JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, E01004, doi:10.1029/2004JE002330, 2005
Hydrological modeling of the Martian crust with application to the
pressurization of aquifers
Jeffrey C. Hanna and Roger J. Phillips
McDonnell Center for the Space Sciences and Department of Earth and Planetary Sciences, Washington University,
St. Louis, Missouri, USA
Received 26 July 2004; revised 14 October 2004; accepted 9 November 2004; published 26 January 2005.
[1] We develop a hydrological model of the Martian crust, including both ancient
heavily cratered terrains and younger basaltic and sedimentary terrains. The porosity,
permeability, and compressibility are represented as interdependent functions of the
effective stress state of the aquifer, as determined by the combination of the lithostatic
pressure and the fluid pore pressure. In the megaregolith aquifer model, the crust is
modeled as a 2 km thick megaregolith, composed of lithified and fractured impact
ejecta, overlying the impact-fractured and partially brecciated basement rock. The
hydraulic properties depend primarily upon the abundance of breccia and the
compressional state of the fractures. The porosity ranges from approximately 0.16 at
the surface to 0.04 at a depth of 10 km, with a sharp discontinuity at the base of the regolith.
The permeability varies from approximately 1011 m2 at the surface to 1015 m2 at depths of
5 km or more and is strongly dependent upon the fluid pore pressure. The hydrologic
properties of basaltic and sedimentary aquifers are also considered. These parameters are
used to model the fluid pressures generated beneath a thickening cryosphere during a
postulated dramatic cooling of the climate at the end of the Noachian. As a result of a
negative feedback between the fluid pore pressure and the permeability, it is more difficult
than previously thought to generate pore pressures in excess of the lithostatic pressure by this
mechanism. The production of the outflow channels as the result of such a climatic change is
deemed unlikely.
Citation: Hanna, J. C., and R. J. Phillips (2005), Hydrological modeling of the Martian crust with application to the pressurization of
aquifers, J. Geophys. Res., 110, E01004, doi:10.1029/2004JE002330.
1. Introduction
[2] There is a substantial body of evidence pointing to the
fact that groundwater plays a central role in the Martian
hydrologic cycle, both past and present. The dendritic valley
networks, which are the earliest recorded fluvial features on
Mars, were likely formed by some combination of surface
runoff and groundwater sapping [Goldspiel and Squyres,
2000; Hynek and Phillips, 2003; Williams and Phillips,
2001]. Either process is suggestive of the existence of a
widespread and shallow groundwater system during the
Noachian epoch. More recently in Mars history, with ages
ranging from Hesparian to Amazonian [Carr and Clow,
1981], the circum-Chryse outflow channels provide the
strongest evidence for the importance of groundwater.
These enormous fluvial features, ranging from tens to
hundreds of kilometers in width and a kilometer or more
in depth, originate from groundwater sources in chaos or
canyon regions [Baker and Milton, 1974; Carr, 1979]. A
number of smaller outflow channels are found throughout
the planet, including Athabasca and Mangala Valles. The
young ages of the channel surface of Athabasca Valles
indicates the persistence of outflow activity into the past
Copyright 2005 by the American Geophysical Union.
0148-0227/05/2004JE002330$09.00
10 to 100 Ma [Berman and Hartmann, 2002]. The most
recent fluvial features, with ages possibly younger than
10 Ma, are small-scale gullies, which occur on the steep
slopes of crater walls, central peaks, and canyon walls in
high latitudes [Malin and Edgett, 2000a]. While the
origin of these features is still uncertain, one interpretation is that they result from the freezing of small,
confined aquifers at depths of several hundred meters
[Gaidos, 2001; Mellon and Phillips, 2001].
