Lunar and Planetary Science XLVIII (2017)
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DID HESPERIAN AMPHITHEATER-HEADED VALLEYS FORM BY GROUNDWATER SAPPING?
M. G. A. Lapotre and M. P. Lamb, 1California Institute of Technology, Pasadena, CA 91125.
Introduction: Groundwater seepage is responsible
for the formation of sapping valleys in rare cases on
Earth, but, where it occurs, it is exclusive to sand-togravel-sized sediments or weakly cemented sedimentary
rock [e.g., 1-3]. Small-scale valleys in loose sand that
result from groundwater seepage typically form amphitheater-shaped canyon heads with roughly uniform
widths over the entire canyon length [e.g., 4-5]. By
analogy to terrestrial sapping valleys, amphitheater canyons on Mars have been interpreted as resulting from
groundwater flow, and have been used to reconstruct
ancient martian hydrology under the assumption that
they were carved by sapping [e.g., 6-7]. However, recent studies suggest that martian amphitheater canyons
carved in fractured bedrock may instead result from
catastrophic overland floods, analogous to canyons of
the Snake River plain in Idaho and of the Channeled
Scablands in Washington [e.g., 8-11]. Understanding
the formation mechanism of such canyons is crucial to
paleohydraulic reconstructions, and thus to our understanding of liquid water on ancient Mars.
While theoretical models of sapping erosion in loose
sediment exist [e.g., 4, 12], there is currently no model
to predict the necessary conditions for sapping erosion
to carve a canyon, and whether groundwater sapping
can carve canyons in fractured cohesive or competent
rock. In order to bridge this knowledge gap, we formulate a theoretical model that couples equations of
groundwater flow and sediment transport that can be
applied to a wide range of substrates including granular
material of different size classes and rock. The model
can be used to infer whether a canyon may have been
carved by sapping and requires only limited inputs that
can be measured in the field/from orbital imagery. We
compare predictions from our model to both experimental and natural terrestrial and martian amphitheaterheaded canyons.
Theoretical Model: In order to build a 1-D model
for groundwater sapping (Fig. 1), we couple Darcy’s
law to equations for sediment transport to predict the
sapping-efficiency factor, f , defined as the ratio of
flow depth in the canyon, hn , to the critical flow depth
for incipient motion of the eroded material. Thus, when
f  1 , eroded material can be transported away from
the canyon head, and sapping erosion may carve a canyon. Conversely, when f  1 , groundwater discharge is
not sufficient to transport the eroded sediment, and
groundwater seepage cannot carve a canyon. We find
f to be a function of ten dimensionless parameters.
From these ten dimensionless parameters, three are
roughly constant on Earth and Mars, such that f is
reduced to a function of the bed slope upstream of the
canyon head, S , the bed slope within the canyon, Sb ,
the ratio of canyon depth ( H c ) to grain diameter, H * ,
the ratio of basin length ( L ) to canyon depth ( H c ),
L * , a Darcy number which relates aquifer permeability
to grain diameter, Da , the particle Reynolds number,
Re p , and the critical Shields stress for incipient motion
of the sediment,  *c , which is a function of Re p . Canyon geometry is conceptualized as in Figure 1.
Figure 1: Conceptual cross-section of the seepage face
at a canyon head.
Comparison to Experimental and Natural Canyons on Earth and Mars: Our model results combined
with permeability constraints show that sapping erosion
is only efficient when eroded clasts are within the
coarse-silt to fine-gravel size range for well sorted sediment. For poorly sorted or consolidated sediment, sapping is limited to sand sizes (Fig. 2). In general, smaller
grain sizes are easy to transport, but seepage discharges
are insufficient to mobilize the grains due to low permeabilities. For larger grain sizes, seepage discharge can
be high due to large permeabilies, but flow in the canyon remains below the threshold needed to mobilize
sediment owing to the larger, heavier grains. Similarly
for competent rock, sapping erosion is only predicted to
occur for very limited grain size and permeability combinations that are characteristic of loose sand, and are
thus unlikely.
We compare our model predictions to (1) results
from sandbox experiments [13-15], (2) valleys carved in
sediments on Earth [16-17] (Fig. 2), and (3) canyons
carved in fractured bedrock on Earth and Mars [10]
(Fig. 2). Our new theoretical model is consistent with
Lunar and Planetary Science XLVIII (2017)
sapping canyons forming in the sandbox experiments
and in known occurences of groundwater-seepage in
sediments on Earth. However, amphitheater-headed
canyons of the Snake River plain and the Channeled
Scablands all fall within a regime with f  1 , inconsistent with a sapping mechanism, and consistent with
field evidence in those regions of canyon formation by
large scale flooding [e.g., 8, 10-11]. Thus, both experimental and field data support our new theoretical model,
which can be applied to constrain the formation mechanism of martian canyons.
Figure 2: Model predictions for the sapping-efficiency
factor, f , as a function of grain diameter and aquifer
permeability. Boxes outline reported ranges in grain
sizes and permeabilities in the sandbox experiments, the
Florida panhandle, lava flows of the Snake River plain,
ID, and the Chaneled Scablands, WA, and fractured
bedrock at Echus Chasma on Mars. We assume the
permeability of consolidated and loose well sorted sediment [18] as conservative lower and upper bounds on
permeability. Note that permeability rolls over and plateaus for larger grain sizes due to inertial effects at the
pore-scale [e.g., 19].
Implication for Hesperian Hydrology: Most amphitheater-headed canyons on Mars are found in lateNoachian-to-Hesperian-aged terrains [e.g., 20]. The
lithology of canyon walls is difficult to constrain due to
obscuration by debris talus. However, the walls of selected canyons near Echus Chasma appear to consist of
discrete lava flows, with sub-vertical fractures (likely
cooling joints) [10]. Based on orbiter-based measurements of joint spacings and other morphological characteristics, we find that the considered canyons cannot
result from groundwater seepage (Fig. 2), unless our
assumed lithology is erroneous, and the canyon walls
instead consist of coarse-silt to fine-gravel sized weakly
consolidated sedimentary rocks.
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These results have critical implications for Hesperian hydrology: while the water volumes involved in carving sapping vs flood canyons need not be significantly
different, erosion rates are orders of magnitude faster in
the case of catastrophic floods, such that liquid water
needs not be thermodynamically stable at the martian
surface over long periods of geologic time in the catastrophic-flood scenario. Thus, our new theoretical model for canyon formation by groundwater seepage erosion
adds to a growing body of evidence that Mars likely lost
its denser atmosphere, and thus most of its surface hydrosphere, early in its history [e.g., 21-23].
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