Geoscience Reference
In-Depth Information
x-distance of transmit-receive
x-distance of transmit-receive
0
0
1 2 3 4
0
1 2 3 4
1
Direct arrivals
Direct arrivals
2
3
d
4
Baseline
Reflections from
layer boundary
Reflections from
layer boundary
Layer boundary
(a) Layer model
(b) Time-distance cross-section
from model, with travel-time
variations caused by elevation
(c) Time-distance cross-section
from model, with static
corrections applied
fIGURe 7.8
Static corrections: (a) definitions and model, (b) field measurements, and (c) field measure-
ments with static corrections applied. “d” is the distance from the baseline to the measurement locations on
the surface.
x-distance along the surface
Transmit-receive
trace locations
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
X
7
8
9
Surface
Direct arrivals
D
r
Reflections, and
reflection hyperbola
Point backscatter
(a) Point reflector model
(b) Time-distance cross-section from model
Distance from Point Center, m
Distance from Point Center, m
Distance from Point Center, m
-5
0
5
-5
0
5
-5
0
5
0
0
0
0.3
0.25
0.2
0.15
0.3
0.25
0.2
0.15
0.3
0.25
0.2
0.15
50
50
50
0.1
0.05
0.05
0.1
0.1
0.05
100
100
100
Depth of Point Scatterer = 0.1 m
(c) Hyperbolic time-distance curves for velocities of 0.05, 0.1, 0.15, 0.20, 0.25, and 0.30 m/ns
Depth of Point Scatterer = 1 m
Depth of Point Scatterer = 2 m
fIGURe 7.9
Backscattered reflection from a point in the subsurface, as a function of surface position: (a) point
model and hypothetical time-distance cross section, (b) change in hyperbola shape as a function of velocity and
depth, and (c) time-distance plots of different velocities of the host material and depths of a point scatterer.
Spatial effects on GPR data are directly related to the velocity of the material. These effects are
summarized in Figure 7.9. A signal reflected from a point in the subsurface (Figure 7.9a) appears as
a hyperbola on the GPR record, because a backscattered reflection occurs when transmit-receive
antennas approach the center of the buried object and when the antennas are moving away from the
object. The shape of the hyperbola is directly related to the velocity, with a flattening of the hyper-
bola corresponding to an increase in velocity. The effect of changing the velocity on the shape of the
hyperbola is shown in Figure 7.9b, and the simple equation that determines the shape of the hyperbola
on the time-distance cross section is
t
(
x
) = 2
r
/
v
, where
t
is the two-way travel time of the backscat-
tered GPR pulse at a distance
x
away from the center of the point, for a velocity
v
of the material.
Figure 7.9c suggests that the velocity of a material can be determined directly from GPR data,
when the data contain an anomaly from a point scatterer (e.g., as approximated by a buried pipe, or
the sharp edge of an object that is crossed by a GPR line of measurement traces). The velocity can
