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Focus Problem propontonicl 1'01 Of If you have heard about earthquakes reported on the news, as an earthquake of magnitude 5.6. By what factor would then you have likely heard numbers from the Richter the energy increase for a one-point increase in magnitude? scale. The Richter scale was developed in the 1930s, and Use this idea to write a formula to compare the energy it has been used for decades to describe and compare the from two different earthquakes of magnitude ml and m2. magnitudes of earthquakes. The Richter scale is a loga- rithmic scale on which a one-unit increase in magnitude It is also said that the energy produced by an earthquake corresponds to a factor-of-ten increase in the amplitude of is proportional to 101 5m, where m is the magnitude. Use the wave recorded by a seismograph. The Richter scale is this idea to write a second formula to compare the energy accurate for rating smaller earthquakes close to the seis- from two different earthquakes of magnitude ml and mz. mometers that measure them, but it is not accurate for Use both your formulas to compare the energy released the most powerful earthquakes (above approximately 8 on in the Indonesia earthquake to the energy released in the the Richter scale). Out of a desire to better describe more earthquake near Japan. powerful earthquakes and take advantage of improved What are the limits of the earthquake magnitude scales? measurement techniques, a new base-ten logarithmic How low or high can the ratings be? What does a negative scale called the moment magnitude scale was developed. magnitude mean exactly? For smaller, less powerful earthquakes, the Richter scale and the moment magnitude scale give the same result. What is the highest magnitude ever recorded for an earth- For larger earthquakes, the moment magnitude scale does quake? How did that earthquake compare to the "average" a better job of indicating the energy of, and the conse- earthquake in amplitude and energy released? quent damage caused by, the earthquake because it also Scientists have been measuring earthquake intensity for incorporates information from longer-wavelength waves about a hundred years, and they are still making improve- into the model. ments. When current measurements and techniques are In 2005, there was a devastating earthquake in Indonesia not sufficient, you have to consider ... that was rated 8.6 on the moment magnitude scale. In 201 1, there was an even stronger earthquake near Japan that was rated a 9.1. By what factor do the amplitudes of WHAT ELSE CAN these quakes differ? On the moment magnitude scale, every increase of 0.2 corresponds to a doubling of the energy. Thus, an earth- WE DO? quake of magnitude 5.8 releases twice as much energy