[3] Despite this dramatic evidence for both ancient and
recent hydrologic activity on Mars, many first order questions regarding the distribution of groundwater and the
hydrologic properties of the Martian crust remain largely
unanswered. Yet any attempt to understand the nature and
history of the action of water on the Martian surface must
hinge upon the assumptions made regarding the hydrologic
properties of the subsurface. This study presents a generalized hydrologic model of the Martian crust that allows for
the modeling of a variety of processes over the wide range
of conditions thought to have existed in the Martian
subsurface, and then applies that model to gain insight into
the origin of the outflow channel floods.
[4] Hydrologic phenomena on Mars range in spatial scale
from gullies at the hundred meter to kilometer scale, to
outflow channels at the scale of tens to thousands of kilometers. For smaller scale features, the local variability in the
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crustal materials and hydrologic properties will be significant, and the range of parameter space that must be considered will span several orders of magnitude. However, on
large spatial scales, the local heterogeneity will average out
and the large-scale hydraulic parameters can be estimated
with a greater degree of confidence. The model here developed is a representation of the large-scale average hydraulic
properties of the Martian crust. To a first approximation,
Martian crustal materials can be divided into three categories:
(1) heavily cratered, Noachian-aged crust that predominates
in the southern highlands; (2) younger basaltic material that
likely makes up much of the crust in the Tharsis and Elysium
volcanic provinces, and which is likely present in smaller
proportions within the crust elsewhere on the planet; and
(3) sedimentary deposits that appear to be most abundant
within closed depressions [Malin and Edgett, 2000b]. Many
terrains are best represented as combinations of the three
types, such as lava flows with interbedded sediments and
impact ejecta, and the northern plains, which are thought to
be made up of an ancient heavily cratered basement [Frey et
al., 2002] overlain by volcanic plains with a thin sedimentary cover [Head et al., 2002]. We model the properties of
the heavily cratered Martian crust based upon the record of
surface impacts and the observed properties of terrestrial
and lunar impact craters, drawing also on the hydrologic
properties of terrestrial and lunar analogs to Martian regolith
material. The younger basaltic and sedimentary regions are
modeled directly after terrestrial aquifers.
[5] This model differs from previous studies in that it
includes the compressibility of the aquifer, and thus allows
for the modeling of time-dependent flow. Furthermore, all of
the hydraulic properties of interest are modeled interdependently using a self-consistent and physically realistic model.
The parameter values can be calculated for any combination
of lithostatic and fluid pore pressure. This flexibility is
essential for modeling many of the hydraulic processes that
are thought to have occurred on Mars involving deeply
buried aquifers and both large and rapidly varying pore
pressures.
[6] In the following sections we review two existing
models of the hydrologic properties of the Martian crust
[Clifford, 1993; MacKinnon and Tanaka, 1989], before
presenting the model that is developed in this study. This
hydrologic model is then used to test the theory that the
large pore pressures necessary to form the outflow channels
could have been generated beneath a downward propagating freezing front [Carr, 1979].
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the aquifer k (m2; 1 darcy = 1012 m2), the fluid dynamic
viscosity m (Pa s), the acceleration of gravity g, and the
density of water rw:
K¼k
rw g
:
m
ð2Þ
The dynamic viscosity of water is temperature dependent
[Demming, 2002], described by the equation:
mðT Þ ¼ 2:4 105 10248=ðT140KÞ ðPa sÞ:
ð3Þ
For Martian gravity, the permeability can be converted to
hydraulic conductivity values by multiplying by a factor
of approximately 2 106 (m s)1 at 273 K. In this study
we report values of the permeability rather than the
hydraulic conductivity, as the permeability is an intrinsic
property of the aquifer material itself and does not require
scaling to account for changes in gravity, fluid density,
and viscosity. The hydraulic head is a potential term,
which includes both the elevation z of a fluid parcel
above a datum, as well as the aquifer pore pressure Ppore:
h¼
Ppore
þ z:
rw g
ð4Þ
Since we are only interested in the gradient of the head,
it does not matter to what datum the elevation is
referenced, as long as it is done consistently throughout
the aquifer.
