Introduction to Seismology: General Waves

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Introduction to SeismologyGeneral Waves

• Jesse Lawrence

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What is a wave?

• Wave A disturbance or variation that transfers
  energy progressively from point to point in a
  medium and that may take the form of an elastic
  deformation or a variation of pressure, electric
  or magnetic intensity potential or temperature.
• -Websters Dictionary

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What is a wave?

• Seismic Wave An elastic deformation that
  transfers energy progressively from point to
  point in a medium.

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Harmonic Wave Solution

• Any function of the form f(x?vt) describes a
  propagating wave as a function of time and
  distance
• where x is distance, v is velocity,
• t is time, A is amplitude, ? is
• angular frequency, and k is
• wavenumber.

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Velocity, Period, Frequency
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A Plucked String

• If you pluck a string that is lengthwise in the x
  direction by applying a tension, ?, in the y
  direction, the force balance between the string
  and applied force is

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Transmitted and Reflected Waves

• Left Side
• Right Side

A
C
B
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Transmitted and Reflected Waves
A
C
B
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Reflection Transmission Coefficients

• Reflection coefficient
• Transmission coefficient
• Reciprocal for orthogonal incidence

A
C
B
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Fixed-End Free-End Reflections

• Normal Reflection
• Fixed-End Reflection
• Free-End Reflections

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Reflected Transmitted Wavelengths
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Kinetic Energy

• Kinetic Energy

For a string m ?dx
average over 1 wavelength 0 - ?
Identity
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Potential Energy

• Strain
• Potential Energy
• Total Energy

(using the Taylor series approximation (1a2)1/2
1 a2/2 for small a)
? is tension.
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Propagating Wave Normal Mode

• Propagating wave solution
• Normal Mode

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Traveling Wave

• Traveling wave
• The modes are orthogonal, so
• The amplitude depends on the frequency

xs source location
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Traveling Wave

• The summation of all frequencies results in
• Destructive interference
• Constructive interference