re
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Wash
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Article history:
Received 28 January 2013
Revised 16 June 2013
Accepted 3 July 2013
Available online 13 July 2013
Keywords:
Mars
Mars, Polar geology
a b s t r a c t
tion (Hays et al., 1969; Shackleton and Opdyke, 1973) and analysis
for the quanti?cation of geological data. New paleoclimate proxies
had to be discovered (Emiliani, 1955), and accepted methods and
interpretations had to be reevaluated and altered (Shackleton,
1967) or even abandoned entirely (Kukla, 1977). The hypothesis
was ultimately con?rmed by synthesizing multiple records, includ-
ing sedimentary, geochemical and paleomagnetic, that when inte-
grated provided a comprehensive history of Earth?s climate cycles
(Imbrie, 1982).
(Cutts et al., 1976) and excited the prospect of a robust martian cli-
iscovering such a
eposits (PL
ustained e
fully characterize layering (Fishbaugh et al., 2010a). As a
determining the optical (Blasius et al., 1982; Fishbaugh and
berg, 2006), spectral (Milkovich and Head, 2005; Perron an
bers, 2009), and radar (Picardi et al., 2005; Phillips et al., 2008)
characteristics of the PLD remains an active area of research (Fishb-
augh et al., 2008).
Two leading perspectives of PLD stratigraphy have emerged
from the resultant studies. High resolution images from Mars
Reconnaissance Orbiter?s (MRO) High Resolution Imaging Science
Experiment (HiRISE) (McEwen et al., 2007) and Context Camera
(CTX) (Malin et al., 2007) have prompted spatially-isolated,
? Corresponding author.
Icarus 226 (2013) 1241?1251
Contents lists availab
ru
.e lE-mail address: schristian@utexas.edu (S. Christian).(Hays et al., 1976; Imbrie and Imbrie, 1980) of periodic signals in
Earth?s geologic record. Testing the hypothesis of orbital climate
forcing required an enormous effort in pioneering new techniques
mate record (Cutts, 1973). The expectation of d
record in the stratigraphy of the polar layered d
persisted (Fishbaugh et al., 2008), leading to a s0019-1035/$ - see front matter  2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.icarus.2013.07.003D) has
ffort to
result,
Hvid-
d Huy-1. Introduction
Investigation of the astronomical theory of climate change
prompted a revolution in the detection (Emiliani, 1955), correla-
Concurrent with rapid advances occurring in terrestrial climate
science, the discovery of layering in the polar deposits of Mars
(Murray et al., 1972; Figs. 1b and 2) provided the only empirical
evidence for periodic climate change on a planet other than EarthMars, Polar caps
Radar observationsShallow Radar (SHARAD) on board NASA?s Mars Reconnaissance Orbiter has successfully detected tens of
re?ectors in the subsurface of the north polar layered deposits (NPLD) of Mars. Radar re?ections are
hypothesized to originate from the same material interfaces that result in visible layering. As a ?rst step
towards verifying this assumption, this study uses signal analyses and geometric comparisons to quan-
titatively examine the relationship between re?ectors and visible layers exposed in an NPLD outcrop. To
understand subsurface structures and re?ector geometry, re?ector surfaces have been gridded in three
dimensions, taking into account the in?uence of surface slopes to obtain accurate subsurface geometries.
These geometries reveal re?ector dips that are consistent with optical layer slopes. Distance?elevation
pro?ling of subsurface re?ectors and visible layer boundaries reveals that re?ectors and layers demon-
strate similar topography, verifying that re?ectors represent paleosurfaces of the deposit. Statistical
and frequency-domain analyses of the separation distances between successive layers and successive
re?ectors con?rms the agreement of radar re?ector spacing with characteristic spacing of certain visible
layers. Direct elevation comparisons between individual re?ectors and discrete optical layers, while nec-
essary for a one-to-one correlation, are complicated by variations in subsurface structure that exist
between the outcrop and the SHARAD observations, as inferred from subsurface mapping. Although these
complications have prevented a unique correlation, a genetic link between radar re?ectors and visible
layers has been con?rmed, validating the assumption that radar re?ectors can be used as geometric prox-
ies for visible stratigraphy. Furthermore, the techniques for conducting a stratigraphic integration have
been generalized and improved so that the integration can be undertaken at additional locations.
 2013 Elsevier Inc. All rights reserved.Integrating radar stratigraphy with high
of the north polar layered deposits, Mars
S. Christian a,?, J.W. Holt a, S. Byrne b, K.E. Fishbaugh
a The Jackson School of Geosciences, University of Texas, Austin, TX 78712, USA
b Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85745, USA
cCenter for Earth and Planetary Studies, Smithsonian National Air and Space Museum,
Ica
journal homepage: wwwsolution visible stratigraphy
ington, DC 20013, USA
le at ScienceDirect
s
sevier .com/locate / icarus
us 21242 S. Christian et al. / Icarmorphologically- and topographically-detailed descriptions of the
north PLD (NPLD) surface (Fishbaugh et al., 2010a, 2010b). In con-
trast to the meter-scale description and delineation of sur?cial
expressions of layering, MRO?s Shallow Radar (SHARAD) (Seu
et al., 2007) has resolved material changes in the NPLD subsurface
(Phillips et al., 2008; Fig. 3). As a result, the de?nition of an internal
Fig. 1. (a) Mars Orbiter Laser Altimeter (MOLA) topography of Planum Boreum overlain
shown in Fig. 3. Circle denotes area containing line intersections used in the crossover an
used to construct subsurface interfaces. Observation 51920 is shown in red, and transect
is denoted by a red circle. The DEM footprint is shown in gray, outlined in purple.
Fig. 2. (a) CTX image P02_001738_2671 shows layering at the study site at a resolution
layers in high resolution (25 cm/pixel). An angular truncation surfaces, denoted by arro
Fig. 3. SHARAD observation 519201. The location of the subsurface study s26 (2013) 1241?1251radar stratigraphy over 100s of kilometers is possible (Putzig et al.,
2009; Holt et al., 2010), albeit at an order of magnitude lower res-
olution than is common in surface studies (McEwen et al., 2007;
Seu et al., 2007).
Apparent repetitions in both visible (Laskar et al., 2002;
Milkovich and Head, 2005; Fig. 2) and radar (Phillips et al., 2008;
by a hillshade. Context box shows location of Fig. 1b. SHARAD observation 51920 is
alysis. (b) Study site of data set integration. Black lines show SHARAD observations
B?B0 (shown in green) gives the location of Fig. 4. The location of a model radar trace
of 6 m/pixel. (b and c) are subimages of HiRISE image PSP_001871_2670 and show
ws, are visible in (b).
ite is outlined by the white box. Transect location is shown in Fig. 1a.
et al., 2009), a diverse suite of high resolution tools (McEwen et al.,
2007; Seu et al., 2007) and techniques (Fishbaugh et al., 2010a,
us 22010b; Putzig et al., 2009; Holt et al., 2008) applied to the NPLD
has made a quantitative investigation possible. Analyzing morpho-
logic and topographic properties of surface layering detected by
HiRISE (Fishbaugh et al., 2010a, 2010b) in conjunction with subsur-
face structure and stratigraphy revealed by SHARAD (Putzig et al.,
2009; Holt et al., 2010) will begin to de?ne the relationship be-
tween visible layering and radar re?ectors.
