Earthquakes result from sudden release of energy, which had earlier accumulated
within the Earth's interior. The energy
release begins at some point in the Earths interior. This point is called the
**hypocenter**
or **focus** of the earthquake. A point on the surface of the Earth,
vertically above the hypocenter, is called the **epicenter.** Distance of
the epicenter from the point of observation (observatory) measured along the
Earths surface is called **epicentral
distance**. For earthquakes occurring within a couple of thousands of
kilometers epicentral distance is measured in kilometers . For distant
ones ,called teleseisms, it is measured in terms of the angle
between the Earths radii passing through the observatory and the epicenter.
Epicentral distance is represented by the symbol D.

Part of the released energy is dissipated within a short distance of the
earthquake source in heating the surroundings and crushing the rock. The
remaining energy travels to far distances in the form of elastic compressional,
shear and surface waves. These waves are called **seismic waves**.
The compressions travel as **P waves **(also
called primary or push waves) and shear as the **S
waves** (or
secondary waves). The P and the S waves travel into the interior of the Earth,
and these are called **body waves**. P wave travels faster than the S wave. **Surface
waves** travel along the surface of the Earth, and are slower than S waves.
Seismographs are used to record seismic waves. The record of an
earthquake is called a **seismogram**. On the basis of the measurements made on the seismogram an earthquake
is assigned a number, which quantifies the size (or strength) of the
earthquake This number is called **magnitude**
of the earthquake. Earthquakes of magnitude less than 3 are called **microearthquakes**.
Before the invention of the seismograph only moderate to strong earthquakes,
where the ground shaking could be felt, were detected. The size of these
earthquakes was measured in terms of the observed effects. On the basis of these
effects an **intensity scale value** was assigned to each such earthquake. This value is
expressed in Roman numbers. Each
intensity scale value was based on a description of the earthquakes felt effects
listed against that value in the intensity scale (see Earthquake Intensity, ^{4.1
}). Depending on these descriptions several intensity scales have
been used in earthquake catalogs. The **Modified Mercalli (MM)** scale is a commonly used intensity scale. In most
intensity scales intensity varies between XII and I. Intensity I is the lowest
assigned to the smallest earthquake, which only instruments could detect, and
intensity XII is the highest assigned to the most destructive one. Empirical
relations have been derived to relate the different intensity scale values to
the energy release in an earthquake (though these could hardly be considered
accurate). Since the intensity scale value is assigned to an earthquake on the
basis of the effects at the place of observations, the assigned intensity scale
value corresponds to that particular place. Consequently, intensity of an
earthquake varies from place to place. Places of equal intensity are joined on
intensity maps to draw **isoseismal
lines** or **isoseismals**.

Locations of the earthquake sources and the recording stations are specified in terms of the latitude, longitude and depth (or elevation from sea level). The distance between the earthquake source and the recording station is calculated using methods of geometry (or trigonometry). In computations on earthquake source locations and travel times the locations of different seismograph stations in a seismological network are, generally, represented in a Cartesian coordinate system (x, y and z coordinates). The epicenter is specified in terms of its latitude and longitude. Depth of the earthquake is available only in some cases. Conversion from one type of coordinates to another type is, often, required in in earthquake source location applications. The figure of the earth deviates from an ideal sphere. The polar diameter is shorter than the equatorial diameter by about 23 kilometers. The earth is, therefore, more like an elliptical object. Distance calculations based on the an spherical earth are corrected to account for the ellipticity, when dealing with precise calculations in seismic velocity studies.

2. Know how to turn the electrical, gas appliances and water supply off.

3. Keep water heaters, gas stoves and other appliances firmly fixed against supports, and keep these switched of when not in use.

4. Top heavy objects should be kept firmly fixed, braced or anchored.

5. Keep inflammable material dispersed, and as far away as possible from electrical and gas lines.

6. Keep a stock of water/dry sand for extinguishing fire at an accessible place (unlikely to be blocked by earthquake damage)

7. Know, establish and practice how to get out of the dangerous areas during an earthquake.

8.Train as many persons as possible in first aid rescue work and fire fighting.

9. Keep stock of drinking water. Some dry food stuff, first aid equipment, a crowbar, shovel, pick and rope, electric torch, some candles and a helmet for every family member.

10. Keep telephone numbers/ addresses of the nearest first aid post and fire station handy (near the telephone if one exists).

Earthquake vibrations start all of a sudden. You may be sleeping, you may be awake, you may be in bath room, may be on a toilet seat or under the shower.

1. If you are in open space, remain calm and quite, move away from any tall structure, tree or pole. Do not panic, and do not run to protect others, until vibrations cease.

2. If you are inside a house, a bulding or in a factory, reamin calm and choose a safe place to move to an open area. Do not use lifts.

3. If caught indoor, take shelter in some safe area away from walls. Do not put lights on, do not light candles or lamps. Torch may be used, if available.

