Lunar and Planetary Science XXX
1191.pdf
KILOMETER-SCALE ROUGHNESS OF GEOLOGICAL UNITS ON MARS: INITIAL RESULTS FROM
MOLA DATA. M. A. Kreslavsky1,2 and J. W. Head1, 1Dept. Geol. Sci., Brown University, Providence RI 029121846 USA misha@mare.geo.brown.edu, 2Kharkov Astronomical Observatory, 35 Sumska, Kharkov 310022,
Ukraine.
dian slope – baseline length plots. In the opposite
case, if all features are much smaller than the baseline, the typical slope is inversely proportional to the
baseline length. This means an inclined segment in
the plot with the power law exponent of -1. Real surfaces are formed of various features of different scales.
As a result, the dependence has inclinations between 0
and -1. For example, for Vastitas Borealis Formation
units (Fig. 1a), the dependence of median slope on
baseline length is steeper for longer baselines. This
means that the topography is dominated by some units
with typical spatial dimension of ~3 km. For some
volcanic plains and, especially, for the dune fields
(Adl, Fig. 1d), the dependence is steeper for shorter
baselines and almost flat for longer baselines. This
means, that short-baseline slopes are controlled by
small-scale features (individual lava flow fronts,
dunes, etc.), while the long-baseline slopes coincide
with regional slopes, and there are no features of inM edian slope, deg
10
Fig. 1
a
N pl1
H vk
H vm
H vg
H vr
A a3
1
0.1
M edian slope, deg
0.01
10
N pl1
N pl2
N pld
N ple
Hr
H vk
A a3
b
1
0.1
M edian slope, deg
0.01
10
N pl1
H vk
A el1
A el3
A a1
A a3
c
1
0.1
0.01
10
M edian slope, deg
Introduction: More than 2.5 million 0.4-kmspaced precise measurements of elevation of the martian surface were obtained in 1998 with the Mars Orbiter Laser Altimeter (MOLA) [1] onboard the Mars
Global Surveyor providing an excellent data set for
study of the km-scale roughness of the surface. We
used statistics of slopes on 0.5-25 km baselines to
characterize the surface roughness of some geological
units in the northern hemisphere of Mars. The technique of slope calculation is discussed in [2].
Geological units: We calculated slope statistics
separately for some of units using regional-scale geological maps [3-5]. We excluded segments of MOLA
passes located 25 km on both sides of the unit boundaries. This was necessary to ensure that whole baselines
are located within a specific unit. In addition, this
diminished the influence of any inaccuracy in locating
of unit boundaries on digitized geological maps and
their possible geodetic errors. As a result, most of
major steep regional topographic slopes (the polar cap
scarps and global dichotomy scarp) were excluded
from consideration. Thus, our statistics reflect the
nature of inner or typical roughness of units rather
than topography associated with their boundaries.
We selected those geologic units where there were
more than 10,000 MOLA measurements per unit.
They are the following: Old heavily cratered highland
plateau units (Npl1, Npl2, Npld, Nple), relatively old
heavily tectonized volcanic plains (Hr); relatively old
Vastitas Borealis Formation units (Hvk, Hvm, Hvg,
Hvr); different younger volcanic plains (Ael1, Ael3,
Aa1, Aa3, Aa4, Aam); relatively young plains of uncertain, probably volcanic origin (Apk, Aps); the polar
cap deposits (Api, Apl); circumpolar mantling deposits (Am) and dune fields (Adl). See [3-5] for more
detailed description.
Roughness characteristics: For each unit we calculated the median slope and quartiles of the slopefrequency distribution for the baselines 0.4, 0.8, 1.6,
3.2, 6.4, 12.8 and 25.6 km long (see [2] for details).
Fig. 1 presents four similar log-log plots of scale dependences of the median slopes. Units Npl1 (typical
highland), Hvk (typical Northern plain), and Aa3 (the
smoothest volcanic plain) are shown in all four plots
for comparison.
If a surface is formed by some features of typical
spatial dimension much longer than the baseline, a
typical slope should not depend on the baseline length.