[8] Transient flow within an aquifer is governed by the
consolidation equation [Domenico and Schwartz, 1990]:
@h 1
¼ r ð KrhÞ:
@t Ss
ð5Þ
The specific storage, Ss (m1), describes the elastic response
of the aquifer to pressure changes:
Ss ¼ rw g nbw þ baquifer ;
ð6Þ
where n is the porosity and bw and baquifer (Pa1) are the
compressibilities of water and the aquifer matrix respectively. The aquifer matrix compressibility is defined as
baquifer ¼
1 @Vtotal
1 @Vpore
1
@n
¼
:
Vtotal @seff
Vtotal @seff
ð1 nÞ @seff
ð7Þ
2. Governing Equations
[7] Before developing the hydrologic model of the
Martian crust, we first review the relevant governing
equations in order to introduce the physical properties of
interest. Steady state flow within an aquifer is governed by
Darcy’s Law:
q ¼ Krh;
ð1Þ
where q is the volumetric flux vector of water per unit area
or Darcy velocity (m/s), K is the hydraulic conductivity
(m/s), and h is the hydraulic head (m). The hydraulic
conductivity describes the resistance to flow within the
aquifer, and is determined by the intrinsic permeability of
Note that the compression of the aquifer depends upon
the effective stress state (seff), defined as the difference
between the lithostatic and fluid pore pressures, rather than
on the lithostatic pressure alone. Since the compressibility of
the pore space is much greater than the compressibility of the
actual mineral grains, the change in the volume of the rock,
Vtotal, with changing effective stress is essentially equal to
the change in volume of the pore space, Vpore. The final
equality in equation (7) can be arrived at by setting n equal to
Vpore/Vtotal, and @Vtotal equal to @Vpore [Domenico and
Schwartz, 1990].
[9] The porosity of the aquifer can be calculated as a
function of the effective stress, again assuming that the
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mineral grains themselves are essentially incompressible
and the bulk compression is accommodated entirely by a
decrease in the pore volume:
0 seff
1
Z
n seff ¼ ðn0 1Þ exp@ baquifer dsA þ 1
0
¼ ðn0 1Þ exp baquifer seff þ 1
for constant b;
ð8Þ
where n0 is the uncompressed porosity. As will be seen in
the sections that follow, in some cases the compressibility is
a function of the effective stress, and equation (8) must
remain an integral expression.
[10] Thus three essential hydrologic parameters are required to represent an aquifer: the porosity, permeability,
and compressibility. The porosity is important for estimating
the total volume of water that may be present (section 4.5), for
modeling the thermal conductivity of the crust (section 4.5),
and for modeling pressurization by the injection of excess
water into the pore space (section 6.2). The permeability, k, is
essential for modeling both steady state and transient flow
within the aquifer (section 6.2). The compressibility, b,
governs both transient flow and the pressurization of the
aquifer (section 6.2). These parameters are interdependent, as
both the nature and the volume of the pore space determines
the permeability, and the compressibility determines dependence of the porosity and permeability on the effective stress.
Furthermore, as it is likely that extremely large pore pressures
were required to form the outflow channels, it is necessary to
consider the variation of these parameters both with depth and
with changing pore pressure.
3. Previous Studies
[11] MacKinnon and Tanaka [1989] modeled the hydrologic properties of the heavily cratered Martian upper
crust, consisting of a thick megaregolith composed of
breccia overlying the impact-fractured basement rock.
