Calculation of true thickness of the bed

 

Q) As per Gutenberg – Richter relationship for global seismicity how many earthquakes of magnitude 2 will be occur, given that number of earthquakes of magnitude 6 to be 100 and b value to be 1.5

 (Thanks to Chandrasekhar, ANU)

Solution:

 The Gutenberg-Richter relationship is log(N)=a-b$M_{s}$

 Where N is the Earthquake frequency or number of earthquakes occurred

$M_{s}$ is the earthquake magnitude

a and b are constant

 

 from the given data of  $M_{s}$ is 6, N = 100 , b= 1.5 then

 log(N)= a - b$M_{s}$

log(100)= a-(1.5)6

2=a-9

a= 11

 

  for $M_{s}$ = 2, N=?

 then log(N)=a- b$M_{s}$

log(N) = 11- (1.5)(2)

log(N)=11-3

log(N)=8

N=$10^{8}$

means $10^{8}$ earthquakes of magnitude 2 will be occur.

Reference : Fundamental of Geophysics, William Lowrie.