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

 Q) A 10Hz seismic wave travelling at 5 km/sec propagates for 1000m through a medium with an absorption coefficient of 0.2 dB/ ʎ. What is the wave attenuation in decibels due solely to absorption?

(Thanks to Chandrasekhar, ANU)

 

Solution: Given that velocity(C) of the seismic wave = 5 km/sec

                                                                                 = 5000 m/sec

  Frequency of the seismic wave (f) = 10 Hz

The relation between frequency, velocity and wavelength is given by, 

 $C=f\lambda$

$\lambda=\frac{C}{f}$

$\lambda=\frac{5000}{10}$

$\lambda=500 m$

 Then for the wavelength 500m the absorption coefficient is 0.2 dB/ ʎ Then what is the wave attenuation for the wave length 1000m

            500 ------ 0.2 dB/ ʎ

 Then 1000 -------? ( let be some X)

$500 \times X=0.2\times 1000$

$X=\frac{200}{500}$

$X= 0.4 dB/\lambda$

 

Therefore, the wave attenuation in decibels due solely to absorption is$0.4 dB/\lambda $

Reference:

An Introduction to Geophysical Exploration by Philip Kearey, Michel Brooks and Ian Hill.