Natural Disasters

Prof. Stephen A. Nelson

Earthquakes: Causes and Measurements

Within the Earth rocks are constantly subjected to forces that tend to bend, twist, or fracture them. When rocks bend, twist or fracture they are said to deform or strain (change shape or size). The forces that cause deformation are referred to as stresses.  To understand rock deformation we must first explore stress and strain.

Stress is a force applied over an area. One type of stress that we are all used to is a uniform stress, called pressure. A uniform stress is where the forces act equally from all directions. In the Earth the pressure due to the weight of overlying rocks is a uniform stress and is referred to as confining stress.  If stress is not equal from all directions then the stress is a differential stress. Three kinds of differential stress occur.

1. Tensional stress (or extensional stress), which stretches rock;
   
   
2. Compressional stress, which squeezes rock; and
   
   
   
3. Shear stress, which result in slippage and translation.

When a rock is subjected to increasing stress it changes its shape, size or volume. Such a change in shape, size or volume is referred to as strain.  When stress is applied to rock, the rock passes through 3 successive stages of deformation.

• Elastic Deformation -- wherein the strain is reversible.

• Ductile Deformation -- wherein the strain is irreversible.

• Fracture -- irreversible strain wherein the material breaks.

• Brittle materials have a small to large region of elastic behavior, but only a small region of ductile behavior before they fracture.

• Ductile materials have a small region of elastic behavior and a large region of ductile behavior before they fracture.

How a material behaves will depend on several factors. Among them are:

• Temperature - At high temperature molecules and their bonds can stretch and move, thus materials will behave in more ductile manner. At low Temperature, materials are brittle.
  
  
• Confining Pressure - At high confining pressure materials are less likely to fracture because the pressure of the surroundings tends to hinder the formation of fractures. At low confining stress, material will be brittle and tend to fracture sooner.
  
  
• Strain rate -- Strain rate refers to the rate at which the deformation occurs (strain divided by time). At high strain rates material tends to fracture. At low strain rates more time is available for individual atoms to move and therefore ductile behavior is favored.
  
  
• Composition -- Some minerals, like quartz, olivine, and feldspars are very brittle. Others, like clay minerals, micas, and calcite are more ductile This is due to the chemical bond types that hold them together. Thus, the mineralogical composition of the rock will be a factor in determining the deformational behavior of the rock. Another aspect is presence or absence of water. Water appears to weaken the chemical bonds and forms films around mineral grains along which slippage can take place. Thus wet rock tends to behave in ductile manner, while dry rocks tend to behave in brittle manner.

Evidence of Former Deformation

Evidence of deformation that has occurred in the past is very evident in crustal rocks. For example, sedimentary layers and lava flows generally are deposited on a surface parallel to the Earth's surface (nearly horizontal). Thus, when we see such layers inclined instead of horizontal, evidence of an episode of deformation is present.

In order to uniquely define the orientation of a planar feature we first need to define two terms - strike and dip.  For an inclined plane the strike is the compass direction of any horizontal line on the plane. The dip is the angle between a horizontal plane and the inclined plane, measured perpendicular to the direction of strike. 

Faults - Faults occur when brittle rocks fracture and there is an offset along the fracture. When the offset is small, the displacement can be easily measured, but sometimes the displacement is so large that it is difficult to measure.

Types of Faults

Faults can be divided into several different types depending on the direction of relative displacement. Since faults are planar features, the concept of strike and dip also applies, and thus the strike and dip of a fault plane can be measured. One division of faults is between dip-slip faults, where the displacement is measured along the dip direction of the fault, and strike-slip faults where the displacement is horizontal, parallel to the strike of the fault.

• Dip Slip Faults - Dip slip faults are faults that have an inclined fault plane and along which the relative displacement or offset has occurred along the dip direction. Note that in looking at the displacement on any fault we don't know which side actually moved or if both sides moved, all we can determine is the relative sense of motion.

For any inclined fault plane we define the block above the fault as the hanging wall block and the block below the fault as the footwall block.

• Normal Faults - are faults that result from horizontal tensional stresses in brittle rocks and where the hanging-wall block has moved down relative to the footwall block.

Horsts & Grabens - Due to the tensional stress responsible for normal faults, they often occur in a series, with adjacent faults dipping in opposite directions. In such a case the down-dropped blocks form grabens and the uplifted blocks form horsts. In areas where tensional stress has recently affected the crust, the grabens may form rift valleys and the uplifted horst blocks may form linear mountain ranges. The East African Rift Valley is an example of an area where continental extension has created such a rift. The basin and range province of the western U.S. (Nevada, Utah, and Idaho) is also an area that has recently undergone crustal extension. In the basin and range, the basins are elongated grabens that now form valleys, and the ranges are uplifted horst blocks.

