Geology Reference
In-Depth Information
(a)
x
x
v
1
z
V
v
2
t
(b)
v
3
t
x
Δ
T
t
0
v
n
-1
v
n
Fig. 4.1
Vertical reflected ray paths in a horizontally-layered
ground.
-x
O
+x
x
Fig. 4.2
(a) Section through a single horizontal layer showing the
geometry of reflected ray paths and (b) time-distance curve for
reflected rays from a horizontal reflector.
D
T
= normal moveout
(NMO).
flector lying at a depth
z
beneath a homogeneous top
layer of velocity
V
. The equation for the travel time
t
of
the reflected ray from a shot point to a detector at a hori-
zontal offset, or shot-detector separation,
x
is given by
the ratio of the travel path length to the velocity
This is the intercept on the time axis of the time-distance
curve (see Fig. 4.2(b)). Equation (4.1) can be written
12
)
(
2
2
t
=+
x z
4
V
(4.1)
2
2
2
2
4
z
V
x
V
2
(4.3)
t
=
+
In a reflection survey, reflection time
t
is measured at an
offset distance
x
.These values can be applied to equation
(4.1), but still leave two unknown values which are re-
lated to the subsurface structure,
z
and
V
. If many reflec-
tion times
t
are measured at different offsets
x
, there will
be enough information to solve equation (4.1) for both
these unknown values. The graph of travel time of
reflected rays plotted against offset distance (the
time-
distance curve
) is a hyperbola whose axis of symmetry is
the time axis (Fig. 4.2(b)).
Substituting
x
= 0 in equation (4.1), the travel time
t
0
of a vertically reflected ray is obtained:
Thus
x
V
2
2
2
2
(4.4)
t
=+
t
0
This form of the travel-time equation (4.4) suggests the
simplest way of determining the velocity
V
.If
t
2
is plot-
ted against
x
2
, the graph will produce a straight line of
slope 1/
V
2
.The intercept on the time axis will also give
the vertical two-way time,
t
0
, from which the depth to
the reflector can be found. In practice, however, this
method is unsatisfactory since the range of values of
x
is
restricted, and the slope of the best-fit straight line has
large uncertainty.A much better method of determining
2
z
V
t
=
(4.2)
0
