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Material Properties

Stress and Strain

How materials respond to stress

 

Earthquakes

Elastic Rebound Model of Earthquakes

Where do Earthquake occur?

Again!

 

Seismic waves

Seismic waves are vibrational waves that travel through the material of Earth. Waves propagate by disturbing some aspect of the material, and the material responding by trying to return to its original state. Seismic waves come in two forms:

Body waves

Body waves travel along paths through the Earth which result in the minimum travel time from the source to the destination. Body waves come in two types:

  1. Compressional waves disturb the volume of material. The material resists this volume change resulting in oscillatory wave motion. Sound waves in air are compressional waves. Compressional seismic waves are called P waves or primary waves because they travel faster than all other waves. P waves travel at about 6 km/sec in the crust and about 8 km/sec in the upper mantle.
  1. Shear waves disturb the shape, but not the volume of material. Solids resist shape changes thus shear waves propagate in solids. Fluids (liquids and gasses) do not resist change shape, so shear waves cannot travel in fluids. Shear seismic waves are called S waves or secondary waves because, although they follow nearly the same paths as P waves, they arrive later because they travel slower. S waves travel about 60% as fast as P waves in the crust and mantle, about 4 km/sec in the crust and 5 km/sec in the upper mantle.

Surface waves

Surface waves, as their name suggests, travel along the Earth's surface. Because they have long wavelengths (distance from one crest to the next) they are called L waves. Because their motion is concentrated at the Earth's surface, surface waves are usually the cause of most damage from earthquakes. Like body waves, seismic surface waves come in two types.

  1. Rayleigh waves propagate with elliptical orbital motion in a vertical plane. Rayleigh waves involve compression. Rayleigh waves are called LR waves.
  1. Love waves propagate with purely horizontal motion perpendicular to the direction of wave travel. Love waves involve only shearing, no compression. Love waves are called LQ waves.

Love waves are slightly faster than Rayleigh waves. Both of these waves move at about 4 km/sec. Since their velocity is nearly the same as S waves, they arrive at about the same time as S waves if the earthquake is near. If the earthquake is distant, S waves arrive before surface waves because the take a shorter path through the interior of the Earth.

Seismograms

Seismograms are recordings of the motion of the ground as a function of time. Seismographs are the instruments that make these recordings. The overall appearance of seismograms changes dramatically as the seismograph is located  further and further from the epicenter of the earthquake.

  1. Local seismograms have a distinct P wave arrival followed by a combination S waves and surface waves. The entire seismogram may be as little as a minute in length.
  1. Distant (teleseismic) seismograms have the P, S and surface waves well separated in time. The P wave arrives first and is most clearly seen on the vertical recording. The S wave may arrive up to 15 minutes later at distant stations. The surface waves are well separated from the S waves since they are forced to take the long path around the surface of the earth. The surface waves arrive as long smooth harmonic waves which can ring on for hours.

 

Measuring Earthquakes

Intensity

  1. Intensity is a measure of the effects of an earthquake at a particular location. It is thus a measure of the apparent size, or "felt" size of the earthquake.
  2. Since intensity does not take into account the distance to the earthquake from the observing location, a small nearby earthquake may produce the same intensity as a larger, but more distant earthquake. Thus an intensity scale does not indicate the absolute size of the earthquake itself.
  3. Intensity scales are used for measuring earthquake effects and hazards, for example for insurance claims and urban planniing.
  4. The most commonly used scale of intensity is the Modified Mercalli scale. It is not a quantitative scale, in other words, the levels of this scale are not related to one another by any mathematical relationship. Because of this, we use Roman numerals to designate the levels of this intensity scale. Thus, we can have an intesity IV or an intensity V, but an intensity of 4.5 would be meaningless.
  5. The 12 levels of the Modified Mercalli scale are based on the effects of the shaking on people, human-made structures, and on the landscape. Here are some examples:

    II.     Felt only by a few persons at rest, especially on upper floors of buildings. Delicately suspended objects may swing.

    IV.    During the day felt indoors by many, outdoors by few. At night, some awakened. Dishes, windows, doors disurbed; walls make creaking sound. Sensation like heavy trucks striking building. Standing automobiles rocked noticeably.