• Reverse Faults - are faults that result from horizontal compressional stresses in brittle rocks, where the hanging-wall block has moved up relative the footwall block.

A Thrust Fault is a special case of a reverse fault where the dip of the fault is less than 15^o. Thrust faults can have considerable displacement, measuring hundreds of kilometers, and can result in older strata overlying younger strata.

• Strike Slip Faults - are faults where the relative motion on the fault has taken place along a horizontal direction. Such faults result from shear stresses acting in the crust. Strike slip faults can be of two varieties, depending on the sense of displacement. To an observer standing on one side of the fault and looking across the fault, if the block on the other side has moved to the left, we say that the fault is a left-lateral strike-slip fault. If the block on the other side has moved to the right, we say that the fault is a right-lateral strike-slip fault. The famous San Andreas Fault in California is an example of a right-lateral strike-slip fault. Displacements on the San Andreas fault are estimated at over 600 km.

Transform-Faults are a special class of strike-slip faults. These are plate boundaries along which two plates slide past one another in a horizontal manner. The most common type of transform faults occur where oceanic ridges are offset. Note that the transform fault only occurs between the two segments of the ridge. Outside of this area there is no relative movement because blocks are moving in the same direction. These areas are called fracture zones. The San Andreas fault in California is also a transform fault.

Earthquakes occur when energy stored in elastically strained rocks is suddenly released. This release of energy causes intense ground shaking in the area near the source of the earthquake and sends waves of elastic energy, called seismic waves, throughout the Earth. Earthquakes can be generated by bomb blasts, volcanic eruptions, and sudden slippage along faults. Earthquakes are definitely a geologic hazard for those living in earthquake prone areas, but the seismic waves generated by earthquakes are invaluable for studying the interior of the Earth.

Most natural earthquakes are caused by sudden slippage along a fault zone. The elastic rebound theory suggests that if slippage along a fault is hindered such that elastic strain energy builds up in the deforming rocks on either side of the fault, when the slippage does occur, the energy released causes an earthquake. This theory was discovered by making measurements at a number of points across a fault. Prior to an earthquake it was noted that the rocks adjacent to the fault were bending. These bends disappeared after an earthquake suggesting that the energy stored in bending the rocks was suddenly released during the earthquake.

When an earthquake occurs, the elastic energy is released sending out vibrations that travel throughout the Earth. These vibrations are called seismic waves. The study of how seismic waves behave in the Earth is called seismology.

• Seismograms - Seismic waves travel through the Earth as vibrations. A seismometer is an instrument used to record these vibrations, and the resulting graph that shows the vibrations is called a seismogram. The seismometer must be able to move with the vibrations, yet part of it must remain nearly stationary.

 

This is accomplished by isolating the recording device (like a pen) from the rest of the Earth using the principal of inertia. For example, if the pen is attached to a large mass suspended by a wire, the large mass moves less than the paper which is attached to the Earth, and on which the record of the vibrations is made.

• The source of an earthquake is called the focus, which is an exact location within the Earth were seismic waves are generated by sudden release of stored elastic energy. The epicenter is the point on the surface of the Earth directly above the focus. Sometimes the media get these two terms confused.

Seismic waves emanating from the focus can travel in several ways, and thus there are several different kinds of seismic waves.

• Body Waves - emanate from the focus and travel in all directions through the body of the Earth. There are two types of body waves:  P -waves and S-waves:

• P - waves - are Primary waves. They travel with a velocity that depends on the elastic properties of the rock through which they travel.

• Surface Waves - Surface waves differ from body waves in that they do not travel through the Earth, but instead travel along paths nearly parallel to the surface of the Earth. Surface waves behave like S-waves in that they cause up and down and side to side movement as they pass, but they travel slower than S-waves and do not travel through the body of the Earth. Surface waves are often the cause of the most intense ground motion during an earthquake.

The record of an earthquake, a seismogram, as recorded by a seismometer, will be a plot of vibrations versus time. On the seismograph, time is marked at regular intervals, so that we can determine the time of arrival of the first P-wave and the time of arrival of the first S-wave. (Note again, that because P-waves have a higher velocity than S-waves, the P-waves arrive at the seismographic station before the S-waves)

• Locating the Epicenters of  Earthquakes - To determine the location of an earthquake epicenter, we need to have recorded a seismograph of the earthquake from at least three seismographic stations at different distances from the epicenter. In addition, we need one further piece of information - that is the time it takes for P-waves and S-waves to travel through the Earth and arrive at a seismographic station. Such information has been collected over the last 80 or so years, and is available as travel time curves.
  
