Earthquake Engineering GE CEE 479679 Topic 13' Wave Propagation 2

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Earthquake EngineeringGE / CEE - 479/679Topic
13. Wave Propagation 2

• John G. Anderson
• Professor of Geophysics

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Combining in Fma

• In this equation, Xi is a body force acting on
  the point, if any.

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The Free Surface
SH

• 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

Motion in and out of the plane of this figure -
hard to draw.
SV
Motion perpendicular to the direction of
propagation causes vertical motion of the free
surface.
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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.

i1
i2
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Two Media in Contact
Transmitted SV

• 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.

Transmitted P
i1
j1
i2
i2
Reflected P
j2
Incoming SV
Reflected SV
Generalized Snells Law
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Realistic Earth Model
p is the ray parameter. It is constant along
the ray
i1
i2

• Eventually, as the velocity increases with depth,
  rays are bent back towards the surface.
• Waves cannot penetrate into layers where ß is too
  large.

ß increases
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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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Seismic Refraction
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i1
Refracted wave
i2

• 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.

ß increases
p is constant along the ray
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Realistic Earth Model
i1
i2

• Due to Snells law, energy gets trapped near the
  surface.
• This trapped energy organizes into surface waves.

ß increases
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Four types of seismic waves Body Waves P Waves
Compressional, Primary S Waves Shear,
Secondary Surface Waves Love Waves Rayleigh
Waves
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Surface Waves

• Love waves trapped SH energy.
• Rayleigh waves combination of trapped P- and SV-
  energy.

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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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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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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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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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Surface Waves Discussion

• Motion of Rayleigh waves is retrograde
  elliptical.

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Site Response

• What is site response
• What causes it
• What are its characteristics.

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Classic example of site effect Mexico City

• Mexico City, Mexico

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Figure 2
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Physics of Site Response

• Layer over half space
• Multiple layers over half space
• Basins
• Topography

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Multiple flat layers
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Basins major phenomena

• Amplification
• Energy trapped
• Conversion to surface waves at basin edge
• Longer duration

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• Basin edge
• Kobe, Japan earthquake disaster.

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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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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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Geotechnical Site Classification

• Many schemes to classify the site.
• Encroaching into the territory that Prof.
  Siddharthan will discuss later.
• But its good to introduce the subject from the
  viewpoint of the seismologist.

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Seed and Idriss (1982)

• 1. Rock sites
• 2. Stiff soil sites (lt 60 m deep)
• 3. Deep cohesionless soil sites (gt 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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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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NEHRP ClassificationShear velocity of
near-surface materials
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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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Results from Panchas ReMi studies in the Central
Truckee Meadows
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Figure 1a
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Figure 3
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Figure 1b
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Figure 5
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Alternate Figure 9
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Figure 3
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Figure 2
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Figure 6
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OLD Figure 7