question archive Earthquakes are complicated events, and so the intent here is not to provide a complete discussion of the science involved in them
Earthquakes are complicated events, and so the intent here is not to provide a complete discussion of the science involved in them
Subject:MathPrice: Bought3
Earthquakes are complicated events, and so the intent here is not to provide a complete discussion of the science involved in them. Rather, we will look at a simplified version of the Richter scale. The Richter scale measures the magnitude of an earthquake by comparing the amplitude of the seismic waves of the given earthquake to those of a "magnitude 0 event", which was chosen to be a seismograph reading of 0.001 millimeters recorded on a seismometer 100 kilometers from the earthquake's epicenter. Specifically, the magnitude of an earthquake is given by: M(x) = log (x/0.001), where x is the seismograph reading in millimeters of the earthquake recorded 100 kilometers from the epicenter.
1) Use the formula for the magnitude of an earthquake and do the following:
a) Show that M(0.001) = 0.
b) Compute M(80,000).
c) Show that an earthquake which registered 6.7 on the Richter scale had a seismograph reading ten times larger than one which measured 5.7.
