Surface roughness mapping at sub-hectometer
scale from HRSC data: new applications for
geologic mapping and impact crater related
processes.
Aurélien Cord a , David Baratoux b , Nicolas Mangold c ,
Patrick Martin a , Patrick Pinet b , Francois Costard c ,
Philippe Masson c , Bernard Foing a , Gerhard Neukum d
and HRSC Co-I team
a European
Space Agency (ESA), ESTEC, RSSD, SCI-SB
Keplerlaan 1, 2201 AZ Noordwijk ZH, The Netherlands
b Observatoire
Midi-Pyrénées, UMR5562
14 av. Edouard Belin, 31400 Toulouse, France
c IDES,
UMR8148, Bat. 504/509
Université Paris-Sud, Fac. des sciences, 91405 ORSAY CEDEX, France
d Free
University of Berlin, Institute for Geosciences/Planetology,
Malteserstr. 74-100, D-12249 Berlin, Germany
Abstract
The quantitative measurement of surface roughness of planetary surfaces at all scales
provides valuable insights into geological processes. Complementary of the analysis
of local topographic data of the Martian surface at kilometer scale, achieved from the
Preprint submitted to Elsevier Science
28 February 2006
MOLA data, and at the sub-centimeter scale, using photometric properties derived
from the multi-angular observation, a first characterization of roughness variations
at a few tens of meters scale is proposed. Relying on a Gabor filtering process, a
powerful tool developed in the context of image classification for the purpose of
image texture analysis has been adapted to handle HRSC data. This derivation of
roughness at the tens of meter wavelength range, combined with analyses at longer
wavelength, gives a new view of the Martian surface. The potential of this approach
has been evaluated for different examples. For these complex areas, different geological units have be identified, mapped and characterized in terms of roughness.
This insight is helpful for geological mapping purposes and to distinguish processes
such as lava flow emplacement and alteration, erosion, impact processes and ejecta
emplacement.
Key words: Geological Processes, Impact Processes, Image Processing, Mars
Surface, Surface Roughness, Textural Variation
1
Introduction
Fluvial, aeolian or glacial activity, impact cratering and landslides are among
various geological processes which are responsible for roughness variations on a
planetary surface, particularly the Martian surface. Those processes control or
are controlled by the grain or rock sizes and their organization on the surface.
The quantitative measurement of surface roughness at any scale can provide
valuable insights into the characterization of and discrimination between these
geological processes. Earlier studies, based on radar and optical determination
of Mars surface properties, have provided first measurements of surface texEmail address: [email protected] (Aurélien Cord).
2
ture on scales ranging from centimeters to kilometers and have demonstrated
that the physical properties of the Martian surface layer can vary significantly
and be used for constraining surface processes (Simpson et al., 1992; Christensen and Moore, 1992). More recent works (Kreslavsky and Head, 1999;
Garneau and Plaut, 2000; Garvin and Frawley, 2000; Sakimoto et al., 1999;
Kreslavsky and Head, 2000) have produced and analyzed global maps of surface roughness at the kilometer scale or at longer wavelengths. They link the
scale dependence of roughness (from 0.6 to 20 km) with potential volcanic
origin, eruption styles or modification of the surface with repetitive deposition and sublimation of seasonal frost. Second, at a very different scale, from
sub-millimeter to centimeter, photometric studies of the surface describe the
surface boundary state inside pixels (Cord et al., 2003; Pinet et al., 2004,
2005a,b,c; Seelos et al., 2005; Shkuratov et al., 2005; Kreslavsky et al., 2006;
Jehl et al., 2006; Pinet et al., 2006; Johnson et al., 2006). In a study of the
Gusev crater roughness properties, it has been shown that the photometric
measurements are very sensitive to the distribution of particles size (ranging
from a few microns to few centimeters) and their organization as a surface in
the very upper planetary layer. For the Gusev crater floor, the photometric
products reveal significant photometric changes between the different constituting units present in the crater. Together with laboratory measurements,
earlier Viking Lander observations and in situ Spirit MER observations, the
interpretation of the optical properties of the soil at Gusev are consistent with
the occurrence of basaltic rock surfaces or packed sands, smoothed by exposure
to wind abrasion and possibly coated with dust, alternately with surrounding
rougher soil surfaces embedded in an aeolian mantling, with features such as
ripples, dunes and soil patches (Pinet et al., 2005a).
3
So far, a quantification of the roughness properties at intermediate scale (i.e.,
tens of meters) is not available for the Martian surface. It appears however now
feasible combining the technique described in the following and the increase
in spatial resolution obtained by imaging devices onboard current planetary
missions (Mars Orbiter Camera / Mars Global Surveyor and HRSC / Mars
Express).