  From the seismographs at each station one determines the S-P interval (the difference in the time of arrival of the first S-wave and the time of arrival of the first P-wave. Note that on the travel time curves, the S-P interval increases with increasing distance from the epicenter.

Thus the S-P interval tells us the distance to the epicenter from the seismographic station where the earthquake was recorded. Thus at each station we can draw a circle on a map that has a radius equal to the distance from the epicenter. Three such circles will intersect in a point that locates the epicenter of the earthquake.

• Magnitude of Earthquakes - Whenever a large destructive earthquake occurs in the world the press immediately wants to know where the earthquake occurred and how big the earthquake was (in California the question is usually - Was this the Big One?). The size of an earthquake is usually given in terms of a scale called the Richter Magnitude. Richter Magnitude is a scale of earthquake size developed by a seismologist named Charles Richter. The Richter Magnitude involves measuring the amplitude (height) of the largest recorded wave at a specific distance from the earthquake. While it is correct to say that for each increase in 1 in the Richter Magnitude, there is a tenfold increase in amplitude of the wave, it is incorrect to say that each increase of 1 in Richter Magnitude represents a tenfold increase in the size of the Earthquake (as is commonly incorrectly stated by the press).
  • A better measure of the size of an earthquake is the amount of energy released by the earthquake. While this is much more difficult to determine, Richter gave a means by which the amount of energy released can be estimated:
     

    Log E = 11.8 + 1.5 M

    Where Log refers to the logarithm to the base 10, E is the energy released in ergs, and M is the Richter Magnitude.

    Anyone with a hand calculator can solve this equation by plugging in various values of M and solving for E, the energy released. I've done the calculation for you in the following table:

    
    
    

From these calculations you can see that each increase in 1 in Richter Magnitude represents a 31 fold increase in the amount of energy released. Thus, a magnitude 7 earthquake releases 31 times more energy than a magnitude 6 earthquake. A magnitude 8 earthquake releases 31 x 31 or 961 times as much energy as a magnitude 6 earthquake.

• The Hiroshima atomic bomb released an amount of energy equivalent to a magnitude 5.5 earthquake.

• Note that the Richter scale is an open ended scale with no maximum or minimum. The largest earthquakes are probably limited by rock strength, although meteorite impacts could cause even larger earthquakes. The largest earthquakes so far recorded are the Chile earthquake in 1960 with a Richter Magnitude of 8.5, and the Alaska (Good Friday) earthquake of 1964 with a Richter Magnitude of 8.6.

• Note that it usually takes more than one seismographic station to calculate the magnitude of an earthquake. Thus you will hear initial estimates of earthquake magnitude immediately after an earthquake and a final assigned magnitude for the same earthquake that may differ from initial estimates, but is assigned after seismologists have had time to evaluate the data from numerous seismographic stations.
  
  
• Although the Richter Magnitude is the scale most commonly reported when referring to the size of an earthquake, it has been found that for larger earthquakes a more accurate measurement of size is the moment magnitude.  The moment magnitude is a measure of the amount of strain energy released by the earthquake as determined by measurements of the shear strength of the rock and the area of the rupture surface that slipped during the earthquake.
  
  The moment magnitude for large earthquakes is usually greater than the Richter magnitude for the same earthquake.  For example the Richter magnitude for the 1964 Alaska earthquake is usually reported as 8.6, whereas the moment magnitude for this earthquake is calculated at 9.2.  Sometimes a magnitude is reported for an earthquake and no specification is given as to which magnitude (Richter or moment) is being reported.  This obviously can cause confusion.  

• The scale is applied after the earthquake by conducting surveys of people's response to the intensity of ground shaking and destruction.
  
  
• Thus, a given earthquake will have zones of different intensity all surrounding a zone of maximum intensity.

• The Modified Mercalli Scale is shown in the table below. Note that correspondence between maximum intensity and Richter Scale magnitude only applies in the area around the epicenter.
  
  
• Thus, a given earthquake will have zones of different intensity all surrounding a zone of maximum intensity.
  
  
• The Modified Mercalli Scale is shown in the table below. Note that correspondence between maximum intensity and Richter Scale magnitude only applies in the area around the epicenter.
  
   

Intensity

Characteristic Effects

Richter Scale Equivalent

• The Mercalli Scale is very useful in examining the effects of an earthquake over a large area, because it will is responsive not only to the size of the earthquake as measured by the Richter scale for areas near the epicenter, but will also show the effects of the efficiency that seismic waves are transmitted through different types of material near the Earth's surface.
  
  
• The Mercalli Scale is also useful for determining the size of earthquakes that occurred before the modern seismographic network was available (before there were seismographic stations, it was not possible to assign a Richter Magnitude).