The union of stratigraphic information from optical and radar
sources at divergent resolutions and spatial scales would ideally
provide not only a comprehensive understanding of NPLD struc-
ture and stratigraphy in three dimensions, but also would supply
the key to a climate record spanning multiple time scales (Milko-
vich and Head, 2005; Phillips et al., 2008). Such a union has been
envisioned as the correlation of a single re?ector to one or many
discrete visible layers (Milkovich et al., 2009). It is, however,
important to note that the hypothesis of a shared mechanism be-
tween the stratigraphies (Nunes and Phillips, 2006) has not yet
been empirically tested. The objectives of this work, therefore,
are to examine the assumption of a shared mechanism between
visible layering and radar re?ectance by comparison of the topo-
graphic, spectral and statistical properties of each; to evaluate
the plausibility of a direct correlation between a single re?ector
and a visible layer or de?ned layer sequence; and to use the results
there from to improve understanding of the relationship between
radar and optical stratigraphies.
2. NPLD stratigraphy
2.1. Optical stratigraphy
Although based on low resolution imagery returned by the Mar-
iner 9 and Viking Orbiter missions, early deductions of PLD compo-
sition, structure and stratigraphy have been supported by
subsequent decades of research. Preliminary studies of the SPLD
concluded that exposures exhibited ??cliff-bench?? topography
resulting from static, near-horizontal, areally-extensive layers of
ice and dust emplaced by air-fall deposition (Murray et al., 1972;
Cutts, 1973). Topography returned by the Mars Orbiter Laser
Altimeter (MOLA) and imagery from the Mars Orbiter Camera
(MOC) have allowed for the veri?cation of original structural infer-
ences in modern study. At both poles layers consistently dip equa-
torward on the order of 1 (Byrne and Ivanov, 2004; Fishbaugh and
Hvidberg, 2006) and demonstrate geometries inconsistent withFig. 3) stratigraphies have been proposed to correlate to martian
insolation cycles. The results, however, have been neither unique
(Putzig et al., 2009) nor robust (Fishbaugh et al., 2010a). Failure
to address the question of martian climate cycles and the in?uence
of orbital forcing using individual polar data sets is reminiscent of
the dif?culties experienced in the terrestrial case decades before
(Imbrie, 1982). This suggests that a similar approach, namely the
integration and correlation of multiple signals, must be attempted
in order to reconstruct a complete climate record for the NPLD.
Both radar and optical stratigraphies are the hypothesized re-
sult of the changing ratio of siliciclastic impurities to water ice in
the NPLD (Nunes and Phillips, 2006; Grima et al., 2009). Through
a shared origin, these signals provide the opportunity to attempt
a stratigraphic integration and correlation, which ?rst requires an
understanding of the relationship between morphologically dis-
tinct visible layers and radar re?ectors. While this relationship
has been qualitatively explored in the south PLD (SPLD) (Milkovich
S. Christian et al. / Icar?ow (Byrne and Ivanov, 2004; Fishbaugh and Hvidberg, 2006). Fur-
thermore, the topographic effects of erosionally-resistant bench
forming layers in the south (Byrne and Ivanov, 2004) and markerbeds in the north (Malin and Edgett, 2001; Fishbaugh et al.,
2010a, 2010b) result in the stair-stepped topography proposed
by early studies (Murray et al., 1972).
Large-scale continuity and uniformity of layering (Cutts, 1973)
has recently been supported by the results of spectral wavelength
matching (Milkovich and Head, 2005), as well as visual correlations
of prominent layers (Byrne and Ivanov, 2004; Malin and Edgett,
2001) and layer sequences (Fishbaugh and Hvidberg, 2006) across
hundreds of kilometers. The lateral extent of uniform layering has
led to the wide acceptance of deposition by airfall sedimentation
(Thomas et al., 1992), however, disruption by truncation surfaces
indicating erosional episodes has also been recognized (Cutts
et al., 1976). While erosional surfaces tend to be expressed locally
and, in the NPLD, to proliferate around the deposit margins (Tana-
ka et al., 2005, 2008; Tanaka and Fortezzo, 2012), they also can oc-
cur at exposures in the interior (Fishbaugh et al., 2010b; e.g.,
Fig. 2c) and may represent periods of either local or regional ero-
sion (Tanaka et al., 2008). Furthermore, large-scale change in the
erosional morphology of NPLD layering (Herkenhoff et al., 2007)
suggests a shift in depositional parameters and potentially indi-
cates one or more disconformable surfaces. Disconformities in vis-
ible layering may relate to regional, buried unconformities
apparent in the subsurface (Putzig et al., 2009; Holt et al., 2010),
however this relationship has not yet been explicitly studied. The
existence of such perturbations in otherwise uniform layering
underscores the incompleteness of the stratigraphic record, while
the uncertainty of their extent and interrelationships within the
NPLD (Tanaka et al., 2008) highlights the limitations of image, or
??outcrop,?? analysis.
With sur?cial data until recently the only means of studying
PLD stratigraphy (Fishbaugh and Hvidberg, 2006), much consider-
ation has been given to variables in?uencing the reliability of the
surface expression of layers. Murray et al. (1972) ?rst commented
on the inconsistency of layer albedo, noting its frequent depen-
dency on exposure orientation and curvature, but also identifying
instances in which neither factor induced a change in brightness.
While the discovery of dust and frost mantling deposits at the scale
of hundreds of meters (Herkenhoff and Murray, 1990) suggested
the inherent albedo of underlying layers might be largely masked,
this could not be veri?ed until imagery at sub-meter resolution
demonstrated that apparent albedo is a function of layer topogra-
phy, morphology and ??younger mantling deposit?? (YMD) (Fishb-
augh et al., 2010a), thus making it an unreliable proxy for
composition and a complicating factor in layer delineation (Her-
kenhoff et al., 2007; Fishbaugh et al., 2010a). Even though the con-
sistency of layer correlations between troughs based on methods
relying on apparent albedo (Milkovich and Head, 2005; Fishbaugh
and Hvidberg, 2006; Milkovich et al., 2008) argues that some com-
ponent of apparent albedo is inherent to the layers (Fishbaugh
et al., 2010a), high resolution topographic and morphologic data
may provide the most reliable means of delineating layer bound-
aries (Fishbaugh et al., 2010a, 2010b).