Since the main goal of the study is to derive roughness from texture, it is
crucial to make a clear distinction between the terms texture and roughness.
The roughness addresses the characterization of a surface geometrical property
through a quantitative parameter describing the intuitive notions of rough or
smooth aspect of the topography. Various definitions of this parameter are
possible. The texture quantifies the homogeneous or heterogeneous aspect of
an object within an image, in digital image analysis context. The texture is
not a surface property but an image property and it relies on the analysis
of the gray-level of an image (in different channels if multi-spectral data are
used).
Different sources contribute to this signal in high-resolution planetary images:
the albedo variation of the surface materials, the photometrical properties
linked with angular conditions of illumination and observation and the intrinsic roughness of the surface at a scale of several pixels. The main point of the
approach detailed in the following is both to enhance the last contribution and
eliminate or reduce the others. As a result, the roughness of geological units
can be inferred at a scale of a few tens of meters.
Both the methodology and the results are illustrated on a set of Martian areas
selected for the occurrence of different geological units. Those regions present
4
impact craters, lava flows of various ages and more or less developed erosion
features. Characteristic roughness variations are expected to be associated
with these different units.
2
Method
In the context of image classification and segmentation, texture content analysis has received much attention during the past decades. Relying on the
comparative study proposed by Randen and Husoy (1999), different filtering
methods have been tested for the texture characterization of the Martian surface, based on high-resolution orbital images. In the present study, the Gabor
filtering approach is applied, as it is both very efficient in terms of discrimination of texture and easy to implement.
Preprocessing
Remove long wavelength variations of albedo
Division by a mean filter 50*50 pixels
Filtering
Gabor filters 29*29 pixels
4 orientations (0˚, 45˚, 90˚, 135˚)
3 frequencies (1.43, 2.00, 3.33) pixel-1
Simulated topographic surfaces
Self-affine surfaces with different
exponent values
Local energy estimation
Magnitude estimation at all frequencies
Low-pass Gaussian filtering 29*29 pixels
Simulated texture
Shading with the same conditions
of illuminations / observations
Final product : RMS image
Comparison with the simulated texture images
Fig. 1. Flow Charts of the texture analysis method developed for roughness quantification of planetary surfaces. Each step is described in the text.
5
All the filtering techniques have a common denominator: the input image is
subject to a linear transform (filtering step), followed by an estimation of the
local energy of the filtered signal. The steps of the process (cf. Fig. 1) are
described in detail in the following subsections. They are illustrated using the
same scene extracted from the HRSC database (a crater centered at 16.3o N,
280.8o E and its surroundings). A geological study of this area is proposed in
section 3.3. Its image before any texture processing is presented in Figure 2.
It is geometrically corrected and projected onto the Digital Elevation Model
(DEM) produced using HRSC data (so called level 4 data).
Fig. 2. Original image from HRSC/Mars Express, orbit number 0071, nadir filter,
with a spatial resolution of 13 m per pixel. Crater center at 16.3o N, 280.8o E. The
horizontal black straight line corresponds to the profile presented in Figure 5. The
vertical lines correspond to the position of pixels 600, 1000 and 1300 linked with
this Figure
Note that all numerical values used in every steps of the process described
in the following (e.g., filter sizes and periods) were experimentally optimized
for the processing of radiance images with a spatial resolution between 10
6
and 25 meters per pixel: 40 small images exhibiting a uniform texture were
extracted from the HRSC database. This preliminary work described in Cord
et al. (2005) intends to determine parameter values that allow a better discrimination between the roughness properties of those images.
2.1 Preprocessing
Using the radiometric calibration, the data are converted in radiance units.
It is then necessary to decorrelate the texture effect from the surface albedo.
For this purpose, we consider the large surfaces with homogeneous albedo and
make some assumptions: (1) In a high resolution planetary image, the albedo
variations corresponding to the geological spatial scale (bright versus dark terrain) have a low spatial frequency signal. (2) The roughness variations induce
some high spatial frequency signal (texture) inside a geological unit and the
texture is characterized by a degree of variation in the radiance values between
neighboring pixels. (3) Images of two surfaces having the same roughness but
different albedos have relative radiance variations that are proportional to the
mean surface albedo. Notice that the contacts between such units can be sharp
and represent a high frequency component that has to be ignored.
In order to eliminate the low spatial frequency signal coming from albedo variation and thus to enhance the high frequency signal coming from roughness,
each pixel of the image is divided by a mean filter of which the 50x50 pixels
size has been determined so that it well handles the mean field information.
