4. The magnitude of an earthquake, measured on the Richter scale, is given by R
ID: 3029032 • Letter: 4
Question
4. The magnitude of an earthquake, measured on the Richter scale, is given by R (1) log Where lis the amplitude registeredon a seismograph located 100 km from the epicenter of the earthquake, and lois the amplitude of a certain small size earthquake. Note: the ncommon logarithm y -log(x) is understood to be base 10. a) Find the Richter scale rates of earthquakes with the folowing amplitudes. 000.000 1000,000,0001. b) On June 15, 1999, the city of Puebla in central Mexico was shaken by an earthquake that measured 6.7 on the Richter scale. Express this reading in terms of lo c) On September 19, 1985 Mexico's largest recent earthquake measuring 8.1 on the Richter scale, killed about 10,000 people. Express the magnitude of an 8.1 reading in terms of lo.Explanation / Answer
# (a)
Given : amplitude = 1,000,000 I0
logs are Base 10. we use Q rather than the subscipted notation just for convenience in coding this response.
log(I/Q) = log(I) - log(Q)
log(I/(1000000*Q)) = log(I) - log(1000000*Q)
= log(I) - [log(1000000)+log(Q)]
= log(I) - [ log (106 ) + log(Q) ]
= log(I) - [ 6 log(10) + log(Q)]
= log(I) - [6+log(Q)]
# when the amplitude is 1000,000,000 I0
then ,
log(I/(1000,000,000*Q)) = log(I) - log(1000,000,000*Q)
= log(I) - [log(1000,000,000)+log(Q)]
= log(I) - [ log (109 ) + log(Q) ]
= log(I) - [ 9 log(10) + log(Q)]
= log(I) - [ 9 +log(Q) ]
#(b) It is probably just :
6.7 = log10 ( 100/ I0 )
apply log rule : a = logb ( ba )
so, 6.7 = log10 ( 106.7 )
log10 ( 106.7 ) = log10 ( 100/I0 )
( 106.7 ) = 100 / I0 { since logs have the same base }
so, I0 = 100 / ( 106.7 )
= ( 22 * 52) / ( 26.7 * 56.7 )
Hence, I0 = 1 / ( 24.7 * 54.7 )
I0 = 0.00002 [ Answer ]
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