Geoscience Reference
In-Depth Information
Cross-set volume
v
(m
3
)
0.01
0
0.1
1
10
100
1000
10000
1
1-5m
3
class
-1
0.1
3.1%
-2
0.01
-3
0.001
-4
0.0001
-5
0.00001
-6
0.00000
-2
-1
0
1
2
3
4
expected maximum
V
max
= 3162 m
3
V
min
= 0.032 m
3
Cross-set volume logarithm (log
v
)
Fig. 17.
The exceedence frequency distribution of cross-set volumes,
EF
(
v
), derived from the distribution of measured
cross-set thicknesses approximated as a two-tier power-law distribution (Fig. 16). Note that the distribution line allows the
number frequency of cross-sets of any particular volume, or volume class, to be predicted. For example, the relative
frequency of beds in a volume class of 1 m
3
to 5 m
3
is 3.1%.
where
x
i
are the measured bed thicknesses and
D
is the distribution's characteristic exponent,
referred to as the fractal dimension. He demon-
strated that the corresponding bed-volume dis-
tribution will similarly follow a power-law
distribution:
highest point constrained by the frequency value
log
EF
(
v
min
) = log
EF
(
x
min
) and the value log
v
min
for
estimated
v
min
= 0.032 m
3
(see Appendix). The
dimensionless coefficient −1.44 is the value of
log
EF
(
v
i
) for log
v
i
= 0. The right-hand limit of
the distribution line indicates the expected maxi-
mum bed-thickness volume, estimated as
v
max
≈
3200 m
3
. On this basis, the relative frequency of
beds of any particular volume, or volume class,
can directly be estimated. For example, the rela-
tive frequency of cross-set beds with volumes of
1 m
3
to 5 m
3
is expected to be 3.1% (Fig. 17). In
this way, the tidal-ridge sandstone bodies in a
reservoir heterogeneity model for the Kristin
Field (Fig. 12) can readily be populated with a
realistic frequency of cross-set volumes.
(6)
EFvv
i
()≈
−
G
i
where
EF
(
v
i
) is the frequency of beds with a vol-
ume greater than
v
i
and
G
is an unknown charac-
teristic exponent (fractal dimension) to be
calculated.
The calculation procedure is given in the
Appendix. The
G
-value is derived directly from
the values of exponents
D
1
and
D
2
(Fig. 16) and the
resulting equation in the present case is:
Comparative remarks on the reservoir model
−
093
.
(7)
EF v
() .
=−
144
v
i
i
As pointed out by Quin
et al
. (2010), the initial inter-
pretation of the Garn Formation in the Halten Terrace
was somewhat confused by the tectono-stratigraphic
situation where the sediment accumulation occurred
in the footwall zone of a major relay structure and
the primary supply of sand was from the hanging
wall; a configuration opposite to that generally
expected in rift basins. It was also not realised that a
secondary internal faulting within the footwall zone
which gives a straight line:
(8)
log(
EF v
)
=−
144093
.
−
. og
v
i
i
This line describes completely the expected
exceedence frequency distribution of bed
volumes (Fig. 17), with the negative
G
-value
defining the line's gradient and with the line's
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