GATE-2018 (24) :Wyllie – Time average equation

17. The amplitude of ground motion generated by an earthquake of magnitude 8 is greater than that of an earthquake of magnitude 5 by a factor of..

A)3                     B)100                    C)300                  D)1000

Solution:

Magnitude is a measurement of the energy released by an earthquake.

The first earthquake magnitude scale was the Richter scale.

The Richter scale is based on the amplitude of seismic waves- the stronger the earthquake, the stronger the seismic vibrations it causes.

The most important thing to remember about Richter magnitude is that it is a logarithmic scale, meaning that an increase of one in magnitude corresponds to a factor of ten increases in the amplitude of ground motion.

Amplitude of seismic wave (A) from an earthquake of magnitude proportional to 10^x

Therefore ,

A_M=8 = K*10^⁸ ------------------------(1)

A_M=5 =K *10^{^5} --------------------------(2)

The ratio between the eq (1) and eq (2) is

(A_M=8/ A_M=5 )= 10^{^8} /10^{^5}

=10^³

A_M=8 = 1000* A_M=5

Reference: https://earthquake.usgs.gov/learn/topics/measure.php