Class Notes - Earthquakes

Review Questions

1. Review material presented during the first week of class. Where do Earthquakes tend to occur? ..... shallow Earthquakes ....... deep Earthquakes?

2. What kind of "action (pushing, pulling or sliding)" takes place at each type of plate margin?

Behavior of Earth Materials

Several experiments can be done to illustrate the behavior of material subjected to a stress - a directed force. For example, you can pull on both ends of a rubber band. If you pull just a little and then let go, the rubber band returns to its original length. The rubber band has behaved elastically.

If you pull much further and then let go you may find that the rubber band has "stretched" and is actually longer than when you started. The rubber band has behaved plastically. The stretching action (pulling or tension) is the stress and the change in length is the strain.

If you keep pulling on the rubber band it will eventually fail (break) or rupture and return to an unstressed position. Stretching stores energy in the object and rupture releases it. If the object fails after behaving plastically it is said to have failed in a ductile fashion. Some materials fail before plastic behavior sets in; this is brittle failure. If you hit the rubber band with a hammer it will deform and rapidly recover its predeformed shape. If you put the rubber band in the ice box for several hours it will probably shatter (brittle) when it is hit.

Get a piece of gum or a bar of "Turkish Taffy -if they make it anymore and "play with it....". Stand it up vertically - what happens? Bend it ....what happens? Cool it off and hit it....what happens? Or, try the same things with silly putty.

Not all materials behave the same way. As the pressure increases (deeper burial) the material may change the way it behaves. For example, many rocks become stronger at higher pressures. Sometimes the rate at which the stress is applied (fast versus slow) makes a difference in the type of behavior. Some become weaker as the temperature increases.

A plot of stress versus strain is given below:



In this stress-strain plot note that when the plot is linear the behavior is elastic. When the plot is curved the behavior is plastic. Elastic strain is recoverable whereas deformation produced by plastic flow is not - a permanent change in shape results. The yield point is the point where elastic behavior stops and plastic behavior begins.

An object may deform elastically but not recover immediately when the stress is relieved; in other words there is a delayed reaction. 10,000' of ice (almost 2 miles) exerts considerable force on the surface it is flowing over. When the ice melts it may take a considerable time (thousands of years, perhaps) for the surface to regain its initial elevation - elastic rebound. In addition to tensile behavior (pulling) rocks will deform when they are pushed together - compression. When we talk about structural geology we will look in more detail at elastic and plastic behavior of Earth materials. In this section we are primarily concerned with what happens when a rock fails and energy is released.

When the "strength of the rock" is exceeded it fails - either in a brittle or ductile fashion. The Dilatancy Model predicts that rocks undergo an increase in volume just before they rupture. Small cracks begin to form. Water may enter these cracks and increase the fluid pressure which further increases the volume of the rock and decreases its strength until rupture takes place. Energy is released and it "propagates" in all directions away from the "point" (focus) where the break occurred. The depth to the focal point is an important piece of information about the quake. Recall, for example, that Earthquakes along mid-ocean ridges are quite shallow whereas those along a subduction zone may be quite deep. If you draw a line from the center of the Earth through the focus and extend it to the surface, the epicenter is the point of intersection of the line with the Earth's surface; the epicenter is the point on the surface closest to the focus.

When you throw a stone into a quiet body of water waves are created which move out from the point of impact. Energy is being propagated along these paths and as it moves some of the energy is lost. The farther the wave travels the lower its energy. Earthquake waves (or the waves produced when an artificial quake is created) can be subdivided into two types:

Body Waves

There are two types of waves which travel within the body of the Earth.

1. P waves are sometimes called compressional waves or primary waves or push-pull waves and they are transmitted (propagated by movements of the material in the Earth parallel to the direction in which the wave is moving.
   

   Imagine a line of stationary cars waiting to enter a freeway. Each car is connected to posts on the side of the road by very strong rubber bands. A speeding car strikes the last car in line. That car moves forward striking the car in front of it which moves forward and so on. The rubber band allows each struck car to move a short distance forward before the car snaps back. Another speeding car impacts the end of the line. If you were to stand off to one side and observe the process you would see the individual cars oscillating about an average position where the direction of movement of the cars is parallel to the direction of the wave.

   The following movie is quite large and may not be practical with a relatively slow modem. Another representation of the propagation of a P wave.

2. S waves are also called shear waves or secondary waves and they propagate by movements of the Earth perpendicular to the direction in which the wave is moving.
   

   Take a piece of rope 12 feet long. Color red foot long section in the near one end of the rope. Tie one end of the rope to a fixed object. Standing about 10 feet from the object, shake the end of the rope with an up and down motion. A standing wave with peaks and valleys is created. If you stand off to one side, you will see the red section move up and down whereas the wave itself moves toward the fixed object.

   Another representation of the propagation of an S wave.

3. The velocity of a P or S wave is a function of the physical properties of the rock the wave is traveling through. Different rocks have different physical characteristics (such as how compressible they are and how the respond to shear stresses) and therefore different P and S wave velocities. In fact, if the velocity of the wave can be measured, it may be possible to predict the type of rock the wave traveled through - indirect detection of rock type!

   The velocity of a P wave is proportional to:

   1. Velocity P wave ~ ((B + G)/Density), where:
      • B = the bulk modulus - the resistance to change in volume
        
      • G = the Shear modulus - the resistance to change in shape
        
      • Density = mass/volume

   2. Velocity S wave = (G/Density)

1. Note that Density appears in the denominator of both (1) and (2). If the numerators of these expressions are held constant, we would predict that the velocities of both waves would decrease with increasing depth of penetration since we know that pressure and density increase with increasing depth. However, observations show that both waves speed up with increasing depth. Therefore, the numerators must be increasing at a greater rate than density; rocks get stronger with increasing depth of burial. The comments above assume that both waves are traveling in the same material.

2. The velocity of a P wave is greater than that of an S wave as the numerator of (1) is larger than the numerator of (2).

3. If a wave passes from one material to another, the wave may speed up, slow down or not change its velocity, depending on the contrast in properties of the two types of material.

4. As a special case, consider a liquid. In general, liquids offer no resistance to changes in shape so that G = 0. Therefore, a liquid will not support the transmission (propagation) of an S wave and a P wave will slow down in a liquid.

5. When P and S waves encounter the surface of the Earth new waves are created. These surface waves are responsible for much of the damage associated with an earthquake. The motion of these surface waves is quite complicated. Watch the motion associated with the propagation of a Rayleigh wave

6. The arrival of a P wave is recorded prior to the arrival of an S wave as the P wave has a higher velocity than that of the S wave that traveled along the same path. The further the recording station is from the epicenter (the location on the surface of the Earth that is closest to the focus), the longer the time between the arrival of the P wave and the arrival of the S wave.