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

 24.  A seismic reflection survey is carried out over a 1500 m thick horizontal layer with a P-wave velocity of 2000 m/s. The travel time of a reflected wave at a surface detector placed 1000m from a surface source is _______ milliseconds.

(Thanks to Pragnath, AU)

Solution:

Given that $V_{p}=2000 m/s=2 Km/s~$;    

d( depth)=1500 m=1.5 Km;      

x(offset distance)=1000m=1 Km.

$T^{2}=\frac{X^{2}}{V^{2}}+(\frac{2D}{V})^2$

$T^{2}=\frac{1^{2}}{2^{2}}+(\frac{2(1.5)}{2})^2$

$T^{2}=\frac{1}{4}+(\frac{3}{4})^2$

$T^{2}=0.25+(1.5)^2$

$T^{2}=0.25+2.25$

$T=\sqrt{2.5}$

$T=1.581 seconds$

$T=1581.13~milliseconds$

Therefore, the travel time is 1581 milliseconds