A commonly-employed method of determining the severity of an earthquake is the R

Question

A commonly-employed method of determining the severity of an earthquake is the Richter scale. A device called a seismograph measures the movements of the earth and compares it to a "standard" seismic event (for which a seismograph would record 0.001 km of movement at a distance of 100 km from the epicenter). The Richter magnitude of an earthquake is the difference in base-10 logarithms of the amplitude of the earthquake and the amplitude of the standard event. Write the magnitude M of an earthquake as a function of its amplitude A (with A_0 the amplitude of the "standard" event). What is the magnitude of an earthquake with amplitude 2 mu m? Rewrite the expression for M as a single logarithm using the properties of logarithms. What amplitude corresponds to the magnitude 5 earthquake near Cuba on January 9, 2014?

Explanation / Answer

a) M = log10(A) - log10(Ao)

= log10(A/Ao)

b) A = 2 microm ; Ao = 0.001 microm

M = log10(2/0.001)

= log10(2000)

= 3.3

c) Use the log property : logX - logY = log(X/Y)

M = log10(A/Ao)

d) M = 5

5 = log10(A/Ao)

A/Ao = 100000

A = 0.001*100000 = 100 microm

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