A comparison between Figures 2 and 3 shows that the preprocessing step is
similar to a high-pass-filtering. The variation of albedo between the different
7
Fig. 3. Image obtained after preprocessing of the original image from Figure 2.
geological units is erased as expected. Another illustration of this is shown on
the top and the middle curves of Figure 5.
From the potential contributions mentioned above to the spatial signal in highresolution planetary images, only the photometric effects linked to angular
conditions of illumination and observation are not taken into account yet.
The last step of the algorithm described in section 2.4 aims to reduce it.
2.2 Convolution
Gabor filters were first suggested for texture description by Jain and Farrokhnia (1991). They are defined by complex harmonic functions modulated
by a Gaussian distribution with multiple orientations. The spatial impulse
response h(x, y) of our filters can be written
2
2
sin(α))
1 − x 2σ+yg2 −2πj (x cos(α)+y
p0
h(x, y) =
e
e
.
2πσg2
8
(1)
It is a complex exponential corresponding to a sinusoid with a period p0 and
an orientation controlled by α that is modulated by a Gaussian envelope with
a scale monitored by the standard deviation σg . The preprocessed image is
convolved with both the real and imaginary parts of the filter.
As stated before, the parameter values were experimentally optimized for the
discrimination between roughness properties of a set of small images exhibiting
a uniform texture extracted from the HRSC database (Cord et al., 2005). The
Gaussian envelope is the same for all filters: the size of the filters is 29x29
pixels, σg is 0.8. Four orientations (α ∈ [0o , 45o , 90o , 135o ] with respect to the
abscissa axis taken as a reference) and three periods characterizing the spatial
scales related to 9,7 and 4 pixels (p0 ∈ [9, 7, 4] pixels) are chosen.
2.3 Local energy estimation
An energy estimate quantifies the high frequency variations of a signal that
corresponds to the energy for an output filtered signal. It is typically performed
in two steps: a non linearity and a smoothing (Weszka et al., 1976).
As a first step, we calculate the magnitude of the outputs from the convolution
at all periods ([9, 7, 4] pixels) and orientations ([0o , 45o , 90o , 135o ]). The results
obtained with the 9 pixels scale for the four directions are presented in Figure
4. Large variations between orientations appear mainly on the edges of the
crater and within the ejecta blanket, showing the ability of the Gabor filter for
detecting geological units boundaries. Then, in order to obtain a texture value
whatever the directionality, the average magnitude based on the orientations
is inferred for each period value. The second step consists in the application of
9
Fig. 4. Images obtained after filtering and magnitude computation. It shows the
contribution of each orientation to the texture value. The orientations from the
horizontal are: (a) 0o , (b) 45o , (c) 90o and (d) 135o .
a low-pass Gaussian filter. We use a 29x29 pixels filter with a scale parameter
(σg ) of 0.8, as for the Gaussian part of the Gabor filter, based on experimental
optimization.
Figure 5 illustrates the first steps of the Gabor filtering process. The highest
spatial frequency values (See for example the top curve value around pixel
number 500 in Figure 5) corresponds to the highest values of the local energy
(bottom curve). To evaluate the consequences of the radiance variations induced by the topography along the profile, it is interesting to focus on the
center of the impact crater (pixels number from 600 to 1300 in Figure 5). The
radiance values (top curve) have important low-spatial-frequency variations
10
Fig. 5. Illustration of the preprocessing, filtering and local energy estimation steps
of the process. Top: Reflectance profile of the original image according to the
cross-section defined in Figure 2. Middle: same profile after the preprocessing step.
Bottom: same profile after the energy estimation. The pixels 600, 1000 and 1300
correspond to geologic features (crater rim, central peak and the other crater rim,
respectively).
that are corrected by the preprocessing step (middle curve) and then do not
affect texture values (bottom curve) that are quite stable in this part of the
profile.
The results obtained so far and named hereafter as textural image are qualitatively consistent with the apparent levels of texture for different units within
the image and reveal the boundaries between them.
11
2.4 From texture to roughness
The objective of this section is to interpret textural images in terms of roughness. Our aim is to quantitatively compare roughness values of different areas
of the Martian surface. It requires the derivation of a value which has to be
independent of the conditions of illumination and observation. Using the process described above, the idea is to estimate the texture of simulated images
for which the roughness is known. The simulated images are shaded surface
images from randomly generated topographies. They are produced under chosen observation and illumination angles identical to those of the studied scene
(HRSC). Each topography is characterized both by its RMS value and its textural properties. Then, each pixel of the textural image is converted into the
RMS value of the synthetic topographic surface which has the same textural
property. The result, named RMS image is independent of the sensor characteristics (as long as the calibration is valid), of the local albedo and of the
angular conditions of illumination. It is possible to compare and/or mosaic
any RMS image obtained at any location of the Martian surface.
