Geoscience Reference
In-Depth Information
The travel time t for the diffracted wave recorded at location C, a horizontal
distance x from B, is given by
x 2
2
α 1
+ z 1
t =
or
= 4 x 2
+ z 1
1 t 2
2
α
(4.91)
This is the equation of a hyperbola (with a greater curvature than the reflection
hyperbola of Eq. (4.65)). The reflection and diffraction travel times are plotted on
the record section in Fig. 4.46(b). The curvature of this diffracted arrival on the
record section decreases with the depth z 1 of the diffracting point P; diffractions
from a deep fault are flatter than those from a shallow fault.
Immediately to the left of point B, the amplitude of the reflection decreases as
Bisapproached until at B the amplitude of the reflection is only half its value well
away from the edge of the reflector. (See the discussion of the Fresnel zone later
in this section.) The diffraction amplitude decreases smoothly with increasing
distance from the edge of the reflector. Since the reflection is tangential to the
diffraction hyperbola at point B, there is no discontinuity either in travel time or
in amplitude to mark the edge of the reflector. However, the diffraction branch
recorded to the left of B has opposite polarity to the branch recorded to the right
of B (they are 180 out of phase). Detection of both diffraction branches can
assist in the location of the edge of the reflector.
Dipping layers
On a CDP record section, the reflection point is shown as being vertically below
the shot/receiver location. Dipping interfaces are therefore distorted on CDP
record sections because the reflection points are not vertically below the shot/
receiver location. The situation is illustrated in Fig. 4.47: the normal-incidence
reflection recorded at location A is reflected from point A and that recorded at
location B is reflected from point B .If z 1 is the vertical depth of the reflector
beneath A and
is the dip of the reflector, then the length AA is given by
δ
AA = z 1 cos δ
(4.92)
and the two-way travel time for this reflection is
2 z 1
α 1
t =
cos δ
(4.93)
Similarly, the length BB is given by
BB = z cos δ
(4.94)
and the two-way travel for this reflection is
2 z
α 1
t =
cos δ
(4.95)
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