Q) Over the distance between two seismic recording sites at different ranges from a seismic source, seismic waves have been attenuated by 5dB. What is the ratio of the wave amplitudes observed at the two sites?
(Thanks to Chandrasekhar, AKNU)
Solution:
The Dynamic range is an expression of
the ratio of the largest measurable amplitude Amax to the
smallest measurable amplitude Amin in a sample function.
Dynamic range is normally
expressed in the decibel (dB) scale used to define electrical power ratios.
dB=10 log(\frac{P_1}{P_2})
we know that power \propto
(Amplitude)^2
then from the above
equation we get
dB=10
log(\frac{A_1}{A_2})^2
dB=20
log(\frac{A_1}{A_2})----------------------------------------(1)
Now using this equation, we get
our solution for the problem
Given that
Dynamic range = 5 dB
Then what is the ratio of the wave’s
amplitudes?
From the equation 1
dB=20
log(\frac{A_1}{A_2})
5=20 log(\frac{A_1}{A_2})
log(\frac{A_1}{A_2})=\frac{5}{20}=\frac{1}{4}
\frac{A_1}{A_2}=10^{\frac{1}{4}}=1.8
Reference: An Introduction to Geophysical Exploration by Philip Kearey, Michel Brooks, and Ian Hill.
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