2.4.1 Synthetic random texture
Shaded surface images are produced from randomly-generated topography
simulating the Martian surface and illuminated under the same angular conditions as for the input image. The topography of planetary surfaces has been
demonstrated to be self-affine over a range of topographic scales (Mandelbrot,
1983; Turcotte, 1987; Balmino, 1993; Smith et al., 2001; Dodds and Rothman,
2000). The power spectrum of the topography, defined as the square of the
coefficients in a Fourier series, has a power-law dependency:
12
(a)
(b)
(c)
Fig. 6. Example of simulated topographic surfaces with β values of 3 (a), 5 (b),
and 9 (c) with the corresponding texture image. The incidence angle is 45o in this
example.
|F (l)|2 ∝ |l|β
(2)
where F is the Fourier transform of a function representing the elevations, l
the wavenumber, and β the exponent of the power law. The topographic surfaces of Venus, Mars, Earth and the Moon all display an exponent value close
to 2 at wavelengths greater than a few kilometers (Balmino, 1993; Turcotte,
1987). This exponent value corresponds to a Brown noise which is explained in
the case of diffusion processes. Topographic surfaces generated from a power
spectrum with such exponent and a random phase in the Fourier space resembles planetary surface topography. However, at shorter wavelengths, there is
a tendency toward relatively steeper slopes or higher values of β (Dodds and
Rothman, 2000). Different values of this exponent, likely corresponding to different geological processes, will be associated with different texture properties
when the topography is illuminated.
In this study, the observation angle is systematically neglected because the
highest resolution images are measured under nadir condition (emergence very
close to 0o ). In order to produce a normogram describing the link between
13
synthetic images (characterized by the exponent of the power law, β in eq.
2) and their associated textures, the following approach is repeated ten times
and averaged for each considered incidence angle (between 15o and 85o ):
(1) Digital Elevation Models (DEMs) (1000 by 1000 pixels) are generated in
the Fourier space using exponent values ranging from 2 to 9. First, the
power spectrum is computed from an arbitrary value according to the
equation 2. The phase corresponding to each wave number is generated
randomly. The surface topography is then obtained by inverse Fourier
transform. Three examples of the surfaces generated by this method are
given for the β exponent values taken equal to 3, 5, 9 with the corresponding hill-shaded image in Figure 6.
(2) Shaded-relief images are computed from each DEM and using the considered incidence angle, with the assumption that the maximum slopes
never exceed 30o , which is the angle of repose of granular material. The
shadows are not computed.
(3) The filtering process is applied on the shaded-relief images exactly in the
same way as described previously to produce synthetic textural images.
(4) The mean value of the synthetic textural images is computed and associated with the corresponding exponent values.
Note that if the incidence angle is very low (less than 15o ) the roughness
generates low values of texture and this signal can be missed. The method
shall therefore not be used for such low incidence angles.
14
2.4.2 RMS images
From this normogram, any textural image value can be associated to an exponent of a self-affine topography. However, we do not state that the topography
is self-affine with the same exponent down to the scale of the considered HRSC
image as we are not able to infirm or confirm this from the present texture
measurements.
We finally present the result using an equivalent surface RMS value, which
is more commonly used in planetary geology studies than the value of the
self-affine exponent (β) for the comparison between roughness properties of
planetary surfaces. The relation between RMS value computed at a given scale
and β is bijective. The RMS value is calculated by filtering the surface with
a high-pass filter (here, a substraction by a smooth filter with a size of 10
pixels) :
RM S = C ∗
s
1 X 2
X
N
(3)
with N the number of pixels and X corresponding to the difference between
the DEM and the low-pass filtered DEM. C is a constant for the normalization
of the RMS. We choose C equal to 103 corresponding to a RMS value close
to 1 in the ejecta of the impact crater in our example for the spatial period
associated with the 4 pixels scale (cf. Fig. 7). We then obtain as a final result
the RMS images or roughness map.
The RMS images relevant to our example (Fig. 2) are plotted in Figure 7.
They are analyzed in detail in section 3.3.
15
Fig. 7. Final outputs of the Gabor filtering process. From top to bottom, RMS
values for the periods corresponding to 9, 7 and 4 pixels respectively.
2.4.3 Validation of the method
This approach relies on some assumptions whose effects on the final product
can not be directly estimated (e.g., the maximum slope angle supposed to be
16
constant on all images, and roughly equal to 30o , the generation of the random
topography supposed to be similar to planetary surfaces). The only way to
provide with a validation of the method is to carry out the comparison between
textural values from images of the same area under different conditions of
illumination and observation.