2.2. Radar stratigraphy
The arrival at Mars of orbital sounding radar has introduced
additional complexity, but also opportunity, in the attempt to de-
?ne a coherent stratigraphy for the NPLD. Mars Advanced Radar
for Subsurface and Ionospheric Sounding (MARSIS) on board Mars
Express (Picardi et al., 2005) demonstrated the ability of sounding
radar to penetrate the icy subsurface to the base of Planum Bore-
um, but its theoretical resolution of 85 m in water ice (dielectric
e = 3.1) (Picardi et al., 2005; Seu et al., 2007) and unfavorable view-
26 (2013) 1241?1251 1243ing geometry frequently did not permit the detection of internal
re?ectors in the NPLD (Picardi et al., 2005). Complementary to
MARSIS? deep-sounding capabilities, the higher resolution
(theoretical vertical resolution of 8.5 m in water ice) provided by
SHARAD (Seu et al., 2007) has allowed the distinction of tens of
re?ectors in the water?ice rich (Grima et al., 2009) NPLD subsur-
face (Phillips et al., 2008; Fig. 3), lending further credence to the
name ??layered deposits?? and providing the opportunity to de?ne
a new type of NPLD stratigraphy.
As with optical imagery, in which delineating a layer has be-
come a complicated task requiring knowledge of many surface
characteristics (Fishbaugh et al., 2010), multiple methods for de?n-
ing radar stratigraphy have been proposed. On one hand, promi-
nent, alternating bands of re?ector-rich and -poor zones have
been identi?ed as containing a potential climate record (Phillips
et al., 2008), and the boundaries between pairs of these zones have
been mapped in order to derive rough volume constraints (Putzig
et al., 2009). On the other hand, the principles of sequence stratig-
If evaluated in a uni?ed context, however, speci?ed radar sections
et al., 1972; Cutts, 1973; Cutts and Lewis, 1982) identi?ed the like-
lihood of layers caused by varying fractions of dust or sand cemen-
ted by volatiles, with recent conclusions favoring a composition of
predominantly pure water ice with small volumes of silicic impu-
rities (Thomas et al., 1992). This conclusion has been supported by
dielectric studies of the NPLD utilizing SHARAD, which suggest
bulk purity of water ice in excess of 95% (Grima et al., 2009). De-
spite the high degree of purity, the distribution of impurities
thought to result in visible layering also have been predicted to
cause the dielectric changes that would give rise to radar re?ec-
tance (Nunes and Phillips, 2006), and one of the primary objectives
of SHARAD was to use such changes to study the internal structure
of the NPLD (Seu et al., 2007). The success of SHARAD in detecting
multiple re?ectors (Phillips et al., 2008), and the qualitative resem-
blance of those re?ectors to visible layer geometries (Smith and
for use in subsurface stratigraphic mapping (Fig. 1b). SHARAD
operates with a 20-MHz center frequency and a 10-MHz band-
470
1244 S. Christian et al. / Icarus 226 (2013) 1241?1251within a large-scale structural context could be linked to morpho-
logically-distinct layers in outcrop, which could then be traced
over tens to hundreds of kilometers through the penetrative nature
of the radar data, thus resolving the primary shortcomings of each
dataset.
This ideal stratigraphic model, however, is predicated on the
assumption of a shared mechanism between radar re?ectance
and visible layering. Early models of layer formation (Murray
74429402
B
3 
?sraphy have been employed to identify signi?cant periods of accu-
mulation and erosion, resulting in a narrative of the history of
Chamsa Boreale (Holt et al., 2010) and the prospect of similarly
deciphering a history of accumulation for Planum Boreum. The
large-scale focus of the radar studies, notably, forms the antithesis
approach to that taken in the optical case and offers the opportu-
nity to unify information at two scales in order to form a more
complete understanding of Planum Boreum?s past.
2.3. Integrated stratigraphy
Until recently, optical and radar stratigraphies have been lar-
gely interpreted in isolation, and when considered in unison, anal-
ysis has been primarily qualitative (Holt et al., 2010) or speculative
(Herkenhoff et al., 2007). Ideally, a quantitative integration of high
resolution outcrop stratigraphy with penetrative radar stratigra-
phy would allow for the maximum exploitation of each of these
tools, resulting in a comprehensive stratigraphic framework for
the NPLD. While optical studies at sub-meter resolution are spa-
tially isolated and, by their sur?cial nature, lack signi?cant infor-
mation about subsurface structure, radar data are unable to
distinguish the morphologic and topographic differences that
may lend important geologic meaning to changes in composition.Fig. 4. Three intersecting SHARAD observations of the study site. Vertical white lines den
Colored lines are the semi-automatically picked bright re?ectors. The location of transewidth, yielding a theoretical vertical resolution of 8.5 m in water
ice (Seu et al., 2007). Lateral resolution is 3?6 km in the cross-track
direction and 0.3?1 km in the along-track direction (Seu et al.,
2007). Observations were chosen based on clarity of the subsurface
re?ectors and proximity to the visible stratigraphic section (Figs. 3
and 4).
2 1190202
B?Holt, 2010), has subsequently increased con?dence in the concept
that visible layers and re?ectors are related. While no quantitative
evidence has yet been presented to support this assumption, the
following methods have been designed to test the relationship be-
tween layers and re?ectors, and to begin to explore what type of
??layer?? a radar re?ector might represent (Fishbaugh et al., 2010a).
3. Study site and datasets
All analyses presented in this work have been applied to a single
NPLD exposure centered near 87.1N, 93.0E (Fig. 1). Optical data
are from HiRISE and CTX, which provide 25 cm/pixel (McEwen
et al., 2007) and 6 m/pixel (Malin et al., 2007) resolution, respec-
tively. Morphological descriptions and boundary elevations of vis-
ible layers are from the stratigraphic analyses of Fishbaugh et al.
(2010a) and Fishbaugh et al. (2010b), which used a digital eleva-
tion model (DEM) constructed from HiRISE stereopair
PSP_001738_2670 and PSP_001871_2670 (Fig. 1b). Due to the
small size of the DEM (16 km in length), the visible dataset was
augmented with CTX image P02_001738_2671 (Malin, 2007;
Fig. 2a).
In the inter-trough region adjacent to the imaged and modeled
outcrop, more than forty SHARAD observations have been selectedote where the observation changes, representing the intersecting traces or lineties.
ct B to B0 is shown in Fig. 1b.
information with minimal information on lateral variation. In order
on. P
cial
f the
us 2to convert the two dimensions of individual observations into
three dimensional subsurface interfaces, tens to hundreds of inter-
secting subsurface observations must be utilized.
