Introduction to Seismology: Surface Waves

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Introduction to SeismologySurface Waves

• Wednesday, November 16, 2005
• Jesse Lawrence
• Office Munk Room 209
• Email jlawrence_at_ucsd.edu
• Webhttp//titan.ucsd.edu/classes/ITS/

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Surface Waves
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Geometry for Love Rayleigh Wave Motion
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The Earth Rings Like a Bell
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Rayleigh Wave Displacement as a Function of Depth
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Horizontal Vertical Rayleigh Wave Motions
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Love Waves

• Constructive interference of SH wave multiples.
• Destructive interference occurs at all but a few
  specific times at a given location
• Time between bounces is given by pX(p), where p
  is the ray parameter.
• The phase velocity is given by
• c 1/p k/?
• Phase velocity is dependent upon frequency, which
  causes dispersion.

X(t)
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Love Waves Continued

• Constructive interference of SH wave multiples.
• When phase velocity varies by frequency
  (dispersion) interference occurs, making energy
  travel at a different velocity called the group
  velocity
• With some math

X(t)
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Love Waves Continued
T
Group Velocity
Phase Velocity

• Phase Velocity
• c k/?
• Group Velocity

SSS
SS
S
X
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Love Wave Geometry

• Love waves occur because incoming SH waves are
  trapped within a Layer
• In other words the layer acts as a waveguide.
• interference between incoming and layer-reflected
  waves.
• This only happens at just the right angle of
  incidence
• This angle is defined by the modes of Earths
  geometry.

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Love Wave Geometry
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Love Wave Dispersion

• Dispersion occurs because longer-period waves
  sample more of the halfspace, and travel at
  faster velocities.

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Displacement of Love Waves

• A Love Wave oscillates as cos(kxr?1z) in a layer,
  but decays exponentially as exp(-kxr?2z) in the
  halfspace below.
• The vertical sensitivities of the modes are the
  eigenfunctions.

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Modes
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Phase v. Group Velocity

• Sum two harmonic waves with slightly different
  frequency and wavenumbers
• u(x,t) cos(?1t-k1x) cos(?2t-k2x)

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Phase v. Group Velocity

• Phase Velocity
• c(?) ?/k(?)
• ? 1/period, k 1/wavelength
• c(?) is distance/time
• Group Velocity
• U(?) d?/dk
• U(?) distance/time

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Fundamental Mode Love Wave Group Phase
Velocities
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Love Wave Group Dispersion
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Love Wave Group Dispersion

• Filter a single wave at a bunch of different
  frequencies/periods.
• Longer periods arrive earlier than shorter ones.

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Walvis Ridge Rayleigh wave group velocity

• Group velocity is lower on the ridge than off the
  ridge because of a shallow low velocity layer at
  85 km depth.

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East Pacific Rise Phase Velocities
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Phase Velocity Oceanic Plate Age
Dispersion curves as function of age
Inverted structure

• Higher velocities for older oceanic plates
• Thick, cold lithosphere leads to higher
  velocities

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Global Surface Wave Maps