Two parts of the considered HRSC image scene of the same area of Mars but
acquired under different illumination conditions have been used to check the
above approach. The two images were acquired during Mars Express orbits
1210 and 1221. The angular conditions of illumination are 29o and 20o and of
emission are 12o and 10o , respectively, and the spatial resolution is 13m/pixel
in both cases.
In Figure 8 are displayed the differences between the two overlapping textural
images and the two overlapping RMS images. It is expressed in percentage of
difference (100.(V 1 − V 2)/V 1). The mean values for the whole area and for
all spatial periods are in table 1.
Period
1
2
3
Texture
29 (19)
29 (18)
28 (17)
RMS
12 (9)
11 (7)
12 (8)
Table 1
Mean value of the difference in percentage between the two overlapping textural
images and the two overlapping RMS images. Numbers in brackets correspond two
standard deviations.
From those results, it appears that the texture values are highly influenced by
the illumination conditions and that this effect is significantly reduced after
filtering. Indeed, the RMS values appear much less dependent of the incidence
17
Fig. 8. From left to right: Image of the overlapping area, difference in percentage
between the 2 textural images for the 3rd period and difference between the 2 RMS
images. The image size is 650 x 3550 pixels, and the spatial resolution 13m/pixel.
The difference images are smoothed by a factor of 14 to minimize any local misregisration residual effect. Grey tone scale describes the image difference expressed in
% for b and c.
18
angle.
The illumination angles are quite close, because among the few HRSC images
overlapping the illumination conditions are very close. However, this example
demonstrates that even with a small angular difference, the texture values
are significantly different while the RMS values are very similar all along the
scene.
2.5 Synthesis
In summary, the methodology presented here gives access to a quantified estimate of the intrinsic local roughness of the surface within a high resolution
image, once the image information is corrected from the instrumental contribution, the surface albedo variation , and the angular conditions of illumination
and observation. However, for its proper implementation, this methodology
requires the image spatial resolution to range from 10 to 25 m, and the incidence angles to be larger than 15o to make sure that the texture is apparent in
the image. Also, one must bear in mind that the high RMS values associated
with image edges may result from an edge effect caused by the Gabor filtering
and thus have no physical meaning.
3
Application to geological investigations
This section presents different examples for which the roughness characterization provides insight for the Martian surface geological investigation. The
roughness maps are compiled into RGB composites using the three roughness
images of different periods (9,7 and 4 pixels). The roughness increase from
19
light to dark : the lighter the image, the smoother the surface.
3.1 Lobate ejecta craters
Martian craters are often surrounded by a continuous lobate ejecta blanket
which origin is still debated (Baratoux et al., 2005). Two main processes have
been invoked: the morphologies of ejecta deposits result from the interaction
with the atmosphere and winds generated during the impact event (Schultz
and Gault, 1979; Schultz, 1992), or they result from surface flow of ejecta material which have been fluidized by melting of the sub-surface ice (Carr et al.,
1977; Costard, 1989). Theoretically, the roughness of the ejecta blanket resulting from surface flow with possible sorting of granular material will be different
from the roughness resulting from scouring, transport and deposition of the
fine fraction with coarser fraction left behind when atmospheric processes are
dominant (Barnouin-Jha and Schultz (1996), see Baratoux et al. (2005) for
more detailed discussion). Nevertheless, many degradation processes exist on
Mars (wind erosion, dust mantling, ice sublimation, etc.) which can modify
the texture of ejecta through time and need to be taken in account in this
analysis.
Figure 9 shows an HRSC image at a regional scale in Chryse Planitia covered
by 6 impact craters of same order of size, of 7 to 13 km. Ejecta blankets of these
craters have very different textures. There is no correlation between the craters
diameter and the texture, meaning no increase in roughness with the size of
crater. Thus nothing indicates that the variations in roughness are due to the
impact process itself. On the other hand, we can plot roughness estimates
associated with different spatial periods for all craters and the background,
20
Fig. 9. On top, image extracted from HRSC database (orbit 1436 36o N , 324o E)and
associated roughness map . On bottom,roughness values for craters ejecta. Period 0
on X-axis and Period 2 on Y-axis. The arrow goes from the youngest to the oldest
craters.
i.e. the smooth plains surrounding craters. The right top corner corresponds
to the roughest terrains whereas close to the origin it reveals the smoothest
terrains. The roughness of ejecta decrease from crater 1 to crater 6., the latter
being close to the mean value of the background. Thus, we interpret this
variation in roughness as being the result of the progressive degradation of
the ejecta by dust mantling and/or wind erosion. Assuming these processes
21
Fig. 10. Images extracted from HRSC database and associated RMS images. From
top to bottom, orbits and center coordinates are: orbit 266 (−44.8o N , 265o E), orbit
1354 (39.2o N , 105.4o E) and orbit 279 (−45.2o N , 264o E). The color RMS images
are plotted using the same threshold as in Figure 9 and therefore are comparable.
being homogeneous at the scale of the image, it is thus likely that the decrease
in roughness corresponds to an increase of the age of the crater. The older the
crater is, the more degraded it becomes. Thus, this example shows that the
variations in roughness might be used to assess the relative age of craters, a
piece of information difficult to access from other methods.
