Their Intensity

 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.

 The Richter Scale was developed in 1935 by Charles Richter in partnership with Beno Gutenberg, both of the California Institute of Technology.Charles RichterBeno Gutenberg 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.Californiaseismometer  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.

 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 I o where I o 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!)

 An earthquake with an intensity ( I) has a Richter scale magnitude of: M = log  (This formula is similar to the sound intensity formula we have used before.)  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”.

The Easter 2010 Earthquake with: M = 7.2 Replace M with = Log Translate into exponential form Multiply both sides by Evaluate : = 15,848,932

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

The Japanese Earthquake Was 63 Times More Intense Than The Easter Earthquake!

  For These Problems Use The Richter Scale Equation: M =Log( ),  Where M is the Magnitude Of An Earthquake, I Is The Intensity Of The Shock Waves, and I 0 Is The Measure Of A Zero-Level Earthquake.   On July 14 th, 2000, an earthquake struck the Kodiak Island Region in Alaska. The earthquake had an intensity of  I= 6,309,573I 0. Find the Richter scale magnitude of the earthquake. (Round to the nearest tenth.)   An earthquake in Japan on March 2, 1933, measured 8.9 on the Richter scale. (Japan has a lot of them.) Find the Intensity of the earthquake in terms of I 0. (Round to the nearest whole number.)   6.8  794,486,234I 0