4.If you are in a car, stop as quickly as safety permits, stay in the car until the vibrations cease.

Though earthquake vibrations cease after some time, the risk due to the earthquake continues. The worst might not have been over.

1. Check the electric and gas appliances for breakage, but do not turn any of these on. Also check the water supply and electric lines. In case of any actual or suspected damage close the supply at the mains.

2. Turn the radio/TV on to get the latest information / warnings/ advice. Keep it on.

3. Stay away from damaged buildings. These may crash later in an aftershock.

The magnitude of the most destructive earthquake, which can affect a site
in future, will depend on how much strain energy has accumulated in the
earthquake zone. On this count a maximum credible earthquake (MCE) can be
associated with each earthquake zone. For specifying the value of the PGA at a
site the location (latitude, longitude and depth of focus) and the magnitude of
the MCE are to be fixed. Depending on the available information on the faults in
the region, the magnitude of the MCE is fixed on the basis of one or more of the
following databases.

1.
The highest earthquake magnitude recorded in historical times.

2.
Paleoseismicity observations.

3.
Fractional fault rupture length.

4.
Total fault length.

5.
Size of the fault zone area.

6.
Fault slip rates.

The
first three of these databases care applicable to all fault types, whereas the
others apply to strike-slip faults only. Use of the maximum historical
earthquake is based on the assumption that the earthquake history of the region
is well documented, length of the historical records is large enough for the MCE
to have occurred during this period and magnitudes of past earthquakes have been
estimated reasonably accurately. This approach is applicable for regions
traversed by faults, where strong earthquakes occur frequently and reliable
catalogs of several centuries are available

The
Paleoseismicity method (see Investigating Faults ^{8.3
}) is based on the use of photo geological and field geology
techniques in mapping active faults to determine rupture lengths and
displacements associated with prehistoric earthquakes. Empirical relations
between earthquake magnitude, maximum surface displacement and fault rupture
length have been derived. The method can be applied in areas where fault scarps
are preserved and stratigraphic studies have been carried out to map faults.

The
fractional fault rupture length method is based on the observation that faulting
in strong earthquakes ruptured between one fifth and one half of the total fault
length [1]^{,}
[2].
Several empirical relations between fault length and earthquake magnitude have
been derived. These relations are, however, applicable to faults of over a few
hundred kilometers length with slip rates of several millimeters per year.
The table given below gives an idea of the kind of length a fault should
have to generate an earthquake of a specified magnitude[3].

**Table-:
Earthquake Magnitude versus Fault Length
**

Earthquake
Magnitude |
Fault
Length (km) |
Earthquake
Magnitude |
Fault
Length (meters) |

8.8 |
1600 |
5.0 |
3400 |

8.5 |
850 |
4.5 |
2100 |

8.0 |
300 |
4.0 |
1300 |

7.5 |
110 |
3.0 |
500 |

6.5 |
15 |
2.0 |
220 |

6.0 |
8 |
1.0 |
80 |

5.5 |
5.5 |
0.0 |
30 |

**Ms
= Log _{10} A + 4.15
**

A
is the fault rupture area in square kilometers.

Relations
between fault displacement D, rupture length L and Magnitude M also exists[5]

**Log
_{10} D = 0.57 M (3.39±**

**Log
_{10} D = 0.86 Log _{10} L 0.46**

L
is in miles and D is in feet. MCE of a fault can be estimated by postulating a
fractional rupture length (one quarter to one half, based on seismological and
geological evidence. The empirical relations between magnitude and fault
length/width do not show a definite correlation over an extended magnitude range
(say between 3 and 8)[6].
A linear relation between magnitude M and Log_{10}D, where D is the
displacement or total fault offset measured in centimeters, is give by:

**M
= 1.32 Log _{10 }( D) + 4.27
**

A
summary of some recent data bases depicting the correlation of earthquake
magnitude with fault length and fault displacement is given in Annexure-1 in the
tabular form for different types of faults [7].

Earthquake occurrences follow a certain pattern, as far
as the occurrence rates of earthquakes of different magnitude are concerned.
The number of earthquakes, small and big ones, occurring on the globe
annually in any single year goes to several tens of thousands. Over ten to
fifteen thousand earthquakes are detected every year by seismographs installed
in different parts of the world. Damaging earthquakes are, comparatively,
small in number. In 1944 Gutenberg and Richter formulated a scaling law of
earthquake magnitudes in terms of a magnitude frequency relation, which
describes the frequencies of earthquakes of different magnitudes occurring in
California. According to this formulation the number of earthquakes, N(M)
occurring annually in a specified area, and having magnitudes equal to or
greater than M is given by:

**Log
_{10} N (M) = a b M **
.

Here
`a and `b are constants determined empirically from observed data. The
constant `a fixes the annual number of earthquakes having magnitudes equal
to or greater than 0 [N(0) = 10^{a}] and `b determines the
distribution of magnitudes in the earthquake population. Values of `a and
`b vary from region to region. The global average of `b has been found
close to unity, so that the number of earthquakes of a specified magnitude M
is about ten times smaller compared to the number of earthquakes of magnitude
M-1. The magnitude frequency relation for the global data is given by[1]:

