Geology Reference
In-Depth Information
0.20
0.40
0.15
Mean grain area = 86 mm
2
Mean area of subgrains = 15 mm
2
0.30
0.10
0.20
0.05
0.10
0.00
0.00
0
8162432404856647280
0
100
Area of grains (mm
2
)
50
150
200
Area of subgrains (mm
2
)
0.30
0.20
Mean major axis length = 16 mm
Mean major axis length = 8 mm
0.15
0.20
0.10
0.10
0.05
0.00
0.00
0
6121824303642485460
0
6
12
18
24
30 36
Major axis length of grains (mm)
Major axis length of subgrains (mm)
0.20
0.30
Mean minor axis length = 6 mm
Mean minor axis length = 3 mm
0.15
0.20
0.10
0.10
0.05
0.00
0.00
14710
13
16
19
22
25
28
0.0
0.8 1. 6 2.4 3.2
4.0 4.8 5.6 6.4
Minor axis length of grains (mm)
Minor axis length of subgrains (mm)
Figure 4.48
Measurements of geometry of grains and subgrains of SY ice from Allen Bay, central Arctic, obtained
in May 1997. Measurements are taken at 10 cm depth [
Johnston,
1998].
was simple but rather lengthy and computationally
exhaustive. Photographs of horizontal thin sections were
digitized into frames of 640 × 480 arrays with gray tone
ranging between 0 and 255. The images were then parti-
tioned into their constituents of pure ice crystals and one
inclusion type; brine pockets or air bubbles. This process
produced binary images. The gray tones that represent
pure ice crystals and inclusions were transformed into a
value representing their permittivities: 3 for ice, 1 for air,
and 80 for brine. Therefore, a binary image that contains
ice and brine had pixel values of either 3 or 80. A segment
of 400 × 400 pixels is extracted from each image and a
window, W, of 200 × 200 pixels was chosen with which to
convolute the main image. The correlation function
R
(
x
,
y
) of the image (i.e., the permittivity) was obtained
by convolving the window over the image segment
S
:
1
n
m
Rxy
(
,
)
W ijSxiyj
(. )( ,
)
(4.2)
WS
WS
j
11
i
where
n
and
m
are the number of pixels in the
x
and
y
directions and
μ
W
,
μ
S
,
σ
W
, and
σ
S
are the mean and
standard deviation of the image segment and the convo-
lution window, respectively. Figure 4.49 shows the binary
images of permittivity and their correlation functions
obtained from horizontal thin sections at three depths:
30, 55, and 120 mm. The size and orientation of the crys-
tals in the binary images are well reflected in the shape of
the correlation functions. At 30 mm depth, the crystals
are small and randomly oriented (isotropic ice expected
in equiaxed snow ice). The correlation function is nearly
isotropic. Trends of asymmetric crystal orientation