4.1. Mapping re?ectors
Cross-sectional radar images of the subsurface are constructed
for each observation by horizontally building up vertical samples,
or traces, of time vs. amplitude data and applying a color scale to
the amplitude values (Putzig et al., 2009). Visible features are then
interpreted using a seismic interpretation platform, here, Schlum-
berger Corporation?s GeoFrame 4.3. Interpretation consists of4. Radar methods
The stratigraphy revealed by ice-penetrating radar provides a
rich history of deposition and erosion (Holt et al., 2010). Often, in
order to decipher this history, it is necessary to construct a
three-dimensional representation of the subsurface material inter-
faces that result in re?ectors. As a nadir-pointing instrument, one
observation by SHARAD records two-dimensional depth-time
(b)
Fig. 5. (a) Subsurface re?ectors at the study site modeled with the nadir assumpti
surface. Assuming the ?rst surface echo originates at the nadir point results in arti?
algorithm. Taking surface topography into account when calculating the location o
Location and orientation of re?ectors are given in Fig. 7.(a)
S. Christian et al. / Icarselecting traces of a bright re?ector at intervals along the re?ec-
tor?s discernible length in a single radar image, or radargram; the
software then implements an amplitude-?tting algorithm to eval-
uate the re?ector in the intervening traces within a user-de?ned
vertical time window. This process results in a semi-automatically
picked line that is ?t tightly to the high-amplitude center of the
re?ector (Fig. 4).
Where SHARAD observations spatially coincide due to orbital
geometry, radargrams can be displayed side-by-side at the trace
of intersection (Fig. 4). This allows individual re?ectors to be con-
?dently identi?ed on multiple observations. Additionally, true
re?ectors can often be distinguished from subsurface clutter by
consulting simulations that predict clutter features (Holt et al.,
2008).
4.2. Constructing re?ector surfaces
Exporting the time delay of the interpreted re?ectors in each
trace for all observations removes interpretations from the seismic
environment to undergo further analysis. The resulting product is a
collection of points, each of which is associated with a re?ector
name, a trace number, and a time. Assuming a dielectric constant
of 3.1 in water ice (Grima et al., 2009), time is converted to depth;additionally, trace number is converted to the nadir latitude and
longitude at the surface using spacecraft navigation ?les. To posi-
tion the subsurface re?ector, the vertical distance between the sur-
face return and subsurface re?ector is calculated; this method
assumes that all ?rst echoes returned from the surface originate
at the nadir point (Fig. 5a).
The assumption of a nadir ?rst echo surface return poses signif-
icant problems for modeling re?ector surfaces in three-dimen-
sions, a task that requires accurate positions for each surface and
subsurface elevation value. In the case of a ?at surface, the nadir
assumption is accurate, however, in the presence of even slight
surface slopes, ?rst echo returns are more likely to originate from
off-nadir sites (Fig. 5b). As a result an algorithm designed to predict
the originating locations for each ?rst echo returned from the sur-
face based on spacecraft coordinates and topographic data from
the Mars Orbiter Laser Altimeter (MOLA) is implemented when cal-
culating re?ector location. Although subsurface interfaces may also
slope, causing a similar effect of subsurface off-nadir return, sub-
surface returns are assumed to originate directly below the ?rst
surface return. This has not been found to cause signi?cant error
in the upper 500 m of the NPLD, the depth to which this study is
Elev. (m)
-2327
-2855
Elev. (m)
-2316
-2817
oints above the surface are the nadir locations of the ?rst radar returns from the
surface geometries. (b) Subsurface re?ectors modeled using the ?rst surface return
?rst radar return from the surface results in a more correct subsurface geometry.
26 (2013) 1241?1251 1245primarily concerned (see Section 4.3).
Each re?ector, represented by a collection of points recording
latitude, longitude and elevation, is imported into ESRI?s ArcGIS
and displayed with a north polar stereographic projection speci?c
to Mars. Slope, aspect and contour maps of elevation are then con-
structed based on the point data. Additionally, inverse distance
weighting interpolation is used to create grids representing each
subsurface re?ector. The grids are displayed in three dimensions
to visualize subsurface topography (Fig. 5). By using multiple, ob-
liquely-intersecting observations spaced closely together and
interpolating between the re?ectors, the across-track lateral reso-
lution of the SHARAD data is arti?cially enhanced.
4.3. Vertical uncertainty
While the ?rst-return algorithm is needed to accurately posi-
tion re?ectors in the horizontal direction, a method is required to
establish the vertical uncertainty of re?ector elevation values.
Well-constrained sources of vertical uncertainty include SHARAD?s
8.5 m theoretical vertical resolution, or the minimum separation
required to distinguish two interfaces in water ice (Seu et al.,
2007), and time sampling resolution of 37.5 ns, or ?1.6 m in water
ice. Additionally, the registration of surface radar returns with the
MOLA Experiment Gridded Data Records (MEGDR) (Smith et al.,
5. Subsurface analysis and topographic comparison
Based on the results of along-trough elevation pro?ling of visi-
ble layers and planar extrapolations of layers between exposures,
the accepted regional model of internal layer structure suggests
that layers dip equatorward at less than 1 (Fishbaugh and Hvid-
berg, 2006). From layer boundary elevations obtained using MOC
imagery co-registered with MOLA, variations in layer thickness
have been reported, implying local variation in accumulation rates
(Fishbaugh and Hvidberg, 2006). Layer pinch-outs and truncation
surfaces are also present in the visible stratigraphic record (Tanaka
et al., 2005, 2008; Fishbaugh and Hvidberg, 2006). Qualitatively,
these characteristics, including low slopes (Smith and Holt,
2010), variation in relative accumulation rates (Putzig et al.,
2009), and pinch-outs and truncation surfaces (Holt et al., 2010)
have been observed by SHARAD in the subsurface. The observed re-
gional similarities between layers and re?ectors warrant a more
quantitative comparison between re?ector topography and geom-
etry and the same properties for visible layers.
Twenty-?ve subsurface re?ectors were interpreted on 45 SHA-
RAD observations to construct a gridded subsurface volume to a
depth of 600 m over an area of 1450 km2 (Fig. 5). The average
dip of the 25 re?ectors is 0.4 to the south. At the regional scale,
this result agrees with the <1 slopes of modeled visible layers
Fig. 6. (a) Mean difference in time delay between the same re?ector on multiple
SHARAD observations at their point of groundpath intersection plotted against the
averaged time delay of the re?ector. (b) Standard deviation of time difference
plotted against mean time delay of the re?ector. Measurements were made in the
saddle region between the main lobe of Planum Boreum and Gemini Lingula, where
subsurface clutter is minimal and re?ectors are continuous for 100s of kilometers.
us 22003) during the ?rst-return correction and re?ector gridding pro-
cess contributes a ?1 m uncertainty (Smith et al., 2001) to eleva-
tion values.