    VII.    Everybody runs outdoors. Damage negligible in buildings of good design and construction; slight to moderate in well-build ordinary structures; considerable in poorly build or badly designed structures; some chimneys broken. Noticed by persons driving cars.

    X.    Some well-build wooden structures destroyed; most masonry and frae structures destroyed with foundations; ground badly cracked. Rails bent. Landslides considerable from river banks and steep slopes. Shifted sand and mude. Water slopped over banks.

    XII.    Damage total. Waves seen on ground surface. Lines of sight and level distorted. Objects thrown into the air.

Magnitude

  1. Magnitude is a measure of the size of an earthquake based on the amount of ground motion measured instrumentally with a seismograph. The distance from the seismograph to the epicenter is included in the calculation, so the magnitude is a true measure of the size of the earthquake at its focus, and does not depend on where the seismograph is located.
  2. Often, several slightly different magnitudes are reported for an earthquake. This happens because the relation between the seismic measurements and the magnitude is complex and different procedures will often give slightly different magnitudes for the same earthquake.
  3. In the 1930, Beno Gutenberg and Charles Richter developed a magnitude scale for nearby or local earthquakes. Today, these magnitudes are called Richter magnitudes, and are abbreviated ML for "local magnitude". Since the seismogram for a local earthquake is simple, the largest amplitude of movement is measured. This is usually in the part of the seismogram generated by a combination of S waves and surface waves which arrive at about the same time for nearby earthquakes.

Magnitude scaling

  1. Unlike local earthquakes, distant or teleseismic earthquakes have long seismograms on which the various phases P, S, and surface waves are often widely separated. The methodology used for local magnitudes cannot be directly applied here. The most commonly used magnitude for shallow distant quakes is the surface wave magnitude, MS, which is measured by the largest amplitude of surface waves having a period of about 20 seconds. Surface wave magnitudes are adjusted in an attempt to closely match local magnitudes, and follow the same scaling relationships.
  2. Deep earthquakes and explosions (such as nuclear tests) do not generate large surface waves. To measure these events, seismologists use body wave magnitudes, mb , which are based on the amplitude of the P wave. These magnitudes are adjusted to closely match local and surface wave magnitudes, and follow the same scaling relationships.
  3. Very large earthquakes, with magnitudes larger than 8, are not accurately measured by any of the above methods. These earthquakes do not produce larger body waves or 20 second surface waves as the grow in size. Their extra energy is radiated in even longer period motion. Thus, MS and  mb  underestimate the size of these earthquakes. Starting about 10 years ago, the moment magnitude, MW began to be used to measure these earthquakes. Moment magnitude is usually larger than surface wave magnitude for the same earthquake. For example, the 1964 Alaska earthquake, the second largest earthquake ever recorded, had a MS of 8.3 and an MW of 9.2. The largest earthquake ever recorded occurred in Chile in 1960 and had a moment magnitude of 9.5. The difference between moment magnitude and other magnitudes accounts for discrepancies in the magnitudes of large earthquakes reported in many textbooks. See the section on seismic moment that follows.

Magnitude Classes

Earthquakes are divided into classes based on their magnitude. These classes are:

Great = > 8
Major = 7 - 7.9
Strong = 6 - 6.9
Moderate = 5 - 5.9
Light = 4 - 4.9
Minor = 3 - 3.9

Seismic Moment

  1. Although magnitude is a measure of the size of an earthquake, it has no direct physical meaning. This is why there are no units to magnitude, just numbers.
  2. The moment of an earthquake is a physically meaningful number. Moment has units of torque, or newton-meters.
  3. The moment of an earthquake is M0 and is:

            M0 = fault area   x    slip on the fault   x    stiffness of the rock around the fault

  1. The moment can be calculated from seismograms, and makes use of all of the data from the P, S and surface waves. The moment can also be measured directly if the length of the fault and slip can be seen at the earth's surface.
  2. Unfortunately, moment is not a "public" friendly number like magnitude, since it involves exponents and strange units. So seismologists convert moment into moment magnitude for public information and consistency with other magnitude scales.

Earthquake frequency

The average number of earthquakes, worldwide, by size is approximately

Great > 8.0 1
Major 7.0 - 7.9 20
Strong 6.0 - 6.9 100
Moderate 5.0 - 5.9 3000
Light 4.0 - 4.9 15,000