Activity 3: Seismic Waves: Basic
Principles | |

By taking into account moment of inertia as well as
mass, we can
eliminate models that
don’t describe the Earth, specifically single shell models with uniform density and those in
which density
decreases linearly with depth. We are left with a model in which density
increases with
depth, but it fails to explain certain data from earthquakes. Before looking at
those data, we
need to look at the
basics of seismic waves. Earthquakes generate two types of waves that travel through Earth’s interior. Primary or P waves cause particles in rocks to jiggle back and forth in the direction that the wave is traveling. In contrast, shear or S waves cause rock particles to move perpendicular to the direction that the wave is traveling. Long before seismologists developed the technology to record the miniscule ground motions caused by earthquakes, mathematicians predicted the existence of P and S waves in elastic bodies. They also derived mathematical relationships between wave velocities and various physical properties: | |

(Eq. 1) | |

The elastic constant used in this equation depends on the type of wave.
Shear-wave deformation
causes rocks to
change shape but
does not affect
their volume. The elastic constant that pertains to shear-wave deformation is known as rigidity R.
Thus the velocity
of shear waves V_{S} is | |

(Eq. 2) | |

A rigid material will
have a larger
value of R
than a material that
is easily deformed. Because they have no rigidity (R = 0), fluids cannot transmit S waves. | |

P waves cause change in
both the volume
and shape of a rock. Thus, P-wave velocity V_{P} depends on the rigidity and a second elastic
constant known as the
incompressibility or bulk modulus C. With this added parameter,
the velocity
equation for P waves is | |

(Eq. 3) | |

Incompressibility is the ease with
which a material
is squashed. The
higher the incompressibilities of a material, the more difficult it is to
squeeze it. The
state of a material strongly influences incompressibility; gases have lower incompressibility than
fluids, which
have lower incompressibilities
than solids. Rocks
have much higher incompressibilities than air. Because both elastic constants are
positive quantities, the additional term in the P-wave equation means that P waves
travel faster
than S waves. | |

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