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.