Characterizing Earthquakes using Engineering Parameters
Earthquake Size

In order to estimate the ground motions at a site, it is necessary to first determine the size of the earthquake which will generate the ground motions. The size of this earthquake can be described in several different ways:

Intensity

Intensity is a subjective, qualitative description of observed damage and the reaction of people and animals to the earthquake. The modified Mercalli intensity (MMI) scale is used to measure intensity in the U.S and other English-speaking countries. Other areas such as Japan (JMA scale) and eastern Europe (MSK scale) use other intensity scales. MMI intensities range from I-XII:

III      Noticed by people
VII    Start of structural damage
X      Major damage
XII    Total damage

A number of intensities from different sites can be plotted on an isoseismal contour map, giving a helpful picture of the distribution of damage. Also, interpretive MMI data is available for many past earthquake which do not have instrumental records. However, intensity is not a good index for design because of its qualitative nature.

Magnitude

Since instruments such the seismograph and accelerometer have made it possible to accurately measure ground motions, a quantitative measure of the size of an earthquake is possible. There are several magnitude scales in use, which often leads to confusion in the reporting of magnitudes. The best scale for scientific and engineering purposes is the moment magnitude (Mw) scale since it is related to the rupture parameters. The most commonly used magnitude scales are:

• Richter local magnitude (ML): log of pendulum displacement of a Wood-Anderson seismometer located at 100 km from the epicenter
• Surface wave magnitude (MS): based on the amplitude of Rayleigh waves with a period of about 20 s; used for distant (>1000 km) earthquakes
• Body wave magnitude (Mb): based on the amplitude of the first few cycles of p-waves; used for deep-focus earthquakes
• Moment magnitude (Mw): based on the seismic moment (M0), a measure of the work done by the rupture, and doesn't saturate like the other scales
Mw = log10 M0/1.5 - 10.7 M0 = mAD
where m = rupture strength of material along fault
A = area of rupture
D = average amount of slip

Estimating Magnitude Based on Fault Length

For a specific fault, the Mw of a potential earthquake can be estimated by relating it to the potential rupture length of the fault using the Wells and Coppersmith (1994) relation:

 Mw = a + b log (SRL) where SRL = surface rupture length in km Strike-slip: a = 5.16 b = 1.12 s = 0.28 Normal: a = 4.86 b = 1.32 s = 0.28 Reverse: a = 5.00 b = 1.22 s = 0.34 All: a = 5.08 b = 1.16 s = 0.28

Maximum displacement along the rupture can also be estimated using Wells and Coppersmith:

 log (MD) = a + bMw (meters) where Strike-slip: a = -7.03 b = 1.03 s = 0.34 Normal: a = -5.90 b = 0.89 s = 0.38 All: a = -5.46 b = 0.82 s = 0.42

Wells and Coppersmith have also developed relationships between magnitudeand average displacement, subsurface rupture length, downdip rupture width, and rupture area [1].

Energy

The total amount of seismic energy released by the earthquake is related to the magnitude, and can be estimated using the relationship by Gutenberg and Richter (1956):

logE = 11.8 +1.5MS (ergs)

Each unit increase in magnitude produces roughly a 32-fold increase in energy release. Also, moment magnitude can be used instead of surface wave magnitude.