EARTHQUAKE SEISMOLOGY I

BY

KIAN H CHONG

Modified by

LAI LEE


Contents


Introduction

Seismology is the study of the passage of elastic waves through the earth. Earthquake seismology is the best tool to study the interior of the earth. When an earthquake or explosion occurs, part of the energy released is as elastic waves that are transmitted through the earth. The waves are then detected and recorded by seismograms, which measure, amplify and record the motion of the ground. The information is then used to determine earthquake locations, the subsurface structures and etc.



This pendulum-mounted seismograph records horizontal motion. The mass is coupled to the Earth by means of a pendulum and a pivot is attached to a rod to constrain the mass to move in the horizontal direction only.

The spring-mounted seismograph records the vertical ground motion. A spring is attached to the mass which is connected to a rod. The rod is attached to a pivot to constrain the mass to move in an up and down direction only.


Basic Physics

There is some basic terminology and physics that describe the various aspects of wave form and motion. The wavelength () is the distance between two adjacent points on the wave that have similar displacements, anone wavelength is the distance between successive crest. Amplitude (A) of the wave is the maximum displacement of the particle motions, or the height of the ripple crest. Period (T) is the time it takes for two successive waves to pass a reference point or the motion to complete one cycle. The cycle of seismic waves or repetitions in a given unit of time is called frequency (f). Frequency and period are related by this relationship:


f = 1 / T [unit: hertz (Hz) or 1/s]


The speed in which the wavefront or ripple crest travel can be detected if the time the wavefront takes to reach a known distance is recorded:


V = distance / time [unit: m/s]


Or if wavelength and frequency are known:






Elastic Coefficients

Elasticity is the behavior of a rock that has been subjected to a stress (force/area), a change in shape (strain), and the rock returns to its original shape. The manner and speed of seismic waves travel through material is controlled by their elastic properties. The linear relationship between applied stress and resulting strain is:


E is the constant of proportionality called Young's modulus. Elongation are measured for each direction, and their ratio is referred to as Poisson's ratio ():


The original volume () change to final volume () when compared to the pressure change is called bulk modulus (). The bulk modulus is a measure of the incompressibility of the material:


When deforming a solid state by simple shear, a shear strain () is induced by applying a shear stress . The ratio of these quantities is the rigidity modulus (G):


Seismic Waves
There are two different types of body waves and two surface waves.

Body Waves

Body waves are seismic waves that travel through the body of the earth. Body waves are reflected and transmitted at interfaces where seismic velocity and/or density change, and they obey Snell's law. The two different types of body waves are:

  1. P-Waves (P stands for primary or pressure or push-pull). These waves are also called longitudinal waves or compressional waves due to particle compression during their transport. These waves involve compression and rarefaction of the material as the wave passes through is but not rotation. P-wave is transmitted by particle movement back and forth along the direction of propagation of the wave. The most correct description of P-waves is it is a dilational or irrotational waves. P-waves has the greatest speed and appears first on seismograms.

  2. S-Waves (S stands for secondary or shear or shake). Also known as transverse waves, because particle motions are transverse to the direction of movement of the wavefront, or perpendicular to the ray. These waves involve shearing and rotation of the material as the wave passes through it, but not volume change. The most correct description of S-waves is it is a rotational or equivolumnar wave. S-waves have speeds less than P-waves, and appear on seismograms after P-waves.







Surface Waves

Surface waves are seismic waves that are guided along the surface of the earth and the layers near the surface. These waves do not penetrate the deep interior of the earth, and are normally generated by shallow earthquakes (nuclear explosions do not generate these surface waves!). Surface waves are larger in amplitude and longer in duration than body waves. These waves arrive at seismograph after the arrival of P- and S-waves because of their slower velocities. The two different surface waves are:

  1. Rayleigh waves or descriptively called "ground roll" in exploration seismology. The particle motion of this wave is confined to a vertical plane containing the direction of propagation and retrogrades elliptically. The particle displacements are greatest at the surface and decrease exponentially downward. Rayleigh waves shows dispersion, and its velocity is not constant but varies with wavelength. This wave is similar to how ocean waves propagate.

  2. Love waves(named for A.E.H. Love, who discovered them) travel by a transverse motion of particles that is parallel to the ground surface. This wave is somewhat similar to S-waves. Love waves occur when there is a general increase of S- wave velocity with depth. The particle motion is transverse and horizontal. Generally, Love waves velocities are greater than Rayleigh waves. Love waves arrives first before Rayleigh waves on seismograph.


