Geology Reference
In-Depth Information
(a)
A
D
z
v
1
h
θ
h'
z'
θ
B
C
v
2
> v
1
γ
(b)
t
t
DA
Reciprocal time
t
AD
t'
i
t
i
Fig. 5.5
(a) Ray-path geometry and
(b) travel-time curves for head wave arrivals
from a dipping refractor in the forward and
reverse directions along a refraction profile
line.
x
Source
Detector
x
h
1
β
1
v
1
α
1
h
2
α
2
γ
1
v
2
β
2
Fig. 5.6
Geometry of the refracted ray path
through a multilayer, dipping model. (After
Johnson 1976.)
v
3
γ
2
where
z
is the perpendicular distance to the interface
beneath the shot, and
q
12
= sin
-1
(
v
1
/v
2
).
Equation (5.9) defines a linear plot with a gradient of
sin(
q
12
+
g
1
)/
v
1
and an intercept time of 2
z
cos
q
12
/
v
1
.
Shooting updip, along the reverse profile
where
z
¢ is the perpendicular distance to the interface
beneath the second shot.
The gradients of the travel-time curves of refracted
arrivals along the forward and reverse profile lines yield
the downdip and updip apparent velocities
v
2d
and
v
2u
respectively (Fig. 5.5(b)). From the forward direction
x
sin
-
g
)
+
2
z
¢
cos
(
q
q
12
1
12
t
¢=
(5.10)
2
v
v
1
v
=
sin
qg
+
v
(
)
(5.11)
1
1
2
d
12
1
1
