Lecture

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Lecture 05- Wave Propagation
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Wave Propagation

• As seismic waves travel through Earth, they
  interact with the internal structure of the
  planet and
• Refract bend / change direction
• Reflect bounce off of a boundary (echo)
• Disperse spread out in time (seismogram gets
  longer)
• Attenuate decay of wave amplitude
• Diffract non-geometric leaking of wave energy
• Scatter multiple bouncing around

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Refraction

• The direction in which a seismic wave is
  traveling can be changed if the wave travels from
  one material into another - (e.g. from the crust
  into the mantle).

earthquake
surface
Moho
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Refraction

• Question What is a real life example of
  refraction ?
• Answer Stick you arm in a fish tank and you will
  notice that the angle of your arm looks funny.
  The speed of light is different in water than in
  air, so the light rays refract across the fish
  tank boundary.

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Wave Refraction

• The change in propagation is often describe as a
  change in angles at the boundary between the
  different rocks or materials.

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Snells Law
i1
sin(i1)
sin(i2)

velocity1
velocity2
velocity1
velocity2
i2
(velocity2 velocity1)
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Snells Law

• Question At the Moho the P-wave velocity jumps
  from 6 km/s (in the crust) to 8 km/s (in the
  mantle). If a ray has an angle of incidence (i1)
  of 20o, what is the angle of refraction (i2) ??
• Answer
• sin(i2) (velocity2 / velocity1) x sin(i1)
• sin(i2) ( 8 / 6 ) x sin(20o) 0.456
• i2 sin-1(0.456) 27.1o

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Refraction

• What happens if we have several layers with
  increasing velocities?

Curved Ray Paths !
earthquake
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Refraction in Earth

• Refraction plays a big role in body wave wave
  propagation because the velocity changes with
  depth in Earth.

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Vertical Component Record SectionJun 09 (160),
1994 003316.20013.841S 67.553W H631km
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Expanded Vertical Component Record SectionJun 09
(160), 1994 003316.20013.841S 67.553W H631km
PKP
P
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Expanded Vertical Component Record SectionJun 09
(160), 1994 003316.20013.841S 67.553W H631km
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P-Wave Refraction
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Wave Reflection

• Reflections are like echoes. When a wave hits a
  boundary between two materials, part is refracted
  and part is reflected.

The reflected angle is equal to the incident
angle.
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Wave Reflection (Echoes)
i1 angle of incidence i2 angle of
refraction i3 angle of reflection
i1
i3
velocity1
i1 always equals i3
velocity2
i2
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Seismic Wave Nomenclature

• We have labels for many of the different waves.

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Seismic Wave Nomenclature

• Some Examples
• PcP a P wave that reflects off the core-mantle
  boundary (CMB)
• PmP A P wave that reflects off the Moho
• PP a P wave which bounces off the Earths
  surface midway between the earthquake and the
  seismometer

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Seismogram Complexity

• The complexity of seismograms is a result of the
  many different waves that arrive at the
  seismometer at different times.
• With experience, and an understanding of seismic
  waves and propagation, you can identify the
  various wiggles using their arrival time and the
  direction of ground vibration.

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Application Earthquake Location

• We can use this simple understanding of wave
  propagation to understand how we locate
  earthquakes using seismograms.
• Well examine a simple example, true calculations
  are more complicated, but the ideas are the same.

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Travel Time

• Travel time, T, is defined as
• T distance / velocity
• Example the travel time of a P-wave is
• Tp distance / P-velocity
• Ts distance / S-velocity
• Since P-waves travel faster than S-wave, the time
  separation between the two is larger at greater
  distances.

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S-P Time Example
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A Rule of Thumb

• Because of the structure of Earth, for distance
  ranges between about 50 and 500 km, we can use a
  formula to estimate the distance from the
  observed S-arrival time minus the P-arrival time
• distance 8 x (S-P arrival time)

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Example

• If the arrival time of an S wave is 093015.0
  (GMT) and the arrival time of a P wave is
  092945.0 (GMT), then the time difference is 30
  s. Thus, the earthquake is located about 240 km
  away from the seismometer.
• But in which direction ???

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Distances and Circles

• In this case, if you know the distance the
  earthquake is from the seismometer, you know the
  earthquake must be located on a circle centered
  on the seismometer, with a radius equal to the
  distance.

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Triangulation

• With three or more stations, you can locate the
  earthquake using triangulation.

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Summary

• As they travel through Earth, seismic waves
  interact with Earth structure (where the
  boundaries between rocks types are located and
  how big are the changes in properties).
• A number of different processes occur, including
  reflection, refraction, dispersion, attenuation,
  and diffraction.
• By studying the propagation of waves, we are able
  to estimate Earths internal structure.