Activity 3: Seismic Waves: Basic Principles
By taking into account moment of inertia as well as mass, we can eliminate models that donít 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 Earthís 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 VS 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 VP 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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