Other potential sources of uncertainty, such as systematic pro-
cessing errors, wave propagation path in the subsurface, and ran-
dom error, are more dif?cult to constrain and, therefore, should
be identi?ed empirically. One method for doing so employs the
orbital crossover analysis (Smith et al., 2001), which assumes that
the elevation at any point on the planet?s surface should be consis-
tent when surveyed multiple times by an instrument. In the case of
the orbital crossover analysis, differences between elevations mea-
sured at the same point on the surface are caused by uncertainties
in the orbiter position and orientation. Following the same princi-
ple, a re?ector in the subsurface should be recorded by SHARAD at
the same depth even when measured on multiple observations. Be-
cause the surface re?ector is registered to the MOLA surface, po-
tential differences in re?ector elevation due to uncertainties in
the spacecraft position and orientation are eliminated, and any
remaining difference in re?ector elevation is the result of radar
wave propagation path or signal processing.
Six subsurface re?ectors varying between mean depths of 44 m
and 783 m were mapped continuously in the region between the
main lobe of Planum Boreum and Gemini Lingula. This area was
chosen based on low surface and subsurface slopes (<1), the ab-
sence of stratigraphic disruption due to troughs, and the lateral
clarity of re?ectors. Nine observation intersections were identi?ed,
and the two-way travel time for each of the six subsurface re?ec-
tors was obtained at each intersecting trace and the adjacent trace
to either side. This resulted in six time delay values for each of the
six subsurface re?ectors at all nine of the intersections. Each travel
time was then normalized to the surface return, and the difference
in time delay was taken between corresponding re?ectors in corre-
sponding traces from intersecting observations.
The difference, or offset, in mean time delay between re?ectors
that are expected to be at the same time delay increases from 0 ns
at the surface to 22 ns for the deepest re?ector studied (Fig. 6a).
Increasing re?ector offset correlates to increasing depth with an
R2 value of 0.67. It is important to note, however, that all values
of mean time delay offset fall below SHARAD?s time sampling res-
olution of 37.5 ns. Therefore, in this case the values obtained for
offset do not add additional vertical uncertainty. The increasing
offset values do, however, suggest that variation in subsurface
pulse propagation path should be taken into account for the deep-
est re?ectors of the NPLD. The linear increase of re?ector offset var-
iance with depth supports this conclusion (Fig. 6b). Variance
increases with a correlation coef?cient of R2 = 0.90 from a value
of 0 ns at the surface to 50 ns for the deepest re?ector. In this case,
the largest standard deviation value, 50 ns, is larger than the time
sampling resolution of SHARAD, indicating that time delay mea-
surements for re?ectors as deep as 783 m can demonstrate addi-
tional vertical uncertainty that is likely caused by variation in
pulse propagation path. These results suggest, however, that verti-
cal uncertainty due to pulse propagation path in the upper 500 m
of the NPLD is negligible.
Therefore, theoretical bandwidth-limited resolution, time sam-
pling and MOLA surface registration are the only identi?ed sources
of vertical error in the stratigraphic section studied. When added in
quadrature, these sources result in a vertical uncertainty of ?4.7 m
for SHARAD re?ectors analyzed with the methods presented here;
note that other methods of interpreting and registering re?ectors
might lead to minor differences in vertical uncertainty. It is, how-
ever, clear that the theoretical resolution (?4.25 m) dominates
uncertainty in the near subsurface and provides a good estimation
1246 S. Christian et al. / Icarof the uncertainty measurement when other values (e.g. pulse
propagation path and radar processing) are not as well
constrained.26 (2013) 1241?1251(Fishbaugh and Hvidberg, 2006). Consistent with the hypothesis
of lateral variations in relative accumulation rates, but not explic-
itly explored for visible layers due to the limitation of
closely-spaced exposures, the gridded re?ectors exhibit changes in
topography over scales of meters to kilometers. Topographic vari-
ation at the 10s of kilometer scale horizontally is consistent be-
tween subsurface re?ectors (Fig. 7a and b), but local variation in
accumulation is suggested by the changing difference between
the two re?ectors (Fig. 7c). In the case of this particular study site,
the zone of increased thickness corresponds with a slope facing
away from the equator (re?ectors sloping towards A in Fig. 3),
which suggests local topography controls accumulation.
While the mean geometries of re?ectors and layers agree, it is
important to determine if the local subsurface topographic trends
revealed by SHARAD are also followed by visible layers. To com-
pare topographic trends between surface and subsurface data, dis-
tance?elevation pro?les of layers were constructed using CTX
image P02_001738_2761 (Fig. 8a); original layers interpreted in
the HiRISE DEM (Fishbaugh et al., 2010a) could not be used be-
cause the small spatial extent of the DEM did not model a long en-
ough exposure for signi?cant comparison. The CTX image was
processed using the Integrated Software for Imagers and Spec-
pro?les, the detrended layer elevations may cross each other when
overplotted as the space between adjacent layers thickens and
thins with position. Fig. 8c shows these detrended elevations from
the SHARAD and CTX pro?les offset by 120 m for clarity.
The pro?le results demonstrate that there is similarity between
the long-wavelength (50 km) topographic variation detected by
SHARAD in the subsurface and the trend followed by visible layers
at the surface (Fig. 8). On either side of the prominent slope break
at 6 km in the SHARAD pro?le, the average slopes of re?ectors
from A?A0 are 0.006 and 0.01, respectively. These slopes are
similarly small as and agree in sign with average CTX/MOLA-de-
rived slopes of 0.0023 and 0.0031 on either side of the slope
break at 9 km, corresponding to the B?B0 direction. Beyond the
second slope break at 26 km, the visible layers record an average
slope of 0.0013 (Fig. 8). The average slope of SHARAD re?ectors
beyond10 km is similar, at 0.0009. It is likely that the 3 km off-
set between the 6 km and 9 km slope breaks in the SHARAD pro?le
and the CTX/MOLA pro?le, respectively, results from changes that
occur in the 10 km gap between the two transects. The offset of
that re?ectors and layers record morphologically related surfaces.
