Seismic refraction method lec22

Seismic Refraction
Method
Overview (2)
Prepared by
Dr. Amin Khalil

Travel time distance graph
T-x graph is made by picking the first
onset of the first arrival seismic
phases. The picked phase should be
defined with great care. For refraction,
which is an active source method, the
first onset should generally be
compressional, hence the polarity of
the onset should be positive. We must
take care because under certain
circumstances the onset is masked
due to noise and we may pick later

Travel time curve
When the picked data is plotted, it will be time
versus distances, that’s why we call it T-X or
travel time distance curve.

• Horizontal interfaces provide a simple
introduction to the construction of T-X
diagrams.
• Close to the source, the first arrival is due to
the direct ray travelling in layer 1.
• This plots as a straight line on the T-X
diagram.
• The slope of the line is the reciprocal of the
layer 1 velocity (assuming distance is on the
X-axis).
• The intercept is zero.

• When the critical distance is exceeded, refraction
occurs and some energy enters layer 2. A
refracted ray then travels at V2 sending return
rays back to the surface as it does so.
• At some point (the cross-over distance) the
refracted ray (being the faster) will overtake the
direct ray and the return rays will become the first
arrivals, despite their longer travel distance.
• It is these that are now plotted on the T-X
diagram

• The T-X diagram thus develops an upper branch
due to the refracted ray.
• This is again a straight line, whose slope is the
reciprocal of V2 .
• There is now an intercept time (T1) whose value is
determined by the layer 1 thickness and the two
velocities
• The intercept time is an example of a delay time
sum, composed of the separate times taken by
the signal to descend to the interface and then to
return to the surface.

11 /VxT 
121
2
V
df
V
cd
V
ac
T 
)cos( ci
h
dfac 
)tan( cihdebc 
)tan(2 cihxdebcxcd 
2)(1
2
)tan(2
cos
2
V
ihx
iV
h
T
c
c


22)(1
2
)tan(2
cos
2
V
x
V
ih
iV
h
T
c
c

22)(1
2
)cos(
)sin(
cos
1
2
V
x
iV
i
iV
hT
c
c
c








Using Seismic Refraction
to Map the Subsurface
Depth{
12
12
2 VV
VVXc
Depth




Interpretation using intercept time
• The intercept time is given by
• Since, in this case, the ray path is symmetrical, the
intercept time is the sum of two equal delay times
12
2
1
2
2
2
VV
VV
zT



• By a similar argument, a third layer
introduces a third branch into the T-X
diagram.
• The slope is the reciprocal of V3 and the
intercept is a composite of the layer 1 and
layer 2 delay times.
12
2
1
2
2
2
13
2
1
2
3
12 22
VV
VV
z
VV
VV
zT





Delay Time Method
• Allows Calculation of Depth
Beneath Each Geophone
• Requires refracted arrival at each
geophone from opposite directions
• Requires offset shots
• Data redundancy is important

x
V1
V2
)cos(
)tan()tan(
)cos( 12221 c
BcBcA
c
A
AB
iV
h
V
ih
V
ih
V
AB
iV
h
T 

Delay Time Method
x
)cos(
)tan()tan(
)cos( 12221 c
PcPcB
c
B
BP
iV
h
V
ih
V
ih
V
BP
iV
h
T 
)cos(
)tan()tan(
)cos( 12221 c
PcPcA
c
A
AP
iV
h
V
ih
V
ih
V
AP
iV
h
T 
)cos(
)tan()tan(
)cos( 12221 c
BcBcA
c
A
AB
iV
h
V
ih
V
ih
V
AB
iV
h
T 
V1
V2

Delay Time Method
x
t T T TAP BP AB0   
Definition:
V1
V2
(7)

ABBPAP TTTt 0







)cos(
)tan()tan(
)cos( 12221
0
c
PcPcA
c
A
iV
h
V
ih
V
ih
V
AP
iV
h
t







)cos(
)tan()tan(
)cos( 12221 c
PcPcB
c
B
iV
h
V
ih
V
ih
V
BP
iV
h







)cos(
)tan()tan(
)cos( 12221 c
BcBcA
c
A
iV
h
V
ih
V
ih
V
AB
iV
h
212
0
)tan(2
)cos(
2
V
ih
iV
h
V
ABBPAP
t
cP
c
p




But from figure above, BPAPAB  . Substituting, we get
212
0
)tan(2
)cos(
2
V
ih
iV
h
V
BPAPBPAP
t
cP
c
p



or
21
0
)tan(2
)cos(
2
V
ih
iV
h
t
cP
c
p













)cos(
)sin(
)cos(
1
2
21
0
c
c
c
p
iV
i
iV
ht











)cos(
)sin(
)cos(
2
21
1
21
2
0
c
c
c
p
iVV
iV
iVV
V
ht



















)cos(
)sin(
)cos(
2
2121
1
2
10
c
c
c
p
iVV
i
iVV
V
V
Vht







2
1
sin
V
V
ic
Substituting from Snell’s Law,



















)cos(
)sin(
)cos(
sin
1
2
2121
10
c
c
c
c
p
iVV
i
iVV
iVht




















)cos(
)sin(
)cos(
sin
1
2
2121
10
c
c
c
c
p
iVV
i
iVV
iVht
Multiplying top and bottom by sin(ic)











)cos()sin(
)(sin
)cos()sin(
1
2
21
2
21
10
cc
c
cc
p
iiVV
i
iiVV
Vht











)cos()sin(
)(cos
2
21
2
10
cc
c
p
iiVV
i
Vht











)sin(
)cos(
2
2
0
c
c
p
iV
i
ht











)sin(
)cos(
2
2
0
c
c
p
iV
i
ht








2
1
sin
V
V
ic
Substituting from Snell’s Law,
1
0
)cos(2
V
ih
t
cp
 (8)
We get

11
)cos(
2
)cos(2
2
PpointatDelay time
V
ih
V
iht
D
cpcpo
TP  (9)

Seismic refraction method lec22

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