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Expected GATE-2022 Geophysics Solution (11)

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 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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