 John Anderson: GE/CEE 479/679: Lecture 13
Geotechnical Classification Schemes
• Geology– Material on a geological map
• For example, for California one simple approach is the “QTM” approach, using the age of the material.
• Q = Quaternary• T = Tertiary• M = Mesozoic
– Whether the location is “erosion-dominated” or “sedimentation-dominated” (rock, soil)
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March 4, 2008 48 John Anderson: GE/CEE 479/679: Lecture 13
NEHRP Category
Description Shear velocity
(m/s)
A Hard rock >1500
B Firm to hard rock 760-1500
C Dense soil, soft rock 360-760
D Stiff soil 180-360
E Soft soil <180
F Special studies soils
NEHRP ClassificationShear velocity of near-surface materials
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March 4, 2008 49 John Anderson: GE/CEE 479/679: Lecture 13
Empirical site response and comparison with measured site conditions at ANSS sites in the
Reno area
Pancha, Anderson, Biasi, Anooshepor, Louie
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March 4, 2008 50 John Anderson: GE/CEE 479/679: Lecture 13
Results from Pancha’s ReMi studies in the Central Truckee Meadows
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March 4, 2008 51 John Anderson: GE/CEE 479/679: Lecture 13
Figure 1a
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March 4, 2008 52 John Anderson: GE/CEE 479/679: Lecture 13
Figure 3
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March 4, 2008 53 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 54 John Anderson: GE/CEE 479/679: Lecture 13
Figure 1b
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March 4, 2008 55 John Anderson: GE/CEE 479/679: Lecture 13
Figure 5
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March 4, 2008 56 John Anderson: GE/CEE 479/679: Lecture 13
Alternate Figure 9
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March 4, 2008 57 John Anderson: GE/CEE 479/679: Lecture 13
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March 4, 2008 58 John Anderson: GE/CEE 479/679: Lecture 13
Figure 3
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March 4, 2008 59 John Anderson: GE/CEE 479/679: Lecture 13
Figure 2
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March 4, 2008 60 John Anderson: GE/CEE 479/679: Lecture 13
Figure 6
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March 4, 2008 61 John Anderson: GE/CEE 479/679: Lecture 13
OLD Figure 7