Problem 3: Richter Scale
The Richter scale is used to measure the strength of earthquakes. The following data shows the correlation between the Richter scale and the number of kilograms of TNT that would release the same energy as an earthquake of this size.
Kilograms of TNT to have this much energy: 0.6, 20, 600, 20,000, 60,000, 20,000,000, 60,000,000
Richter Magnitude: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0
Sketch a graph showing these figures with the Richter scale along the horizontal axis. What type of graph do you think this is? Why? Describe the features of the graph.
b:
The Richter scale measures the energy of an earthquake by determining the size of the greatest vibrations recorded on a seismograph: Mw = 2 - log10(Mo) - 10.7, where Mo is the seismic moment measured in dyne-centimeters. The moment magnitude Mw roughly agrees with the Richter scale. Rearrange the equation to make Mo the subject: Find the value of Mo for an earthquake that measures 6 on the Richter scale. If Mo = 10^5, determine the strength of this earthquake on the Richter scale (Mw) without the use of a calculator.