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geophone spacing fixed at no more than one-quarter of
that width. In this case the horizontal resolution will be
limited only by the physics of the seismic wave, not by
the survey design.
4.4.2 Design of detector arrays
Each detector in a conventional reflection spread con-
sists of an
array
(or
group
) of several geophones or hy-
drophones arranged in a specific pattern and connected
together in series or parallel to produce a single channel
of output. The effective offset of an array is taken to be
the distance from the shot to the centre of the array. Ar-
rays of geophones provide a directional response and are
used to enhance the near-vertically travelling reflected
pulses and to suppress several types of horizontally trav-
elling
coherent
noise. Coherent noise is that which can be
correlated from trace to trace as opposed to random
noise (Fig. 4.12).To exemplify this, consider a Rayleigh
surface wave (a vertically polarized wave travelling along
the surface) and a vertically travelling compressional
wave reflected from a deep interface to pass simultane-
ously through two geophones connected in series and
spaced at half the wavelength of the Rayleigh wave. At
any given instant, ground motions associated with the
Rayleigh wave will be in opposite directions at the two
geophones and the individual outputs of the geophones
at any instant will therefore be equal and opposite and be
cancelled by summing. However, ground motions asso-
ciated with the reflected compressional wave will be in
phase at the two geophones and the summed outputs of
the geophones will therefore be twice their individual
outputs.
The directional response of any linear array is gov-
erned by the relationship between the apparent wave-
length
l
a
of a wave in the direction of the array, the
number of elements
n
in the array and their spacing
D
x
.
The response is given by a response function
R
λ
Reflector
Fresnel zone
Fig. 4.11
Energy is returned to source from all points of a
reflector.The part of the reflector from which energy is returned
within half a wavelength of the initial reflected arrival is known as
the Fresnel zone.
structively to build up the reflected signal, and the part of
the interface from which this energy is returned is
known as the first
Fresnel zone
(Fig. 4.11) or, simply, the
Fresnel zone. Around the first Fresnel zone are a series of
annular zones from which the overall reflected energy
tends to interfere destructively and cancel out. The
width of the Fresnel zone represents an absolute limit on
the horizontal resolution of a reflection survey since re-
flectors separated by a distance smaller than this cannot
be individually distinguished.The width
w
of the Fresnel
zone is related to the dominant wavelength
l
of the
source and the reflector depth
z
by
12
wz
=
(
2
for
z
>>
l
)
(
l
)
The size of the first Fresnel zone increases as a function
of reflector depth. Also, as noted in Section 3.5, deeper-
travelling reflected energy tends to have a lower domi-
nant frequency due to the effects of absorption. The
lower dominant frequency is coupled with an increase in
interval velocity, and both lead to an increase in the
wavelength. For both these reasons the horizontal reso-
lution, like the vertical resolution, reduces with increas-
ing reflector depth.
As a practical rule of thumb, the Fresnel zone width
for the target horizons should be estimated, then the
sin
sin
n
b
b
R
=
where
=
D
x
bp l
a
R
is a periodic function that is fully defined in the inter-
val 0 £
D
x
/
l
a
£ 1 and is symmetrical about
D
x
/
l
a
= 0.5.
Typical array response curves are shown in Fig. 4.13.
