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```• Reflected wave from a horizontal layer
• Reflected wave from a dipping layer
• Refracted wave from a horizontal layer
• Refracted wave from a dipping layer
• Diffracted waves
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Hydrogeological studies of acquifers
Engineering geology
Shallow faults
Mapping Quaternary deposits
Ground investigation for pipe and sewerage
tunnel detection
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Depth of groundwater level
Depth and location of hardrock
Elastic medium parameters
Permafrost
Glaciology
• Refracted Waves
• Mainly horizontal Wave propagation
• Only refracted waves are used. (Lower layer must
have higher velocity than upper layer)
• Distribution of velocity as well as the depth and
orientation of interfaces between layers
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Reflected Waves (“Echo lot principal”)
Mainly vertical wave propagation
Complete seismic recording is used
Distribution of the velocity variation
Direct wave
Reflected wave
Refracted wave
Source
Direct wave
t
t = 1---x
v
x
o
x
x
x
x
v = x--t
v
Velocity of direct wave is derived from the distance and
travel time
Reflection: Horizontal reflector
x
A
B
x
o
4S2=4h2+x2=t2v2
s
h
a
C
h
s
v
t2=(4h2+x2)/v2
Reflection: Horizontal reflector
for x=0:
t2v2=4h2
t(x=0)=t0=2h/v
t0
or
h=t0v/2
h
t2v2=4h2+x2
t2= x2/v2+t02
Reflection: horizontal reflector
t2v2 = 4h2+x2
t2v2 - x2 = 4h2
h
t2v2 - x2 =1
4h2
4h2
Hyperbola
x>>h Þ
t= x
v
Moveout
1
Difference in travel time t(x1 ) und t(x2 ):
2
x22- x12
t 2- t 1 »
2v2t0
Normal Moveout
1
0
0
Difference in traveltime t
0
und t(x):
1
x12
DT=t1- t0 »
2v2t0
t2v2=4h2+x2- 4hxcos(90+Q)
X=-2hsinQ
t2v2=4h2+x2+4hxsin(Q)
Hyperbola:
DTdip
[x+2hsin(Q)] 2
t2v2
=1
[2hcos(Q)]2 - [2hcos(Q)]2
-x
x
h
Q
h
x
90+Q
DTdip= tx-t-x = 2xsinQ
v
sin ic
v1
v1
=
Û sin ic =
sin 90 v 2
v2
Propagation of seismic waves
(Roth et al., 1998)
Direct wave
Reflected wave
Refracted wave
h
TSG = TSA + TAB + TBG = 2TSA + TAB
(
x - 2h tan ic )
h
=2
+
v1 cos ic
v2
x 2h cos ic
= +
v2
v1
Refraction: horizontal reflector
t
1
----v1
1
----v2
2
2
x 2h v 2 – v1
t = -----+ -------------------v1 v 2
v2
ti
x
xcross
x
t = -----t
+
v2 i
x
h
v1
v2
v2 + v1
xcros = 2h -----------v 2 – v1
x sin(q c + a ) 2 z a cosq c
td =
+
v1
v1
For small slopes (a < 100):
x sin(q c - a ) 2 zb cosq c
+
v1
v1
vd + vu
v2 »
2
tu =
x sin(q c + a ) 2 z a cosq c
td =
+
v1
v1
For small slopes (a < 100):
x sin(q c - a ) 2 zb cosq c
+
v1
v1
vd + vu
v2 »
2
tu =
Every point on a wavefront can be considered as a secondary
source of spherical waves
Surface
V=1.6 km/s
800 m
Reflection:
tr» t0+dt
h
t0=2h/v
Reflection /Diffraction
dt =x2/(4vh)
Diffraction:
td» t0+2dt