22
Other HRSC images are used to observe 3 craters ejecta more in details (Fig.
10). The first one has a high roughness especially at small scale. It is possible
to distinguish two rings that are not visible on the image alone. The second
example has a blue signature corresponding to a high roughness at small scale
but also a brown color at the northern edge similar to the roughest ejecta of
figure 9. In the third example, different units can be distinguished based on the
roughness map. Notice that the center of the crater has the same roughness
property than the ejecta. A common characteristic of these craters ejecta is
the similarity of the roughness but also their location, 45 mid-latitude region.
These regions are affected by specific degradation processes due to dust/ice
deposition and subsequent sublimation (Mustard and Cooper, 2001). Pitted
terrains are especially visible on the HRSC image of the third example. Thus,
here the texture corresponds to this specific degradation process explaining
that the roughness found inside the Crater is similar to the one on the ejecta.
The examples of ejecta blankets textures described above thus lead to the
following conclusions: (i) The texture of the ejecta corresponds more often to
a degradation stage of the ejecta than to a state of roughness inherited by the
impact process, (ii) only young and fresh craters may have texture directly
relying to the impact process (iii) a regional differential roughness of the ejecta
can be used to determine the relative age of the different craters (iv) in some
cases, the values of roughness can permit to recognize specific degradation
processes such as the pitted terrains of the mid-latitude regions.
23
3.2 Wind streaks
Wind streaks are various bright or dark streaks observed immediately behind
crater rims or other topographic obstacles. They are linked both with zones of
erosion and deposition induced by wind flows around these obstacles (Sagan
et al., 1973; Greeley and Ivsersen, 1985; Tanaka et al., 1992). Bright streaks
behind craters are especially formed by differential deposition of dust in a
”shadow zone” characterized by lower wind speeds. They are thus composed
mainly of small size grains, which could create a very thin layer. It is confirmed
by images of the same areas taken over different Martian years show variations
in the size and shape of some streaks. In that case, the mantling will not affect
the texture of the surface. This is what we observe in Figure 9, an image
previously used to study lobate ejecta blankets. Indeed, the HRSC image of
this figure displays many wind streaks which do not appear on the roughness
map, implying that the wind streaks are here thin enough to have no effect
on the roughness at the scale of the measurement (HRSC image resolution of
few tens of meters).
Figure 11 shows different examples of wind streaks visible on the roughness
map. First, a 15 km diameter crater exhibits a large wind streak. Dune fields
cover large part of the image and explain the highest texture value in the
image. Notice that because the high frequency albedo changes induced by
dark dunes and bright floor does not respect the hypothesis of low albedo
variations inside a geological area, the RMS values does not corresponds to a
”true” roughness on the surface. However, the smoothest areas, brightest on
the roughness map, has ”true” roughness values. It is located on the central
part of the large wind streak observed on the visible image. Thus, only part
24
Fig. 11. Images extracted from HRSC database and associated RMS images. From
top to bottom, orbits and center coordinates are: orbit 1425 (66.3o N , 323.3o E),
orbit 228 (14o N , 158o E) and orbit 1152 (−13.5o N , 161o E). The color RMS images
are plotted using the same threshold and therefore are comparable.
25
of the wind streak displays a specific texture different than the background.
A similar observation can be made more generally in the two other regions
of figure 11. Wind streaks stretch often over kilometers long behind craters.
Most streaks are detected on the roughness map but with a shorter length and
width, the smoother texture being detected immediately behind the crater.
Different remarks can be made at the following of these observations. First,
one can say that sometimes the hypothesis of constant albedo of the materials
in the studied area is not respected. Then the texture variations are due to
local albedo variations and not to the real roughness, as it is clear for the dune
field in the first image. Second, texture and albedo are not directly correlated:
the whole bright albedo of the streak does not correspond to the whole surface
of smooth texture. Part of the wind streaks shows the same roughness than
the plain all around corresponding then to a very thin layer of dust, changing
albedo but not roughness, and smaller roughness values are really an effect of
smoothing induced by the eolian patterns. Third, the fact that the roughness
is identified only at the proximity of the topography shows the existence of a
gradient of dust thickness from the crater rim to the more distal part far away
from the crater where the roughness of the plain is not modified.
