Course:MATH110/Archive/2010-2011/003/Teams/Graubunden/Homework 13

Earthquakes are measured by the Richter Scale which assigns a number to quantify the amount of seismic energy released by an earthquake. The Richter magnitude is calculated by the amplitude of the largest seismic wave of the earthquake and is based on the logarithmic scale of base 10. This means that for each whole number you go up on the Richter Scale, the seismograph records the amplitude of the ground motion which goes up ten times. Therefore, the concept of the Richter Magnitude Scale and how it works on the logarithmic scale is that as each whole number increases in magnitude, the amplitude increases by a tenfold increase. The formula for the magnitude scale is M^L=Log10A-Log10Ao(δ)

A is equal to the maximum of the seismograph, Ao depends on the epicentral(the point of the earth's surface directly above the focus of an earthquake)distance of the station which is δ.

The relative difference in strength between earthquakes is calculated using the formula

=(10^x)^(3/2)

where x is difference in magnitude between earthquakes as measured by the richter scale. For example, an earthquake whose relative strength is 1 level higher on the richter scale is approximately 31.6 times stronger than the weaker earthquake. A difference of 2 in magnitude is closer to 1000 times stronger.