Question

An earthquake has intensity I = 105,760R, where R is the intensity of the reference quake.Find the measure of the earthquake on the Richter scale.

Answer 1

The Richter scale is a logarithmic scale (base 10).

log₁₀(I/R)=log₁₀(105760)=5.02.

However, if I₁ and I₂ are the intensities of two earthquakes and R₁ and R₂ are their respective Richter scale numbers, then in practice, R₂-R₁=1.0 when I₂/I₁=√1000, that is log(I₂/I₁)=3/2=1.5. So I₂ is about 32 times stronger than I₁, because 32 is approximately √1000. A difference of 2 on the Richter scale means 1,000 times (32² approx=10³) stronger. A difference of 3 (10^4.5) means about 32,000 times stronger. A difference of 4 (10⁶) means 1,000,000 times stronger. 

If the reference earthquake has a Richter value of r (intensity=R) and 5.02/1.5=3.35 approx, then "I" should correspond to about 3.35+r. So if, r=1 then I=4.35 on the Richter scale.