We may expect qualitatively that a roughness at the 40 meters scale would
require a thickness of material of a few meters to smooth the surface enough
to be detected. A more precise estimation would require a complete modeling
such as done by Forsberg-Taylor et al. (2004) for progressive dust deposition
but this is not the aim of the study. Nevertheless, this result shows that the
wind streaks are composed by thicker dust deposits than previously supposed,
leading to the conclusion that these streaks formed under geologic long periods
without change in the wind direction.
26
The observation of the roughness of wind streaks thus lead to interesting
conclusions about the formation of these features: (i) Some wind streaks are
not visible on the roughness map involving a very thin accumulation whereas
other ones are detected involving meters thick accumulation of dust (ii) the
whole streaks is not visible on the roughness map implying a gradient in
the accumulation of dust from the crater rim to more distal terrains (iii)
the thickness inferred to smoothen the terrains suggests that wind streaks are
features existing with the same pattern over geological times under same wind
direction.
3.3 Lava flows and geological mapping
A region has been chosen from the coexistence of different geological units and
landforms that may have different physical properties such as fresh lava flows
and crater ejecta. The geological map (Scott and Tanaka, 1986) shows that
the studied area is located at the junction between the Late Hesperian outflow
channel of Kasei Valles at the extreme right of the image and Amazonian
overlapping lava flows coming from the Tharsis plateau. The selected HRSC
image shows the different overlapping lava flows with lobate front indicating
a southeast slopes. This is confirmed by the MOLA topography which shows
a gradual slope to the southeast at the west of the impact crater. The MOLA
map also shows a topographic plateau east of the impact crater with a surface
dipping 1.2o to the west. The fact that the crater is located on this slope
explain that the lava flows buried only the western part of the ejecta blanket
of this crater (Fig. 12).
For clarity, using the spatial resolution (13 m/pixel), the pixel size periods (9,
27
-1200 m
(a)
- 100 m
(b)
(c)
(d)
Fig. 12. (a) High-resolution (13m/pixel) image of the studied area, from HRSC
image h0071 0000. (b) Topography from MOLA data. (c) Simplified geological
cross-section of the studied crater. The vertical exaggeration is 14. (d) RBG composite of the RMS roughness values produced for the three periods. Red, green, blue
respectively correspond to 9, 7 and 4 pixels
28 periods. The roughness increases from
light to dark: the lighter the image, the smoother the surface.
7 and 4 pixels) are converted into meters (120, 90 and 50 meters, respectively).
In roughness map, most geologic units visible on the image can be defined very
easily using the roughness map (Fig. 12.d) . They have been divided in different
regions of interest (ROI) that we can compare to a reference area, sampled in
the plain located south of the crater and displayed with the yellow polygon. At
the extreme east, the very rough unit compared to the reference corresponds to
striated units of the Kasei valley floor. The craters ejecta (blue ROI) appears
very similar to the reference at 50 and 90 meters whereas it becomes rougher
at period of 120 meters. This likely indicates that the ejecta are degraded,
with only the largest heterogeneities being preserved from smoothing by dust
mantling. Lava flows display a very homogeneous texture compared to the
other units. A typical lava area, in green ROI, is similar to the reference at
120 meters, but becomes rougher with the decrease of the period at 50 meters.
Additionally, the roughness is also variable inside some of these units suggesting local variations of the surface properties. For example, a particular area in
the lava flows displays a very smooth texture (red ROI). It is even smoother
than the reference and will be referred as SL (smooth lavas). Looking carefully
at the HRSC image, by stretching the histograms as much as possible, does
not permit to see the same pattern on the image. It thus corresponds to a
roughness variation in the same geologic unit not visible on the image without
this processing. Two possibilities can be proposed for the origin of the SL subunit. First, it may correspond to a roughness directly inherited from the lava
flow, for example because the center of the lava flow was at higher temperature
or higher velocities and created smoother lava flows just like pahoehoe lava
flows form close to rougher aa flows. Alternately, the dust mantling affecting
the ejecta blanket is posterior to the lava flows and has smoothed the lava
29
flows too, with a stronger smoothing in the SL region. Our method allows the
detection of the feature, but it is not possible to discriminate between this two
hypothesis.
