CE G615- Earthquake

Engineering
Instructor: Dr. J S Kalyana Rama
Lecture Handout-1
BITS Pilani Size And Strength of Earthquake
Hyderabad Campus
Topics to be covered
• Magnitude

• Intensity

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude
• Magnitude is a quantitative measure of the actual size of the earthquake.

• The magnitude of an earthquake is related to the amount of energy released by

the geological rupture causing it, and is therefore a measure of the absolute size
of the Earthquake.

• Richter (1935) based on the data from Californian earthquakes, defined the
earthquake magnitude as the logarithm to the base 10 of the largest displacement
of a standard seismograph (called Wood-Anderson Seismograph with properties
T=0.8 sec; m=2800; and damping nearly critical ≈ 0.8) situated 100 km from the
focus

• The most common modern magnitude scales are surface wave magnitude and
body wave magnitude.

• Richter’s local magnitude does not distinguish between different types of waves.

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
❑ An increase in magnitude (M) by 1.0 implies 10 times higher waveform amplitude
and about 31 times higher energy released.
❑ For instance, energy released in a M7.7 earthquake is about 31 times that
released in a M6.7 earthquake, and is about 1000 (≈31×31) times that released in
a M5.7 earthquake.
❑ Most of the energy released goes into heat and fracturing the rocks, and only a
small fraction of it (fortunately) goes into the seismic waves that travel to large
distances causing shaking of the ground enroute and hence damage to structures.

Did you know?

The energy released by a M6.3 earthquake is equivalent to that released by the

1945 Atom Bomb dropped on Hiroshima!!

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
Why do we need to define the size of an earthquake?
(1) We need some way to measure quantitatively the size of an earthquake so
that we can compare the sizes of different events.

(2) Our measure of earthquake size must be based on basic physical principles.

What data can we use to measure earthquake size?

(1) We can use measurements of the sizes of waves on seismographs (easy to
measure).

(2) We can use measures of deformations of the ground (limited to large

earthquakes; hard to measure).

(3) We can use earthquake felt or damage effects (limited to large earthquakes;
observations often imprecise).

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

 Magnitude (Cont..)
Why seismogram amplitudes vary with distance from the earthquake focus:
Geometric Spreading: For hypocentral distance Rh, amplitude decreases as 1/Rh for body
waves; for epicentral distance Re, amplitude decreases as 1/(Re)1/2 for surface waves.
(1) Anelastic attenuation: Friction in the rock during seismic wave passage absorbs energy
from the seismic wave, decreasing the wave energy as e -γX where γ is the attenuation
coefficient and X is the distance traveled by the wave.

Total attenuation effect:

e-γX/X (body waves)

or
e-γX /(X)1/2 (surface waves)
where X is the distance traveled by the wave

Anelastic: the property of a solid in which deformation depends on the time rate of change of stress as well as on
the stress itself

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
Why magnitude formulas are based on A/T or A
Gutenberg and Richter (1942) argue that magnitude formulas should be based on
the wave amplitude A divided by the wave period T (or A/T). If a wave period for
the magnitude measurement is specified, then the magnitude can be based on A
only.
The reason for this is that A/T is a measure of the ground velocity in the wave.
Ground velocity is important because the kinetic energy of the wave is E=1/2 m
v 2.

If we take the logarithm of the kinetic energy formula, then we get

log10(E)= log10(1/2)+log10(m)+log10(A/T)
or
log10(E)= log10(1/2)+log10(m)+log10(A)-log10(T)

These have the form of magnitude formulas, and they allow magnitude to be
related to energy. Gutenberg and Richter worked out relationships between
energy and magnitude
Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus
Commonly used magnitude scales to measure
magnitude of earthquake
Local Magnitude Scale (ML)

This scale is also called Richter scale. This scale is calculated as follows:
ML = log A – log A0 = log A/A0

ML = local magnitude (Richter magnitude scale)

A = maximum trace amplitude (in mm), as recorded by standard Wood-Anderson
seismograph. The seismograph has natural period of 0.8 sec, damping factor of 80%
and static magnification of 2800. It is located exactly 100 km from the epicenter.

A0 = 0.001 mm. This corresponds to smallest earthquake that can be recorded.

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)

Approximate correlation between local magnitude, peak ground acceleration and duration of shaking
(g = acceleration due to gravity) (Courtesy: Day, 2002)

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
Surface Wave Magnitude Scale (Ms)

This scale is calculated as follows:

Ms = log A′ + 1.66 log Δ + 2.0

where, Ms = Surface wave magnitude scale.

A′ = maximum ground displacement, μm.
Δ = epicenter distance to seismograph measured in degrees.
This magnitude scale is typically used for moderate to large earthquakes (having
shallow focal depth). Furthermore, seismograph should be at least 1000 km from
epicenter.

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
Moment Magnitude Scale (Mw)

In this scale, seismic moment M0 is calculated first as follows:

M0 = μAfD

M0 = seismic moment (N.m)

μ = shear modulus of material along fault plane (N/m2). It has a value of 3 × 1010 N/m2
for surface crust and 7 × 1012 N/m2 for mantle.
Af = area of fault plane undergoing slip, measured in m2. (length of surface rupture
times depth of aftershakes).
D = average displacement of ruptured segment of fault, measured in meters.

