Distance of geophone from the source of disturbance (m) Time of first arrival (t x 10-3)
2.5
11.2
5
23.3
7.5
33.5
10
42.4
15
50.9
20
57.2
25
64.4
30
68.6
35
71.1
40
72.1
50
75.5
seismic refraction survey site data
Solution:
Velocity Calculation
first arrival time of P wave versus distance of geophone from source
of disturbance
In Figure 3.46, the time of the first arrival of p-waves is plotted against the distance of the
geophone from the source of disturbance (explosion or hammering). The plotted graph has three
straight-line segments. The velocity of the top three layers can be calculated as:
Slope of segment:
0a=1υ1=timedistance=23×10−35.250a=υ11=distancetime=5.2523×10−3
υ1=5.2523×10−3=228 m/s (top layer)υ1=23×10−35.25=228 m/s (top layer)
Slope of segment:
ab=1υ2=13.5×10−311ab=υ21=1113.5×10−3
υ2=1113.5×10−3=814.8 m/s (middle layer)υ2=13.5×10−311=814.8 m/s (middle layer)
Slope of segment:
bc=1υ3=3.5×10−314.75bc=υ31=14.753.5×10−3
υ3=14.753.5×10−3=4214 m/s (third layer)υ3=3.5×10−314.75=4214 m/s (third layer)
After analysis of the results given in Table 3.12, it indicates that the third layer is a Rock
Layer.
Thickness of Layers
From Figure 3.46, xc=10.5mxc=10.5m, So
Z1=12υ2−υ1υ2+υ1xcZ1=21υ2+υ1υ2−υ1
xc
Thus,
Z1=12814.8−228814.8+228×10.5=3.94mZ1=21814.8+228814.8−228
×10.5=3.94m
Again, from (Eq. 3.81),
Z2=12[Ti2−2Z1υ32−υ12υ3υ1]υ3υ2υ32−υ22Z2=21[Ti2−2Z1υ3υ1υ32−υ12
]υ32−υ22
υ3υ2
The value of Ti2Ti2 (from figure 3.46) is 65 x 10-3 s. Hence,
Z2=12[65×10−3−2×3.9442142−22824214×228]4214×814.842142−814.82=12.66mZ2=21
[65×10−3−2×3.944214×22842142−2282
]42142−814.82
4214×814.8=12.66m
Thus, the rock layer lies from the surface of the ground at a depth of:
Z1+Z2=3.94+12.66=16.60mZ1+Z2=3.94+12.66=16.60m
Note: Equations and the number of equations which used in this article are taken from reference
section source.