This corresponds to a horizontal segment in the me-
d
N pl1
H vk
A ps
A dl
A pi
A a3
1
0.1
0.01
0.1
1
10
B aseline length, km
100
Lunar and Planetary Science XXX
1191.pdf
ROUGHNESS OF GEOLOGICAL UNITS ON MARS: M. A. Kreslavsky and J. W. Head
1
Fig. 2
0.1
Fig. 3
1
short baseline
exponent -0.21
Hvk
long baseline
exponent -0.51
Earth
Hv…
Npl…
Am
volc. plains
Api,Apl
Adl
Hr
Apk, Aps
Median slope, deg
Median slope, deg
10
0.01
termediate scales.
We approximated the dependence of median slope
on baseline length with a power law separately for
short baselines (0.4, 0.8, 1.6 km) and for long baselines (6.4, 12.8, 25.6 km) (Fig. 2). In Fig. 3 we plotted
the short-baseline exponent against short-baseline (0.8
km) roughness for the set of units. In Fig. 4, the longbaseline exponent is plotted against the short-baseline
exponent. The point “Earth” in the diagrams (Fig. 3
and 4) refers to Earth continents. The data for baselines of 1.9 km and longer were extracted [2] from the
GTOPO30 digital elevation model and then were extrapolated to the short baselines.
The quartile ratio characterizes the form of the
slope-frequency distribution. For the exponential distribution the ratio is ~4.8. We plotted the quartile ratio
for 0.8-km baseline against the 0.8-km baseline
roughness and the short-baseline exponent (Fig. 5, 6).
Discussion: The diagrams (Fig. 3–6) show that
the statistics of roughness for all four highland units
are similar (see also Fig. 1b). The topography of the
highlands is probably largely inherited from heavy
bombardment, and morphologically observed traces of
erosion, sedimentation and tectonism have not influenced it at these scales.
All four Vastitas Borealis Formation units in all
diagrams are very close to each other despite apparent
differences in surface morphology. Observed surface
features (knobs, grooves, rampart craters) contribute
little to the slope statistics. The slope distribution is
dominated by ~3 km long ~0.3° steep irregular background features, almost indistinguishable in the images. The similarity of slope statistics among the Vastitas Borealis Formation subunits suggests a possible
similarity of surface formation and/or modification
processes.
The circumpolar mantling deposits (Am) are much
younger than the Vastitas Borealis Formation, they are
thick enough to cover virtually all preexisting craters,
and they have exactly the same slope statistics as the
Vastitas Borealis Formation. These terrains may have
been formed by the same repeating or ongoing processes that produced the roughness of the Vastitas Borealis Formation.
0.1
0
0.2
0.4
0.6
0.8
Short baseline exponent
1
Earth
Hv…
Npl…
Am
volc. plains
Api,Apl
Adl
Hr
Apk, Aps
Fig. 4
Long baseline exponent
100
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
Short baseline exponent
1
1
Fig. 5
Median slope, deg
1
10
Baseline length, km
Hv…
Npl…
Am
volc. plains
Api,Apl
Adl
Hr
Apk, Aps
0.1
4
5
6
Quartile ratio
7
7
Quartile ratio
0.1
Hv…
Npl…
Am
volc. plains
Api,Apl
Adl
Hr
Apk, Aps
Fig. 6
6
5
4
0
0.2
0.4
0.6
0.8
Short baseline exponent
1
Plain units Apk and Aps adjacent to Vastitas Borealis to the South differ in slope statistics, mainly in the
quartile ratio (Fig. 5, 6). This confirms their origin to
be distinctive from Vastitas Borealis Formation.
References: [1] Smith D. E. et al. (1998) Science,
279, 1686–1692. [2] Kreslavsky M. A. and Head
J. W., Frequency distribution of kilometer-scale slopes
on Mars…, this issue. [3] Tanaka K. L. and Scott D.
H. (1987) USGS, Map I-1802-C. [4] Greeley R. and
Guest J. E. (1987) USGS, Map I-1802-B. [5]
Scott D. H. and Tanaka K. L. (1986) USGS, Map I1802-A.