Visible layers are currently understood to represent paleosurfaces
(a)
S. Christian et al. / Icarus 226 (2013) 1241?1251 1247trometers version 3 (ISIS 3), an in-house software developed by
the U.S. Geological Survey (USGS) for the processing of imagery
collected by NASA planetary missions. Image P02_001738_2761
was imported to ISIS 3, radiometrically calibrated, striping was re-
moved, and the image was projected using the north polar stereo-
graphic projection for Mars. Following processing, the image was
co-registered with MOLA topography in the ArcGIS software. Ele-
vations of CTX layer boundaries were extracted from underlying
MOLA topography at 10 km intervals along 75 km of the trough
exposure. Distances were measured following the curvature of lay-
ers, and thus are not straight-line distances but rather along-
trough distance (Fig. 8c). A model radar observation subparallel
to the trough exposure was constructed by de?ning a transect
through the highest density of SHARAD ?rst returns along the
trough-ward edge of the gridded area. Traces falling within
300 m (a value within the lateral resolution of the radar) of the
transect were selected, and the elevations of subsurface re?ectors
in these traces were recorded. To facilitate comparison of layers
and re?ectors at different elevations and sampled at different
along-track distances we overplot their detrended elevations. In
order to detrend the elevations for each layer/re?ector, a best-?t
plane (constructed in polar stereographic space separately for each
feature) was subtracted. This procedure removes the elevation off-
sets between the layers and any long-baseline tilts thus highlight-
ing the local structure of the NPLD. In contrast to the raw elevation
Fig. 7. Gridded subsurface re?ectors contoured at 10 m intervals. Re?ectors are the
between the two. Note the kilometer-scale topography, as well as the variability in mod
visible as gray points in (a and b). The distribution of points determines how well a subsu
these cases, the lack of points near the outcrop prevents a reliable extrapolation.of the NPLD (Thomas et al., 1992). By structural agreement with
visible layering, re?ectors can be used as a proxy for visible layer
geometry and topography in the subsurface. It is important to note,
however, that shared surface morphology does not require re?ec-
tors and layers to represent the same surfaces resulting from the
same material changes. Therefore, no unique causal relationship
is implied by shared morphology.
6. Signal analysis
The effort to ?nd a climate signal in the NPLD has prompted
spectral analyses of albedo-depth pro?les using MOC images (Las-
kar et al., 2002; Milkovich and Head, 2005; Perron and Huybers,
2009). Of these studies Fourier analyses conducted on images at
the current study site and in adjacent troughs returned prominent
?rst and (b) 20th in the interpreted stratigraphic sequence, and (c) the differenceslope breaks in addition to meter and kilometer-scale topographic
variation in the subsurface (Fig. 7) emphasizes the variability of
topography over distances of less than 10 km and calls into ques-
tion any con?dence in elevations derived from planar extrapola-
tion or re?ectors over that distance.
Topographic agreement between re?ectors and layers at both
the 100s of kms and the 10s of kms scales provides strong evidenceeled elevation differences. Interpreted radar returns used to grid each re?ector are
rface plane extrapolated to the exposure would re?ect true subsurface geometry; in
lanes (blue points) and visible layers (red points). (b) MOLA surface elevation along the
(A to A0) and layers (B to B0). SHARAD re?ectors are the upper set, and have been offset
us 2wavelengths of 33, 24, and 21 m in addition to a broad peak
between 15 and 18 m (Milkovich and Head, 2005). If radar and
optical layering share a genetic link, similar wavelengths are ex-
pected to exist in re?ectors at the same site.Fig. 8. (a) Locations at which elevation data were taken for the SHARAD subsurface p
line from A to A0 , parallel to the B to B0 transect. (c) Detrended elevations of re?ectors
from the visible layers elevations by 120 m for clarity.
1248 S. Christian et al. / Icar6.1. Fourier analysis
The uninterpreted radar trace containing amplitude data vs.
time delay is analogous to the albedo-depth pro?les extracted from
MOC images (Laskar et al., 2002; Milkovich and Head, 2005; Perron
and Huybers, 2009), and therefore can be analyzed for comparison
with visible wavelengths. A trace 10 km from the trough expo-
sure was chosen for the frequency analysis based on the clarity
and apparent conformity of the subsurface re?ectors. All traces
within 0.03 km2, or 0.5% of a Fresnel zone, were aligned with the
chosen trace and averaged together in order to create a model ra-
dar trace for the current study site (Fig. 1b). Surface effects due to
the greater dielectric contrast between ice and free space were
minimized by removing data exhibiting high amplitudes related
to the ?rst surface return. The resultant model trace was de-
trended to remove the effects of attenuation with depth, time de-
lay was converted to depth below the surface (assuming water ice),
and the 500 m section below the surface was isolated. Because the
uncertainties associated with the interpretation algorithm (e.g.,
surface alignment) do not apply to the construction of the model
trace, the average of the resulting wavelengths is reliable down
to the vertical resolution limit of SHARAD in water ice, or 8.5 m.
A fast Fourier transform (FFT) for the model radar trace returned
peak values at 31, 21, 18 and 16 m, with a broader peak between 24
and 29 m (Fig. 9). These wavelengths correspond most closely to
the 24, 21 and 18 m visible wavelengths detected at the adja-
cent trough (Milkovich and Head, 2005). The similarity between
power spectra suggests that the recurrence of visible layers shares
similar recurrence values with radar re?ectors. These results imply
that layers and re?ectors share common vertical recurrence dis-
tances, providing the ?rst numerical evidence supporting the26 (2013) 1241?1251hypotheses that re?ectors and layers are related not only through
paleosurface morphology, but also by an underlying formation
mechanism that responds to the same environmental forcing.
6.2. Statistical analysis
The FFT analyses of uninterpreted optical and radar data dem-
onstrate that similar characteristic signals exist in both data sets,
however, the frequency analysis provides little insight into the
stratigraphic context of layering. In an effort to contribute geologic
meaning to prominent visible layering, the stratigraphic analysis of
layering in the DEM included a k-means clustering analysis of the
vertical separation distance, or the vertical distance between the
lower boundary of one layer to the upper boundary of the subja-
cent layer (Fishbaugh et al., 2009), between marker beds (Fishb-
augh et al., 2010b). The clustering analysis consists of an iterative
process wherein the user de?nes a number of clusters, and the sta-
tistical software chooses that same number of random values from
within the data set to represent initial cluster centers. Each datum
Fig. 9. Spatial wavelengths detected in the upper 500 m of a model SHARAD trace
averaged from multiple traces. Location of the model trace is given in Fig. 1b.
Vertical gray lines and bars represent the locations of dominant peaks reported in
the analysis by Milkovich and Head (2005).
tors record a signal of interactions between the surface and atmo-
us 2is then assigned to the nearest cluster center, the cluster mean is
calculated, and the data are reassigned to the nearest cluster center
based on the new means. The process continues until the clusters
means are stable and no datum reassignments are made.
For the visible stratigraphy, the k-means clustering analysis on
the separation distances between visible layers returned clusters of
6.3, 12.5, 21.0 and 30.7 m (Fishbaugh et al., 2009). It has been
noted that the 21.0 m and the 30.7 m separation distances closely
resemble the dominant 29 m wavelength as well as the secondary
21 m peak apparent in the Fourier analysis at the same site (Milko-
vich and Head, 2005; Fishbaugh et al., 2009). These results not only
suggest that marker bed separation is related to the albedo signal
detected throughout the NPLD (Fishbaugh et al., 2010b), but also
suggest that the visible layers de?ned using topographic and mor-
phologic characteristics reliably in?uence the surface albedo. Fur-
thermore, the agreement between signals in the uninterpreted
albedo pro?les and the constructed stratigraphic section serves
as veri?cation that layers have been meaningfully interpreted.
