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Home , Epicenter, Moment magnitude scale, P wave, Seismic wave

Geotechnical Engineering

by Dr. Deepankar Choudhury Professor Department of Civil Engineering IIT Bombay, Powai, Mumbai 400 076, India. Email: [email protected] URL: http://www.civil.iitb.ac.in/~dc/

Lecture – 11 Module – 4

Strong Ground Motion

IIT Bombay, DC 2 Size of

IIT Bombay, DC 3 Magnitude and Intensity Intensity • How Strong Earthquake Feels to Observer – Qualitative assessment of the kinds of damage done by an earthquake – Depends on distance to earthquake & strength of earthquake – Determined from the intensity of shaking and damage from the earthquake Magnitude • Related to Release. – Quantitative measurement of the amount of energy released by an earthquake – Depends on the size of the that breaks – Determined from Seismic Records 4 IIT Bombay, DC Measuring Earthquakes • Seismogram is visual record of arrival time and magnitude of shaking associated with seismic . Analysis of seismogram allows measurement of size of earthquake. • Mercalli Intensity scale Measured by the amount of damage caused in human terms- I (low) to XII (high); drawback: inefficient in uninhabited area • Richter Scale- (logarithmic scale) Magnitude- based on amplitude of the Related to earthquake total energy IIT Bombay, DC 5 Intensity

How Strong Earthquake Feels to Observer Depends On: • Distance to / • of site • Type of building /structure • Observer’s feeling

Value varies from Place to Place • Modified Mercalli Scale - I to XII

IIT Bombay, DC 6 Ref: Wikipedia IIT Bombay, DC 7 Modified Mercalli Intensity Scale

IIT Bombay, DC 8 Earthquake Magnitude

 ML - Local (Richter) magnitude

 MW - Seismic Moment magnitude

 MS - magnitude m  b- Body wave magnitude

IIT Bombay, DC 9 Local Magnitude of Earthquake • Magnitude – Richter scale measures the magnitude of an earthquake, based on seismogram independent of intensity – Amplitude of the largest wave produced by an event is corrected for distance and assigned a value on an open- ended logarithmic scale – The equation for Richter Magnitude is:

ML = log10A(mm) + (Distance correction factor) Here A is the amplitude, in millimeters, measured directly from the photographic paper record of the Wood-Anderson seismograph, a special type of instrument. The distance factor comes from a table given by Richter (1958). 10 IIT Bombay, DC Richter’s Local Magnitude Right side diagram (nomogram) demonstrates how to use Richter's original method to measure a seismogram for a magnitude estimate After you measure the wave amplitude you have to take its and scale it according to the distance of the from the earthquake, estimated by the S-P time difference. The S-P time, in seconds, makes t. The equation behind this nomogram, used by Richter in Southern California, is:

ML = log10A(mm) +3 log10[8 t (sec)]-2.93 11 IIT Bombay, DC Richter Scale: Related to intensity – M=1 to 3: Recorded on local seismographs, but generally not felt – M= 3 to 4: Often felt, no damage – M=5: Felt widely, slight damage near epicenter – M=6: Damage to poorly constructed buildings and other structures within 10's km – M=7: "Major" earthquake, causes serious damage up to ~100 km (Gujarat 2001 earthquake). – M=8: "Great" earthquake, great destruction, loss of life over several 100 km – M=9: Rare great earthquake, major damage over a large region over 1000 km

12 IIT Bombay, DC Correlations

IIT Bombay, DC 13 Surface Wave Magnitude Richter’s local magnitude does not distinguish between different types of waves. At large distances from epicenter, ground motion is dominated by surface waves. Gutenberg and Richter (1956) developed a magnitude scale based on the amplitude of Rayleigh waves.

Surface wave magnitude Ms = log10A + 1.66 log10 +2.0 A = Maximum ground displacement in micrometers = Distance of seismograph from the epicenter, in degrees. Surface wave magnitude is used for shallow earthquakes

IIT Bombay, DC 14 Body Wave Magnitude

For deep focus earthquakes, reliable measurement of amplitude of surface waves is difficult. Amplitudes of P-waves are not strongly affected by focal depth. Gutenberg (1945) developed a magnitude scale based on the amplitude of the first few cycles of P- waves, which is useful for measuring the size of deep earthquakes.

