2. Logarithmic, or inverse exponential functions, scale an
extremely large range of numbers (very large to very
small) to numbers that are easier to compare and/or
comprehend.
Example: The pH scale measures the acidic
concentration, H+, of liquids. It ranges from 0 to 14.
Similarly, the Richter Scale determines the magnitude
of an earthquake. It uses numbers we can relate to and are
more comfortable working with. It’s scale represents the
magnitude of an earthquake in the range from 0 to 10.
3. The Richter Scale was developed in 1935 by Charles Richter in
partnership with Beno Gutenberg, both of the California Institute
of Technology.
The scale was originally intended to be used only in a particular
study area in California, and on seismograms recorded on a
particular instrument, the Wood-Anderson torsion seismometer.
Richter originally reported values to the nearest quarter of a unit,
but values were later reported with one decimal place.
His motivation for creating the local magnitude scale was to
separate the vast number of smaller earthquakes from the few
more intense earthquakes observed in California at the time.
4. The Richter scale measures the ‘magnitude’ of an
earthquake as a logarithmic function by converting the
intensity of shock waves I into a number M, which for
most earthquakes range from 0 to 10.
The Intensity, I, of an earthquake is in terms of the
constant Io where Io is the intensity of the smallest
earthquake, called zero-level earthquake, and is
measured on a seismograph near the earthquake’s
epicenter.
The Easter Earthquake of 2010 was M = 7.2. The
recent earthquake in Japan measured had M = 9.0!
(Recently Upgraded!)
5. An earthquake with an intensity (I) has a
Richter scale magnitude of: M = log
Where is the measure of a zero-level
earthquake or the normal ‘background’ earth
movement as previously mentioned. It can often
be considered as ‘negligible”.
0
I
I
0
I
6. The Easter 2010 Earthquake with: M = 7.2
Replace M with 7.2 7.2 = Log
Translate into
exponential form
Multiply both sides by
Evaluate : = 15,848,932
0
EI
I
0I E0
7.2
10 I = I
0I
0
7.2
10 EI
I
=
EI
7. The Japan 2011 Earthquake with: M = 9.0
Replace M with 9.0
Translate into
exponential form
Multiply both sides by
Evaluate : = 1,000,000,000
0
9.0 log JI
I
=
9.0
10 J
0
I
=
I
0I
9.0
010 JI I=
JI
0I
8. The Intensityof the Japan Earthquake
Comaprison Ratio
The Intensityof the Easter Earthquake
=
=
1,000,000,000
15,848,932
63 times more intense!
The Japanese Earthquake Was 63 Times More Intense
Than The Easter Earthquake!