A similar veri?cation of radar interpretations with respect to a
fundamental signal embedded in the amplitude data can be con-
ducted. In the radar data set, the value of greatest similarity to
Table 1
Stratigraphic succession of optical and radar separation distances. Comparison begins
at the top of the visible and radar stratigraphic sections and records thickness of
material between marker beds or re?ectors, respectively, down through the column.
Layer separation difference
(?1.4 m)a,b
Re?ector separation difference
(?9 m)b
24.5 15
36 18.4
26.4 15.8
14.6 15.9
16 23.5
30 26.7
34.2 30.3
40.1 18.6
28 16.6
21.3 16.3
10.6 19.4
17.2 17.7
31.2
a Separation distance values after Fig. S2 in Fishbaugh et al. (2010b).
b Error is propagated from uncertainty in the layer and re?ector elevations,
respectively.
S. Christian et al. / Icarthe vertical separation distance of optical layering is the vertical
distance between pairs of radar re?ectors. By making this compar-
ison to visible separation distances, we are expressly comparing
the vertical spacing of radar re?ectors to the recurrence of marker
beds.
In order to obtain the vertical distances between re?ectors, for
each trace containing multiple subsurface re?ectors, the elevation
difference was taken between each re?ector and its subjacent
re?ector. Difference values from all traces containing the re?ector
pair were then compiled, and a random sample of 1420 values was
selected to prevent biasing towards re?ector pairs present in more
traces, which would weight the cluster results towards those val-
ues. The clustering analysis was performed on 34,080 data points,
or 1420 values for each of 24 re?ector pairs, using SAS?s JMP 7.0.
Tests were run with three, four, ?ve and six clusters and, consid-
ered alongside cumulative plots, which helped to visualize differ-
ence values for which there were more data points, and
histograms, ?ve clusters were determined to best represent the
distribution of values and their frequencies. Furthermore, it is
important to note that cluster mean values do not shift signi?-
cantly when clusters are added; rather, the additional cluster
means re?ect previously underrepresented concentrations of data.
Note that this method assumes a constant separation distance
between re?ectors, or else the cluster means would most likely
Furthermore, while angular truncation surfaces and disconfo-
rmities (Tanaka et al., 2008) have been widely recognized in the
NPLD, and a sequence stratigraphic interpretation of the deposits
had been postulated (Cutts and Lewis, 1982), the lateral persis-
tence of erosional surfaces was not veri?ed until SHARAD revealed
the subsurface structure of layering (Holt et al., 2010). At the cur-
rent study site, a radar discontinuity and an unrelated visible
unconformity have been independently identi?ed; it is easy to con-
clude that similar local discontinuities exist elsewhere in the NPLD.
When attempting to decipher the climate record, erosional sur-
faces at regional and local scales must be taken into account.sphere due to changing atmospheric conditions. While it is beyond
the scope of this work to propose layer-re?ector correlations to
orbital periods utilizing both data sets, the addition of radar to
stratigraphic interpretation of the NPLD raises new complications
in the search for a fundamental climate signal. The detection of
previously-identi?ed visible wavelengths in the upper 500 m of
the radar stratigraphy provides a length-scale over which atmo-
spheric change occurred that must be integrated with change
occurring at the scale of higher-frequency visible layers as well
as at the largest scale of the packet and inter-packet radar
structures.represent the thickening and thinning of material between
re?ectors. Based on our interpretations, we believe this is a valid
assumption for most re?ector pairs. In the case of one re?ector
pair, the upper re?ector appears to terminate against the lower
re?ector, and therefore the values for that pair were omitted from
the analysis. Otherwise, the assumption of constant thickness is
valid. The clustering analysis on radar re?ectors returned values
at 11.8, 15.8, 20.3, 27.9, and 35.3 m. These values agree closely
with optical data, notably the 21 and 29 m spectral wavelengths
and the 12.5 m separation distance.
7. Discussion
Agreement between the qualitative and quantitative character-
istics of the radar and visible stratigraphic columns aligns with
predictions about the ability to augment surface stratigraphic
interpretations with subsurface stratigraphy (Fishbaugh and Hvid-
berg, 2006). The potential for stratigraphic integration presented
here raises new questions concerning the search for a climate sig-
nal in the NPLD, the frequency and visible expression of layering,
and how far the stratigraphic integration can be taken.
7.1. Climate
In the effort to constrain accumulation rates and NPLD age, the
possibility of relating visible layering in the upper kilometer of the
deposits to the 51 kyr precession (Laskar et al., 2002), and 120 kyr
obliquity (Milkovich and Head, 2005) cycles have been explored.
Additional efforts have focused on tying the subsurface packet?in-
ter-packet structure of radar facies to the 2.4 Myr eccentricity
modulation period or low-obliquity phases (Phillips et al., 2008),
and the relationship of regional patterns in the radar stratigraphy
have been compared to multiple proposed correlations to orbital
periods (Putzig et al., 2009). The range of orbital cycles still under
consideration as candidates for causing layering demonstrates the
continuing lack of consensus and understanding of how the NPLD
respond to climate change.
The detection of the 12, 21 and 29 m wavelengths and clusters
in the radar stratigraphy veri?es that both visible layers and re?ec-
26 (2013) 1241?1251 1249The con?rmation of existing regional and local hiatal surfaces,
including disconformities and angular truncation surfaces, at the
vertical scale of SHARAD highlights the dominant assumption
in depth, given the strong inclination to attribute re?ectors to dust
of an individual re?ector calls into question any attempt to con-
us 2underlying correlations of re?ectors and layers to orbital periods,
namely, that the radar trace or brightness pro?le contains a record
complete enough to draw a connection. The solution to unraveling
the correlation of terrestrial deposits to Milankovich cycles lay lar-
gely in the ability to use continuous deep ocean records (Imbrie,
1982). The profusion of visible (Tanaka et al., 2008; Fishbaugh
et al., 2010a) and radar (Holt et al., 2010) unconformities chal-
lenges the ability to ?nd a meaningful, fundamental climate signal
in the re?ectors and layers of the NPLD.
7.2. Unique solution
While the results of the signal analyses and geometrical argu-
ments support the idea that radar re?ectors and visible layers are
genetically related, the question remains as to whether or not an
individual re?ector can be uniquely correlated to one or more dis-
tinct visible layers.
7.2.1. Elevation comparison
The direct correlation of re?ectors to visible layers requires that
at the topographic surface of the NPLD (here, the trough wall) the
linear interpretations representing layers and the planar interpre-
tations representing gridded re?ectors spatially coincide so that
elevation comparisons can be made along the line of intersection.