Moment magnitude scale Mw is interrelated with M0 as follows:

Mw = 0.67 log M0 – 10.7

This scale is found to work best for strike-slip faults

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)

Source: http::/neic.usgs.gov/neis/eqlists/eqstats.html

Approximate relationships between the moment

magnitude scale Mw and other magnitude scales
(Courtesy: Day, 2002)

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
Description Richter Earthquake Effects Frequency of
Magnitudes Occurrence
Micro Less than 2.0 Microearthquakes, not felt. About 8,000 per day
Very minor 2.0-2.9 Generally not felt, but recorded. About 1,000 per day

Minor 3.0-3.9 Often felt, but rarely causes damage. 49,000 per year (est.)
Light 4.0-4.9 Noticeable shaking of indoor items, rattling noises. 6,200 per year (est.)
Significant damage unlikely.
Moderate 5.0-5.9 Can cause major damage to poorly constructed buildings 800 per year
over small regions. At most slight damage to
well-designed buildings.
Strong 6.0-6.9 Can be destructive in areas up to about 100 miles across 120 per year
in populated areas.
Major 7.0-7.9 Can cause serious damage over larger areas. 18 per year
Great 8.0-8.9 Can cause serious damage in areas several hundred miles 1 per year
across.
Rare great 9.0 or greater Devastating in areas several thousand miles across. 1 per 20 years

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Richter Approximate TNT for Seismic Energy Yield Example
Magnitude

0.5 5.6 kg (12.4 lb) Hand grenade

Magnitude (Cont..)
1.0 32 kg (70 lb) Construction site blast

1.5 178 kg (392 lb) WWII conventional bombs

2.0 1 metric ton late WWII conventional bombs

2.5 5.6 metric tons WWII blockbuster bomb

3.0 32 metric tons Massive Ordnance Air Blast bomb

3.5 178 metric tons Chernobyl nuclear disaster, 1986

4.0 1 kiloton Small atomic bomb

4.5 5.6 kilotons Average tornado (total energy)

5.0 32 kiloton Nagasaki atomic bomb

5.5 178 kilotons Little Skull Mtn., NV Quake, 1992

6.0 1 megaton Double Spring Flat, NV Quake, 1994

6.5 5.6 megatons Northridge quake, 1994

7.0 32 megatons Largest thermonuclear weapon

7.5 178 megatons Landers, CA Quake, 1992

8.0 1 gigaton San Francisco, CA Quake, 1906

8.5 5.6 gigatons Anchorage, AK Quake, 1964

9.0 32 gigatons 2004 Indian Ocean earthquake

10.0 1 teraton estimate for a 100 km rocky bolide impacting at 25

km/s

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Magnitude (Cont..)
Measuring the earthquake

Length

Slip

Depth

Source: USGS15
public domain

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Intensity
• Intensity is a qualitative measure of the actual shaking at a location during an

earthquake, and is assigned as Roman Capital Numerals.

• There are many intensity scales. Two commonly used ones are the Modified

Mercalli Intensity (MMI) Scale and the Medvedev-Sponheur-Karnik (MSK) Scale.

• Both scales are quite similar and range from I (least perceptive) to XII (most

severe). The intensity scales are based on three features of shaking – perception

by people and animals, performance of buildings, and changes to natural

surroundings.

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Intensity (Cont..)
Some of the most common intensity scales are:
1. Mercalli-Cancani-Seiberg (MCS): 12-level scale used in southern Europe
2. Modified Mercalli (MM): 12-level scale proposed in 1931 by wood and Neumann, who adapted
the MCS scale to the California data set. It is used in North America and several other countries
3. Medvedev-Sponheuer-Karnik (MSK): 12-level scale developed in Central and Eastern Europe
and used in several other countries
4. European Macroseismic Scale (EMS): 12-level scale adopted since 1998 in Europe. It is a
development of the MM scale
5. Japanese Meteorological Agency (JMA): 7-level scale used in Japan. It has been revised over
the years and has recently been correlated to maximum horizontal acceleration of the ground.

Source: B.A.Bolt, Earthquakes, W.H.Freeman and Co., New York,

For further information refer to Pankaj Agarwal and 1993
Introduction to Engineering Seismology by Dr. P. Anbazhagan (IISC Bangalore)

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Intensity (Cont..)

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Intensity (Cont..)

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Isoseismal Map
The distribution of intensity at different places during an earthquake is shown graphically
using isoseismals, lines joining places with equal seismic intensity.

Isoseismal Map of the 2001 Bhuj (India)

Earthquake (MSK Intensity)

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Radiated Seismic Energy = Es
Conservation of Energy
Total energy before = Total energy after
P.E. = Es + crushing of rocks + heat

P.E. built up from strain in rocks as two sides of faults move past each
other

Es = radiated seismic energy

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Radiated Seismic Energy = Es

Es = Mo (1.6 x 10-5) Note:

• where Es is measured in ergs 1 kilowatt hour =

3.6 x 1013 ergs
• and Mo in dyne-cm typical house
Es = Mo (1.6 x 10-5) 15 KW hours

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Earthquake Energy
The total seismic energy released during an earthquake is often estimated from the expression
by Gutenberg as follows

log E = 1.5 Ms + 11.8

Where E is in ergs. As the magnitude increases by one unit, the energy increases by
a factor of 31.6 and the difference between two units of magnitude is a factor of 1,000
on energy release. Similarly, mb and Ms are related to seismic energy E (Where E is
expressed in joules (1joule = 107 ergs)) by the following empirical relations

log E = 2.4 Mb – 1.3

log E = 1.5 Ms + 4.2

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

Earthquake Energy

Correlation between surface wave magnitudes Ms and energy released during earthquakes

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

References
• University of Buffalo
• University College London
• Binghamton University
• Kettering University
• Earthquake Tips-C V R Murthy
• U S Geological Survey
• NICEEE
• EERI
• IIT Kanpur Manuals
• Earthquake Resistant design of structures by Pankaj Agarwal

Instructor: Dr. J S Kalyana Rama BITS Pilani, Hyderabad Campus

 BITS Pilani
Hyderabad Campus

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