Body wave magnitude mb = log10A – log10T +0.01 + 5.9 A = Amplitude of P-waves in micrometers T = period of P-wave = Distance of seismograph from the epicenter, in degrees.

IIT Bombay, DC 15 Source: Richter (1958)

IIT Bombay, DC 16 Limitations of Ms and mb due to Magnitude Saturation Magnitude saturation, is a general phenomenon for approximately Mb > 6.2 and Ms > 8.3.

As Mb approaches 6.2 or MS approaches 8.3, there is an abrupt change in the rate at which frequency of occurrence decreases with magnitude.

Though the rupture area on the fault is large, the predictions will saturate at these magnitudes.

Because of this magnitude saturation, estimation of magnitude for large earthquakes through Mb and M becomes erroneous. s IIT Bombay, DC 17 Seismic - Moment Magnitude

A Seismograph Measures Ground Motion at One Instant But -- • A Really Great Earthquake Lasts Minutes • Releases Energy over Hundreds of Kilometers • Need to Sum Energy of Entire Record • based on seismic moment (Kanamori, 1977) and doesn’t depend upon ground shaking levels. • It’s the only magnitude scale efficient for any size of earthquake.

IIT Bombay, DC 18 Moment Magnitude • Moment-Magnitude Scale – Seismic Moment = Strength of Rock x Fault Area x Total amount of Slip along Rupture

M0 = A D (in N.m) [Idriss, 1985] Where, = of material along the fault plane in N/m2 (= 3x1010 N/m2 for surface and 7x1012 N/m2 for ) A = area of fault plane undergoing slip (m2) D = average displacement of ruptured segment of fault (m)

Moment Magnitude, Mw = 2/3 x [log10M0(dyne-cm) –16]

Moment Magnitude, Mw = - 6.0 + 0.67 log10M0(N.m) [Hanks and Kanamori (1979)] – Measurement Analysis requires Time IIT Bombay, DC 19 Seismic - Moment Magnitude

• Most magnitude scales saturate towards large earthquakes

with m b > 6.0, M L > 6.5, and M S > 8.0. The moment magnitude M w (Kanamori 1977) represents true size of earthquakes, as it is based on seismic moment, which in turn is proportional to the product of the rupture area and

dislocation of an earthquake fault (Aki 1966). M W is defined as,

MW = 2/3log10M0− 6.05

where M 0 is the scalar seismic moment in Nm. MW does not saturate, this is the most reliable magnitude for describing the size of an earthquake (Scordilis 2006).

IIT Bombay, DC 20 Rigidity of Crust and Mantle for Seismic Moment Estimation

IIT Bombay, DC 21 Correlation between Mw and ML • The distribution of M W versus M L is shown Fig. and the correlation is given by Kolathayar et al. (2012) for India by considering 69 earthquake data, 2 MW=0.815(±0.04)ML+0.767(±0.174), 3.3≤ML≤7, R =0.884

IIT Bombay, DC 22 Correlations between various magnitude scales

Heaton et al. (1982)

IIT Bombay, DC 23 Seismic Energy

Both the magnitude and the seismic moment are related to the amount of energy that is radiated by an earthquake. Gutenberg and Richter (1956), developed a relationship between magnitude and energy. Their relationship is: logES = 11.8 + 1.5Ms

Energy ES in ergs from the surface wave magnitude Ms. ES is not the total “intrinsic” energy of the earthquake, transferred from sources such as gravitational energy or to sinks such as heat energy. It is only the amount radiated from the earthquake as seismic waves, which ought to be a small fraction of the total energy transferred during the earthquake process.

IIT Bombay, DC 24 Local Magnitude - Seismic Energy correlation

Gujarat (2001)

Size of an earthquake using the Richter’s Local Magnitude Scale is shown on the left hand side of the figure above. The larger the number, the bigger the earthquake. The scale on the right hand side of the figure represents the amount of high explosive required to produce the energy released by the earthquake. 25 Frequency of earthquakes

IIT Bombay, DC 26 Frequency of earthquakes

IIT Bombay, DC 27 Example Problem

IIT Bombay, DC 28