Earthquake Terminology

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 Earths 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 Earths 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 Earths 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.

1. Be aware of what to do and what not to do before, during and after an earthquake.

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).

What to do when Earthquake Occurs:

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.

What to do after the earthquake

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.

Maximum Credible Earthquake

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

A formula for estimating the surface wave magnitude, Ms of the MCE using fault rupture area was proposed by Wyss[4].

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±0.72)

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 Log10D, 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 Frequencies

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 . (1)

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) = 10a] 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  (2)

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     (3)

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.

Assumptions In Statistcal Analysis

Earthquake occurrences are modeled, statistically, under two basic assumptions, namely[3]:

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).

Once the parameters l and b are fixed important parameters of the earthquake process, e.g. return periods and probabilities of earthquakes of different magnitudes can be mathematically calculated.

Extreme Value Analysis

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, yj (j =1,2, N) arranged in an ascending order the probability of occurrence of an earthquake exceeding the jth magnitude is given by:

G (y) = j/(N+1) .. (7)

Using the values of G(y) calculated in this manner for successive values of j and plotting these against y (which corresponds to the jth value of the magnitude in the list) the parameters a and b can be estimated[1]

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.