(i) Determine the vertical two-way travel-time (t0) and average velocity to each reflecting interface. (ii) Calculate the depth of each reflector and the thickness of each layer. (iii) Find the true velocity (interval velocity) of each layer.
The following table gives two-way travel times of seismic waves reflected from different reflecting
interfaces in a horizontally layered medium.
Plotting the data on a t2-x2 plot, the best-fit straight lines (1), (2) and (3) have the following
equations, with x = (distance [km])2 and y = (travel-time [s])2:
(i) Determine the vertical two-way travel-time (t0) and average velocity to each reflecting interface.
(ii) Calculate the depth of each reflector and the thickness of each layer.
(iii) Find the true velocity (interval velocity) of each layer.
(iv) Verify your results by calculating the total vertical travel-time for a wave reflected from the
deepest interface.
(v) If a seismic ray leaves the surface at an angle of 15° to the vertical, how long does it take to
return to the surface after reflecting from the basement? At what horizontal distance from the
shot-point does this ray reach the surface?
![Geophone to Travel-time [s] to
Shot-point
First
Distance [m]
Reflector
0.299
0.566
0.841
1.117
1.393
500
1000
1500
2000
2500
Second
Reflector
0.364
0.517
0.701
0.897
1.099
Third
Reflector
0.592
0.638
0.708
0.799
0.896](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfe2f0f3-e78f-405b-92d6-f137d3a3d54e%2Fe412fdc8-a881-4ece-9df1-29c36271fcc0%2Fmfx0r1_processed.png&w=3840&q=75)
![[$]
(travel-time)²
2.0
1.5 (3) y = 0.07567x+0.3319
1.0-
Plot of t²-x²
(1) y = 0.3086x + 0.01240
(2) y = 0.1792x+0.0880 (1)
0.5
0
1
2
3
(distance)²
4
(2)
(3)
5
6
[km²]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfe2f0f3-e78f-405b-92d6-f137d3a3d54e%2Fe412fdc8-a881-4ece-9df1-29c36271fcc0%2F00f5k3_processed.png&w=3840&q=75)
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