**Log
_{10} N (M) = 8.24
1.03 M **

The
value of `a is dependent on the size of the area under consideration, and
is defined for a one year time interval, whereas `b is a ratio, and is
independent of the area as well as time. The global magnitude frequency
relationship, if normalized for an area enclosed by a three hundred km radius
circle[2],
will transform to

**Log
_{10} N (M) = 5.0
1.03 M **

According
to this relation, on an average, an earthquake of magnitude 6.0 or greater can
affect a three hundred km radius circular area once in fifteen years.

Establishing
a magnitude frequency relationship in order to estimate the possible number of
earthquakes of different magnitudes during a specified interval is the first
and foremost requirements of investigating regional seismicity. The study
becomes more accurate and complete if such relationships are established for
each tectonic structure (fault or fault zone). The earthquake magnitude
frequency relation forms the basis of statistical analysis methods in dealing
with the problem of seismic risk evaluation.

1.
The number of earthquakes in a year is a Poisson random variable with a
definite mean , say l,
and

2.
The earthquake magnitude M is a random variable distributed with
cumulative distribution function F(M) = 1.0 e^{-}^{bM}
(M³0).

When it comes to designing earthquake resistant structures, it is the
largest earthquakes the region of interest, which is of concern rather than an
accurate knowledge of the smaller earthquakes. The maximum yearly magnitudes
of earthquakes have been analyzed using the extreme event theory[3],[4].
In this formulation, the annual highest earthquake magnitude in a region is
distributed according to a cumulative distribution function G(y) given by:

**G
(y) = Exp [- a
Exp (- b
y)]
. (4)
**

a
and b
are constants, and these are related to the constants `a and `b of the
magnitude frequency relationship as follows:

**a
= Exp (a Log _{e} 10) and b
= b Log _{e }10
(5)**

The
above equation yields

**Log
_{e} [- Log _{e }{G (y)}] = Log _{e} a
- by
(6)**

Using
data on maximum yearly magnitudes for a number of consecutive years, the
values of the parameters a
and b,
and hence the constants `a and `b can be estimated using least square
methods. For the annual maximum magnitudes, y_{j} (j =1,2,
N)
arranged in an ascending order the probability of occurrence of an earthquake
exceeding the j^{th} magnitude is given by:

**G
(y) = j/(N+1)
.. (7)
**

This page was updated on 12 January, 2011

1] R.D. Sharma, Sushil Gupta and Sanjeeve Kumar, Bulletin of the Indian Society of Earthquake Technology

[2] Gumbel,E.J.(1958). Statististics of Extremes. California University Press. N.Y.

[3] Epstein,B. and Lomnitz,C.(1966). A model for the occurrences of large earthquakes., Nature, 211,954.

[4] Based on analysis of global earthquake data for the period 1964-95: R.D. Sharma, Sushil Gupta and Sanjeeve Kumar, Bulletin of the Indian Society of Earthquake Technoloy

[5] In engineering design practices an area of 300 kilometers radius is investigated for evaluation aseismic design parameters. It is believed that an earthquake at distances farther than this is not likely to affect the well engineered structures adversely.

[6] C.Lomnitz (1976). Global Tectonics And Earthquake Risk, Developments In Geotectonics,5, Elsevier Publishing Company.

[1] Albee, A.L. and Smith, J.L. (1966), Earthquake characteristics and Fault activity in Southern California. Engineering Geology in California, Association of Engineering Geologists.

[2] Slemmons, D.B.(1981). Geologic Consideration for Microzonation : In Proc. Joint U.S.-P.R.C. Microzonation Workshop. Inst. Engineering. Mech. Harbin, China.

[3] Housener,G.W.(1975). Strong Ground Motion. In: Earthquake Engineering. R.L.Weigel (Ed.). Prentice Hall, N.J.

[4] Wyss, M. (1978). Estimating Expectable Maximum Magnitude of Earthquakes from Fault Dimensions. Proc. VI Symp. Earthquake Engineering. University of Roorkee, India.

[5] Bonilla, M.G.(1975). Surface faulting and Related Effects in Earthquake Engineering. In R.L. Weigel (Ed.) Earthquake Engineering. Prentice Hall, N.J.

[6] Chinnery,M.A. (1969). Earthquake Magnitude and Source Parameters. Bull. Seism. Soc. Am. Vol. 59, pp 1969-82.

[7] Slemmons,D.B.(1979). Evaluation of Geomorphic Features of Active Faults for Engineering Design and Siting Studies. In D.Buesh (Ed.) Geomorphic Applications in Engineering Geology: A state of the art course held at California State University, Los Angles, Nov. 10-11.

This page was updated on 12-01-11