A final remark about this region is the comparison between lava flows and
craters ejecta. The roughness of lava flows is inherited from the physical properties of the flow and modified later by wind erosion or dust deposition, beginning by the smallest period. As most lava flows (except the SL area) are
rougher than the reference with significant texture at the 50 m period, the
amount of dust present is not able to hide completely the topography. This
may come from the younger age of the lava flows relative to the reference. Because, the roughness is more important at 50 meters than at 120 meters, we
interpret that the lava flows are not composed of large blocks of rock (several
tens of meters large) but has a pattern at a few meters scale corresponding
to the cooling of typical fluid lavas. On the contrary, the ejecta of the impact
crater are rough at periods of 120 meters, and this is also true for most ejecta
blankets of figure Figure 9. Thus, it appears that ejecta are systematically
rougher than lava flows, because they display roughness at large spatial scales
periods despite being covered by dust at shorter scales. The rough ejecta surface, inherited from the fragmentation and emplacement mechanism seems not
to be completely affected by degradation at the larger scales. Moreover the
degradation process efficiency could depend of the initial lithology. For ejecta
blanket, the low frequency information of texture could be used to characterize
the roughness created at the time of ejecta emplacement.
As explained in the introduction, the roughness was previously described at
different scales by Kreslavsky and Head (2000). The values they calculate in
the studied area are presented in Table 2. It is clear that at all the scales
30
COLOR
BASELINE (km)
Lava Flow
Ejecta
R
9.6
123
167
G
2.4
96
153
B
0.6
86
138
Table 2
Value of the kilometer scale roughness from Kreslavsky and Head (2000). The values
are in DN, averaged in the few pixels available around the crater. It is possible to
convert DN into a physical unit corresponding to profile curvature, but it is less
convenient for a relative comparison.
they worked (0.6, 2.4 and 9.6 km), really larger than the ones used here,
the roughness of the ejecta is systematically higher than the one of the lava
flow. Combining the two approach, it appears that above a scale of about
50 m, the ejecta are systematically rougher than the lava flow. It probably
comes from the blocky aspect of the ejecta that are partially, but not totally
covered/smoothered by dust.
The example of this geologically interesting region leads to some main conclusions: (i) the roughness map can be used as a powerful tool to help in the
mapping of geological units as well as in the mapping of subunits not identified on the original image (ii) the physical properties of each units can be used
to describe and interpret more in detail each units (iii) the ejecta of Martian
craters are rougher than the lava flow at the site of investigation implying that
it is possible to distinguish roughness signatures which are not all related to
degradation processes.
31
4
Discussion and Conclusion
The approach described in this study provides a method for the description of the surface roughness, which is linked to surface blocky aspect and
rock size distribution and organization. The quantities derived can be related
both to the state of degradation of the surface material (e.g., amount of dust
mantling) and/or to its geological and geomorphological properties (e.g., lava
flow type, ejecta properties). Its combination with available data (e.g., topography, high resolution images, thermal emission) and different analysis
methods (e.g., thermal inertia, macroscopic roughness, crater count) could be
fruitful. In particular, the Thermal inertia calculated from the day / night
temperature (THEMIS) is only influenced by the few first millimeters to few
tens of centimeters of the surface (in the case of bed rocks) and allows the distinction between rocky and dusty surfaces. The approach developed here may
detect and quantify the indurated dust that does not have a typical thermal
signature for fine particles. Such a combination will be useful for improving
the description of the surface state and its physical modeling.
Moreover, a wide range of applications can be considered, that may lead to a
systematic analysis and classification of the Martian surface roughness.
Regarding ejecta blankets textures of impact craters, the texture corresponds
more often to a degradation stage of the ejecta than to a state of roughness
inherited by the impact process. In some case, the roughness estimates can be
used for recognizing specific degradation processes such as the pitted terrains
of the mid latitude regions. However, roughness variations along the ejecta are
linked to both the impact process and the subsurface materials properties, in
32
particular for some double-lobbed ejecta present on the Martian surface.
Regarding lava flows, a diversity of roughness would be available which could
be related either to differing states of weathering (evolution from fresh lava
flows to sandy areas) or to the type of lava itself implying that it is possible
to distinguish roughness signatures which are not all related to degradation
processes.
Regarding features detection, the roughness map can be used for the mapping
of geological units as well as subunits not identified on the original image.
Moreover, wrinkle ridges or fractures are highlighted by this algorithm and
could be used for a detailed mapping of such features, given the coverage of
HRSC data.
Regarding age evaluation, the edge enhancement produced by a filtering approach may be useful for crater detection and counting. Additionally, a regional differential roughness of the ejecta can be used to determine the relative
age of the different craters. Crater ejecta with identical roughness may be in
the same state of degradation and then formed at the same moment. This can
be useful for the detection of secondary craters.
Regarding aeolian processes, the smoothing of a surface by dust deposition
may be characterized by its roughness properties. Some wind streaks are not
visible on the roughness map involving a very thin accumulation whereas other
ones are detected involving meters thick accumulation of dust. Such a thickness
suggests that wind streaks are features existing with the same pattern over
geological times under same wind direction.
33
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