Seismic Wave Velocities



The velocities of P- and S-waves are given below in terms of the density () and elastic coefficients of a material:





If we note that the bulk modulus (K) and the rigidity modulus (G) are always positive and recall that Poisson's ratio () is less than or equal to 0.5, then evidently the velocity of P-waves must always be greater than S-waves by a big factor. Shear waves (S-waves) cannot propagate through liquid. This is evident when we substitute G = 0 for liquids, then the velocity of S-waves goes to zero. This is how it was determined that the outer core consists of liquid.
There are a few general rules to the velocity ranges of common materials:


Below is a list of velocity estimation of common waves:




Earthquake Locations
The earthquake focus or hypocenter is the point where the earthquake originated. This location is specified bylatitude, longitude, and depth beneath the surface.
The location of earthquakes are determined from at least three seismic stations. Given a single seismic station, the seismogram records will yield a measurement of the S-P time. This will allow the distance between the station and the event to be located. Multiply the seconds of S-P time by the velocity of the waves gives the distance of the epicenter, the point on the surface directly above the focus. Drawing a circle on a map around the station's location, with a radius equal to the distance, shows all possible locations for the event. With the S-P time from a second station, the circle around that station will narrow the possible locations down to two location. With a third station's S-P time that one can draw a third circle that should identify which of the two previous possible points is the real one. The diagram below illustrates this method.



In practice, this is not as simple because the earth is not flat nor homogenous. The P- and S- wave velocities are not globally constant. The focal depth is also unknown. Focal depths are determined from the measurement in travel time between the P phase and the reflected P-wave at the earth's surface. Most earthquakes are shallow and none have been detected below a depth of 700 km.
Magnitude and Intensity
Earthquake magnitude is most commonly reported using the Richter scale magnitude , named after geophysicist Charles F. Richter, who developed it. The magnitude number is assigned to an earthquake on the basis of amount of grond displacement, which is measured by a seismograph. Since the Richter scale is logarithmic, then for every unit increase in Richter magnitude, ground displacement increases by a factor of ten, while energy release increases by a factor of thirty.
Another way of describing the size of an earthquake is by the earthquake's intensity which measures the effects on humans on surface features. The surface effects produced by an earthquake of a given magnitude vary considerably as a result of such factors as local geologic conditions, quality of construction and distance from epicenter. The most widely applied intensity scale in the U.S. is the Modified Mercalli Scale. The following is the abridged version of the Modified Mercalli Scale:
INTENSITY ----DESCRIPTION
I----Not Felt.
II----Felt by persons at rest on uppper floors.
III----Felt indoors---hanging objects swing. Vibration like passing of light trucks.
IV----Vibration like passing of heavy trucks. Standing automobile rock. Windows, dishes, and doors rattle; wooden walls or frame may creak.
V----Felt outdoors. Sleepers wakened. Liquids disturbed, some spilled; small objects may be moved or upset; doors swing; shutters and pictures move.
VI----Felt by all; many frightened. People walk unsteadily; windows and dishes broken; objects knocked off shelves, pictures off walls. Furniture moved or overturned; weak plaster cracked. Small bells ring. Trees and bushes shaken.
VII----Difficult to stand. Furniture broken. Damage to weak materials, such as adobe; some cracking of ordinary masonry. Fall of plaster, loose bricks, and tile. Waves on ponds; water muddy; small slides along sand or gravel banks. Large bells ring.
VIII----Steering automobiles affected. Damage to and partial collapse of ordinary masonry. Fall of chimneys, towers. Frame houses moved on foundations if not bolted down. Changes in flow of springs and wells.
IX----General panic. Frame structure shiffted off foundations if not bolted down; frames cracked. Serious damage even to partially reinforced masonry. Underground pipes broken; reserviors damaged. Conspicuous cracks in ground.
X----Most masonry and frame structure destoryed with their foundations. Serious damage to dams and dikes; large landslides. Rails bent slightly.
XI----Rails bent greatly. Underground pipelines out of service.
XII----Damage nearly total. Large rock masses shifted; objects thrown into the air.


Reference

1. Burger, Robert H., 1992. Exploration Geophysics of the Shallow Surface. Prentice Hall Inc. New Jersey. 7-19.
2. Fowler, C.M.R., 1995. The Solid Earth: An Introduction to Global Geophysics. Cambridge University Press. New York. 76-96.
Illustration."http://www.seismo.unr.edu/ftp/pub/louie/class/100/seismic-waves.html"
3. Beck, A.E. Physical Principles of Exploration Methods: An Introductory Text For Geology and Geophysics Students. New York: Wiley, c 1981
UCD Phys Sci TN 269.B387 1981
4. Sharma, P. Vallabh. Geophysical Methods in Geology, 2nd ed. New York.
UCD Phys Sci QE 501.3.S48 1986
5. Press, Frank; Siever, Rfaymond. Earth, 4th ed. New York: W.H. Freeeman and Company, 1985
6. Montgomery, Carla W. Environmental Geology, 3rd ed. Wm. C. Brown Publishers. 1991


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