Geology Reference
In-Depth Information
and from the reverse direction
t
1
v
=
sin qg
-
v
(
)
(5.12)
2
u
12
1
1
Hence
t i 2
t i 1
-
1
qg
+=
sin
sin
(
vv
vv
)
12
1
12
d
-
1
-=
(
)
qg
12
1
12
u
x
Solving for q and g yields
1
2
1
2
=
[
sin
-
1
vv
) +
sin
-
1
vv
]
q
(
(
)
z 1
12
12
d
12
u
z 2
v 1
[
-
1
-
1
]
=
sin
vv
) -
sin
vv
)
g
(
(
Δ
z
1
12
d
12
u
A
B
v 2 > v 1
Knowing v 1 , from the gradient of the direct ray travel-
time curve, and q 12 , the true refractor velocity may be
derived using Snell's Law
Fig. 5.7 Offset segments of the travel-time curve for refracted
arrivals from opposite sides of a fault.
vv
2
=
sin q
1
12
The perpendicular distances z and z ¢ to the interface
under the two ends of the profile are obtained from
the intercept times t i and t i ¢ of the travel-time curves
obtained in the forward and reverse directions
these reciprocal times (or end-to-end times) is a useful means
of checking that travel-time curves have been drawn
correctly through a set of refracted ray arrival times
derived from a reversed profile.
t
=
2
z
cos
v
q
i
12
1
5.2.5 Faulted planar interfaces
\=
zvt
2
cos
q
1
i
12
The effect of a fault displacing a planar refractor is to off-
set the segments of the travel-time plot on opposite sides
of the fault (see Fig. 5.7). There are thus two intercept
times t i1 and t i2 , one associated with each of the travel-
time curve segments, and the difference between these
intercept times D T is a measure of the throw of the fault.
For example, in the case of the faulted horizontal refrac-
tor shown in Fig. 5.7 the throw of the fault D z is given by
and similarly
zv 1
¢=
¢
2
cos q
i
12
By using the computed refractor dip g 1 , the respective
perpendicular depths z and z ¢ can be converted into
vertical depths h and h ¢ using
z
cos
D
q
hz
=
cos g 1
D
T
ª
v
1
and
Tv
Tv v
vv
D
D
1
1 2
z
ª
=
D
cos
12
q
)
(
2
-
2
hz cos g 1
¢= ¢
2
1
Note that the travel time of a seismic phase from one
end of a refraction profile line to the other (i.e. from shot
point to shot point) should be the same whether mea-
sured in the forward or the reverse direction. Referring
to Fig. 5.5(b), this means that t AD should equal t DA .
Establishing that there is satisfactory agreement between
Note that there is some approximation in this formula-
tion, since the ray travelling to the downthrown side of
the fault is not the critically refracted ray at A and in-
volves diffraction at the base B of the fault step. However,
the error will be negligible where the fault throw is
small compared with the refractor depth.
 
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