Seismology: A Physical Approach
Sympson Placide
Abstract
The importance of seismology will be discussed. The physical models for seismic source will be described, and the actual source parameters will be presented including the relationship between the parameters. The effect of earthquakes on the ground will be covered along with the engineering aspects.
Introduction
Seismology is the study of earthquakes and seismic waves. According to the United States Geological Survey, earthquakes have caused 600,000 fatalities around the world from the year 2000 to 2010. The time of occurance, the locality, and the strength still need to be usefully predicted in order to minimize loss from natural disaster. In the common treatment of earthquakes, it's assumed that the motion has a specific beginning and a definite origin (Scheidegger 12). It can only be studied by using mathematical models and physical models. Physical relationship will be discussed for the seismic source models. The mathematical relationship between parameters will be presented. A superficial look at the effect of seismic waves on the ground, and the engineering aspects will be taken into consideration. Energy will be expressed in ergs.
1. Seismic source model
As shown in figure 1 below, an earthquake is usually represented by a focus that has a specific location and becomes activated at a particular time. It is mentioned the physical process might occur at such focus, and it's the cause of the seismic wave patterns noted. It's not easy to understand the physics of the seismic source. The attempts at understanding it rely on mathematical model and physical models. In this model, the focus is located near 600 km below earth (Scheidegger 13-17). Here is a link of a compatible figure below.http://www.yorku.ca/esse/veo/earth/image/1-10-15.JPG
Figure 1: Physical representation of seismic source
2. Source Parameters
Three parameters: magnitude, energy, and volume are more universally significant. It's arduous to determine the energy radiated by an earthquake. As a result, relative to the focal process, a characterization of the strength, magnitude, was determined empirically. It was defined by Richter. Only the maximum amplitude of a seismic record is considered. The relation between the magnitudes M of earthquakes at standard epicentral distance of 100 Km, and the maximum recorder trace amplitude B (mm) is given by:M1-M2=logB1-logB2 (1)
For the validity of the relation (1), the seismogram is supposed to have been recorded on a standard torsion seismometer of free period 0.8 sec, static instrumental magnification of 28000 and damping ratio of 50: 1. The zero of the scale is defined by setting M=3 for B=1mm. As remarked, the magnitude depends on a particular type of instrument (Scheidegger 17-19).
It's very difficult to observe the amount of energy radiated by an earthquake, so for study purpose one has to calculate the energy emitted by the earthquake source in elastic waves from the energy flux passing through a seismic station. A good summary of the procedures has been given by Bath with the energy measured in ergs. As energy- class K of an earthquake one has designated the power of 10 of the number of ergs released:
K=logE (ergs) (2)
The relation between the energy and various magnitude scales is as follows
log E=α +βM (3)
Where α and β are empirical coefficients. It can only be an approximation (Scheidegger 19).
The volume is the region at the vicinity of the focus in which the elasticity conditions no longer apply. Bath and Duda identified the earthquake volume with the total volume occupied by the "aftershocks". By this simple procedure, it is found there is direct relationship between the three parameters. The volume increases with magnitude as does the energy (Scheidegger 21).
3. Effect on the ground
The motion of the ground is a quasi-oscillatory motion (Scheidegger 23-32). An important aspect of analysis of early records of earthquakes was the first arrival of the P-wave. It's known as the first vertical motion (Brumbaugh 87). It is deduced to be one of the causes of building being toppled over. The motion of the ground is the result of the impingement of elastic waves (Scheidegger 23).4. Engineering aspects
The right type of foundation for a site condition is vital in order to minimize the damage (Brumbaugh 215-216). For instance, Pier or Caisson pile foundation must be used for tall and heavy building instead of mat foundation that are used in apartment in the United States. The length of duration of a potential earthquake must be taken into consideration while building to resist earthquake (Scheidegger 32-34). It's found that ground Oscillation acts through their velocities at frequencies above the frequency of a building that usually range between 2 Hz to 8 Hz (Scheidegger 33).5-Conclusion
Naïve physical and mathematical models were presented for the seismic source, the source parameters. The effect on the ground of the physical process that occurs at a focus below the ground was discussed including the actual engineering application of the known facts about seisms. A more complex model that can usefully predict the time of occurance, the locality, and the strength is needed to fight seisms in modern days.References
Brumbaugh, Earthquakes Science and Society, Prentice hall, Inc. 1999.Scheidegger, Physical Aspects of Natural Catastrophes, Elsevier Scientific Publishing Company, 1975.