At 87.1N, 93.0E, the current study site, an elevation comparison
is not possible due to the 10 km distance between SHARAD re-
turns and the NPLD exposure. As in previous studies where the
re?ectors did not intersect the surface, planar extrapolation must
be used to close the intervening distance between the two stratig-
raphies (Milkovich et al., 2009). The results of along-trough pro?l-
ing (Fig. 8) and re?ector gridding (Figs. 5 and 7), however, suggest
that extrapolation may not be able to reproduce re?ector topogra-
phy with the accuracy required for a re?ector-to-layer correlation.
The re?ector and layer elevation pro?les reveal long-wave-
length topography on the horizontal scale of 50 km (Fig. 8). More
importantly, gridding of subsurface interfaces reveals lateral topo-
graphic variation at scales similar to and shorter than the extrapo-
lation distance (Fig. 7). Contour maps derived from the gridded
re?ectors demonstrate that elevation changes of >20 m can occur
over horizontal distances of 5 km (Fig. 7). If the vertical scale of
subsurface topography were smaller than SHARAD?s vertical
uncertainty (?4.7 m), an extrapolation could be performed over
the required distance with minimal uncertainty. Because topo-
graphic variation exceeds SHARAD uncertainty, however, extrapo-
lating the re?ector planes by 10 km could potentially smooth
topographic features that would in?uence the elevation at which
the re?ectors would outcrop. Furthermore, while the elevation of
the gridded surfaces within the aerial extent of the SHARAD data
points (Fig. 7) are accurate to the resolution of the radar, the
extrapolated grids outside of the data point cloud are effectively
unconstrained and do not provide reliable elevations. While a di-
rect comparison of re?ector elevations to layer boundary eleva-
tions is not discounted as a potential method for stratigraphic
integration, it is not considered reliable at this study site.
7.2.2. Separation distance matching
The similar results of the k-means clustering analyses on the
differences between subjacent radar re?ectors and the separation
distances between marker beds con?rms that the material inter-
faces causing re?ectors occur at intervals comparable to those ex-
pressed between prominent visible layers. This result suggests that
a comparison could be made between the vertical sequence of vis-
ible separation distances and the vertical sequence of radar differ-
1250 S. Christian et al. / Icarences. In other words, counting down from the top in stratigraphic
succession, the mean differences between subjacent radar re?ec-
tors should be similar to the mean separation distances betweenclude that a single layer morphology represents the change of
material responsible for radar re?ectors.
8. Conclusions
Agreement between the geometric, topographic, frequency and
statistical properties of radar re?ectors and visible layers provides
the ?rst quantitative evidence for a shared origin at the surface of
the north polar deposits of these two types of paleosurface. Radar
re?ectors can be used as a proxy for visible layering in the NPLD
subsurface. Furthermore, the radar reveals the expected, but
uncharacterized, presence of local subsurface structure (e.g., dis-
conformities, topographic variation) resulting from spatially-vary-
ing accumulation patterns of the NPLD.
Meter- and kilometer-scale relief on subsurface interfaces, as
well as stratigraphic features such as disconformities, underscore
the importance of using multiple observations when studying the
subsurface of even a limited area. The three-dimensionality of
the subsurface environment necessitates a high density of data,
as well as accurate data positioning through predicting the in?u-
ence of surface topography on the originating location of the ?rst
surface return. Both of these considerations must be made when
attempting to accurately interpolate and visually represent subsur-concentration, it remains a possibility that we cannot presently
exclude.
7.2.3. Resolution
The disparity in resolution between imagery and radar data cre-
ates an additional complication in attempting a re?ector-to-layer
correlation. Because the resolution of SHARAD dominates the ver-
tical uncertainty, a single re?ector represents a ?4.7 m range of ele-
vations; the material change causing the re?ector cannot be
located within that elevation range. A visible layer, on the other
hand, can represent a package of material as thin as <1 m (Fishb-
augh et al., 2010b), and the interpreted layer boundary that would
be correlated to is accurate to within ?1 m (Fishbaugh et al.,
2010b). At the present time, it is impossible to determine if a
re?ector uniquely correlates to one of two visible layers occurring
within that re?ector?s elevation range. The spatial coincidence of
multiple visible layers or layer boundaries with the elevation rangemarker beds. Results from this analysis demonstrate reasonable,
although not complete, agreement (Table 1). Of 13 visible layer
separation distances and 12 re?ector separation distances, eight
intervals agree within the compounded error of the radar and opti-
cal methods. Note that this does not inherently imply that matched
intervals between the radar and visible stratigraphies occur at the
same elevations.
While the radar stratigraphy exhibits a similar underlying sig-
nal to the visible stratigraphy, and possibly a similar stratigraphic
succession, two scenarios remain as possible explanations for the
geometric and statistical similarities between stratigraphic sec-
tions. The ?rst is the case of the unique correlation, in which the
climatic and atmospheric change that causes visible layers concur-
rently causes the electric change responsible for radar re?ectors
(e.g., changing dust concentration). In this scenario a radar re?ec-
tor and its correlative visible layer will represent the same paleo-
surface. Alternatively, a layer and a re?ector may each represent
paleosurfaces of the deposit formed at different times, but modu-
lated by the same orbital period. While the second scenario is
somewhat harder to conceptualize and has not been considered
26 (2013) 1241?1251face material interfaces.
Extrapolation of gridded subsurface interfaces to the nearest
outcrop for correlation to visible layers is similarly complicated.
us 2sight into the discussion and helped to improve the work.
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Acknowledgments
We would like to thank Sarah Mattson, Nathaniel Putzig, Patrick
Russell, and Sarah Milkovich for their help in developing this pro-
ject conceptually, critiquing the results, offering suggestions for
improvement, and providing additional raw and processed data.
Thanks also to Ken Herkenhoff and T. Charles Brothers, who have
contributed alternative methods that advanced the study. Reviews
by K. Tanaka and an anonymous reviewer provided additional in-The orbital geometry of the sounding radar in?uences the angle at
which the outcrop is approached; in many cases, the signal is lost
many kilometers from the outcrop due to surface slopes, and the
subsurface interface must be extended over distances large enough
to include signi?cant relief on the re?ector surface, leading to
uncertainty in the projected elevation at the outcrop. Therefore,
despite the agreement between fundamental characteristics of vis-
ible and radar stratigraphies, a unique solution correlating each ra-
dar re?ector with one or several visible layers remains to be
discovered.
Due to the dif?culties in conducting a unique correlation at the
present study site, including kilometer-scale topography as well as
visible angular truncation surfaces and a radar disconformity, anal-
ysis at a second study site using the same methods is underway
(Russell et al., 2011; Christian et al., 2011). The factors at the cur-
rent site that inhibit a unique correlation will be largely mitigated
at the new site by a favorable geometry of the radar intersection
with the outcrop, which will minimize re?ector extrapolation dis-
tance, a lack of subsurface structure, and continuity of the re?ec-
tors with a substantial region of the NPLD, which will lend
insight into accumulation patterns and re?ector genesis (Christian
et al., 2011). Thus, a unique correlation remains possible. If such a
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