Figure 1
Arrowed rectangular 800x800m pattern on the hill is an example of lunar
ruin-like formations (long.=301.11 deg.; lat.=85.59 deg.; Clementine image:
LHD6749R.318).
PRELIMINARY SEARCH
FOR RUIN-LIKE FORMATIONS ON THE MOON
Alexey V.Arkhipov
rai@ira.kharkov.ua
Institute of Radio Astronomy, 4 Krasnoznamennaya, Kharkov, 310002,
Ukraine
ABSTRACT
1. INTRODUCTION
2. METHODOLOGY
2.1 PRELIMINARY FRACTAL TEST
nmax sk2 = (gk /nmax) S [ log M(ri) - n log ri - C]2, i=1
where: k is the number of test square; gk is the apparatus factor or
average (s*/sk)2 from a lot of HIRES images (s* is sk in the center of
image at gk=1); nmax is the number of used scales up to M(ri)=0. Then the
average dispersion <s> is estimated from these regional squared residuals.
The analysis
of 733 HIRES images (0.75mm-filter; the polar zones up to 75o-latitudes;
112-115 orbits) shows that s distribution is the classical
Gaussian function. According to the Student's criterion for 12 estimations,
if the inequality (sk -<s>) > 1.796 ( S(sk -<s>)2/11)1/2 is true
in any test square, this area could be considered as anomalous with a probability
of 0.95.
2.2 RECTANGULAR TEST
2.3 SAAM IMAGE
2.4 GEOLOGICAL TEST
3. RESULTS OF THE SEARCH
Figure 1
Arrowed rectangular 800x800m pattern on the hill is an example of lunar
ruin-like formations (long.=301.11 deg.; lat.=85.59 deg.; Clementine image:
LHD6749R.318).
An example of picturesque ruin-like formations on a hill is shown in Fig. 1. The traditional explanations in terms of crossing of impact fault systems seem inadequate for such compact and closed formations. The Moon did not have conditions (a thin crust above melted mantle) for Venus-like tessera terrains. So the origin of these anomalies is problematical. As a rule, lunar base projects would be expected to show the rectangular patterns of subsurface constructions [7-9]. Formally, such complexes could be classified as (a) and (b) patterns. The (c)-type bands in Fig. 2 are a puzzle. Theirs depth from shadows (~10 m) is about the average thickness of the regolith layer on the Moon. Theirs flat bottoms and geometry remind one of modern projects for lunar regolith mining (e.g. [10]). Some depressions of (b)-type could be interpreted in mining terms too.
Figure 2
The curious shallow depressions of ~8m-depth and ~100m-width
can be seen in the box after filtration of the image's fine structure,
and again in the schematic at the top left (long.=28.31 deg.; lat.=79.11;
Clementine image: LHD5502Q.290).
Of course, this visual impression should be tested by some objective
procedure. The modified fractal Carlotto-Stein method was used for
this purpose. First, the range of HIRES image brightness was increased
linearly up to 256 gradations. Then convert the image into an intensity
surface in a 3-D rectangular frame of coordinates (x and y are the pixel
coordinates; z is its brightness). The Carlotto-Stein method [5] can be
thought of as enclosing the image intensity surface in volume elements.
These volume elements are cubes with a side of 2r; where r is the
scale in terms of pixel coordinates or its brightness. Let Vr be the average
minimal volume of such elements enclosing an image intensity surface
at some point. Then the surface area is Ar = Vr/2r. As a function of scale,
Ar characterizes the size distribution of image details. The fractal
linear relation between log Ar and log r is a good approximation for natural
landscapes. However, the self-similar fractals do not approximate artificial
objects as a rule. That is why M.J. Carlotto and M.C. Stein used the average
of the squared residuals e of the linear regression log Ar=blog r + g
as a measure of artificiality.
Unfortunately,
e depends on the number of pixels in an image. Therefore, it is difficult
to compare different images. Moreover, the shadows increase e and generate
false alarms. These problems could be resolved by the non-linear regression:
log Ar = a (log r)2 +blog r + g,
where the factor a is independent of the image size. The shadows lead to a >0, but artificial objects have a <0.
Figure 3
The diagram of fractal properties of analyzed images: the random set
of HIRES files (crosses), HIRES images of ruin-like formations (black squares),
and aerospace photographs of terrestrial archaeological objects (opened
squares).
This effect is shown in Fig. 3. There factors a and b are calculated for the random set of HIRES images (crosses) and aerospace photographs of terrestrial archaeological objects (white squares). The fragments of images of the following archaeological sites were used in our analysis: Giza tombs in Egypt (KVR-1000 satellite) and El-Lejjun Roman legionary fortress, Jordan, (CORONA satellite) [11]; the Cerro Vidal trinchera , the Cerro Juanaquena trinchera and Pueblo She' in Galisteo Basin (New Mexico, aerial photographs [12]). The parameter a values for lunar ruin-like formations (black squares) is distributed between the geological background (crosses) and archaeological objects (opened squares). Some formations have a as low as the known archaeological sites.
Figure 4
The shadow effect for the parameter a of geological background (crosses)
and ruin-like formations (black squares) on the Moon. The regression relating
a of the random image set and zenith angle of the sun (Zsol) is shown as
the dashed line. The adopted criterion for target selection (regression
- 3sa) is shown as the solid line.
The weak effect of low sunlight could be seen in Fig. 4. At any zenith angle of the Sun (Zsol), the ruin-like formations have systematically lower a than the random set of HIRES images does. The average linear regression relating a of the random set and Zsol is shown as a dashed line. The standard deviation of the crosses from this regression is sa =0.0113. A minimal deviation of 3sa (solid line) is adopted as a formal criterion for the final selection. The selected objects on the Moon listed in Table I all have reasonable levels of archaeological interest.
4. CONCLUSIONS
ACKNOWLEDGEMENTS
REFERENCES
Longitude Latitude Type
Dimensions
Image
Description
(deg.)
(deg.)
(km)
________ _______ ____
_________ _____________
____________________
28.04
-76.45 a
5.3 x 5.6 LHD0132B.290
separate group of
rectangular walls and
qadrangular hills
28.31
79.11 c
1.2 x 1.5 LHD5502Q.290
curious pattern of linear
and broken band
depressions of ~100m-
width and ~8m-depth
(Fig.2)
31.06
78.84 c
0.3 x 1.3 LHD5256Q.293
rectangular zigzag band
of flat depression of
~20m-depth
151.21 -76.24
b
0.8 x 0.8 LHD0470B.112
rectangular claster of
depressions
246.08 81.88
a
2.2 x 2.2 LHD7638R.343
rectangular walls of
100m-width and the
box-like hill of
300x300m
301.11 85.59
a-b 0.8
x 0.8 LHD6749R.318
complicated
rectangular structure
on the top of a hill (Fig. 1)
(This web page produced for Alexey Arkhipov by Francis Ridge of
The Lunascan Project)
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