They assumed that the Martian crust is made up of initially
impermeable igneous rock that has been fractured by
impacts. Citing fracture widths resulting from the Danny
Boy nuclear test explosion [Nugent and Banks, 1966], they
represented the deep Martian crust as a basement rock
permeated by fractures with an average aperture of 5 mm
and a spacing of 3 m, resulting in a porosity of 1.5 103
and a permeability of approximately 109 m2. They
suggested that overlying this fractured basement rock is
a 1 – 2 km thick megaregolith of impact ejecta, this based
on Monte Carlo simulations of the ejecta thickness on a
surface with a random distribution of impacts [Woronow,
1988] and on observations of apparent crustal discontinuities in this depth range. The hydraulic properties of this
ejecta layer were modeled using clast size distributions
from the Nevada Test Site [O’Keefe and Ahrens, 1985]
and from the Meteor Crater ejecta. They calculated that
this loosely packed Martian ejecta layer has a porosity
between 0.1 and 0.2 and that the permeability is likely less
than 1014 m2.
[12] While the MacKinnon and Tanaka [1989] model is
a good conceptual representation of the ancient Martian
crust, it does not include the variation of porosity and
permeability with increasing confining pressure or chang-
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ing pore pressure. The permeability of terrestrial materials
decreases by several orders of magnitude at depths of a
few kilometers [Huenges et al., 1997; Manning and
Ingebritsen, 1999]. While fractures can have arbitrarily
large apertures with little to no overburden or if they have
been filled with particulate matter, the aperture of unfilled
fractures decreases with increasing confining pressure. The
fracture apertures measured at the site of the Danny Boy
explosion are much larger than those typically found in the
terrestrial crust, and are more similar to those measured in
recently activated faults. Active motion along a fault is
followed by a period of dramatically increased permeability due to the formation of large aperture fractures within
the fault. However, the increase in aperture and permeability is a temporary effect and the wide apertures are not
stable over geologic time [Gudmundsson, 2001]. This
estimate of the fracture aperture may be representative of
the time period immediately following an impact, but it is
inflated above typical values for stable fractures at shallow
depth by a factor of about 50, and neglects the variation of
aperture with depth [Snow, 1970]. Since the permeability
depends on the cube of fracture aperture, this overestimation of fracture aperture leads to overestimation of the
permeability by a factor of as much as 105. Furthermore,
their model does not include the compressibility of the
aquifer and thus cannot be used to model aquifer pressurization or transient flows.
[13] The most widely cited model of the hydrologic
properties of the Martian crust is that of Clifford [1981,
1993] and Clifford and Parker [2001]. This model assumed
an exponential decrease in porosity with depth due to the
elastic compression of the pore space and was based on the
lunar model of Binder and Lange [1980] scaled to Mars
gravity:
nð zÞ ¼ 0:2 ez=6:5 km
Moon
¼ 0:2 ez=2:8 km
Mars;
ð9Þ
where z is the depth in km below the surface. The Binder
and Lange [1980] model was loosely based on lunar seismic
velocities, which were originally interpreted to suggest
closure of fractures and pores at the 20-km seismic
discontinuity [Keihm and Langseth, 1977]. The lunar
equation above simply fits an exponential decrease in
porosity from 0.2 at the surface to 0.01 at 20 km depth, and
does not attempt to fit the seismic data in between these
values, which shows a discontinuity at the base of the
megaregolith as well as the second discontinuity at 20 km
[Toksoz et al., 1974; Watkins and Kovach, 1973].
[14] Alternatively, Toksoz et al. [1974] suggested that the
20 km seismic discontinuity may correspond to a compositional change rather than the closure of the pore space.
Support for this interpretation of the seismic data came from
analysis of the geoid to topography ratios around lunar
basins, which indicates that the discontinuity is due to a
density interface as would exist between an upper anorthositic crust and a lower noritic crust [Wieczorek and Phillips,
1997].
[15] More recent analyses of the lunar seismic data [Khan
and Mosegaard, 2002; Khan et al., 2000; Longonné et al.,
2003] have called into question the existence of the 20 km
seismic discontinuity altogether. Khan et al. [2000], using
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HANNA AND PHILLIPS: HYDROLOGICAL MODELING OF THE MARTIAN CRUST
Figure 1. Conceptual model of the breccia and fractures
beneath an isolated impact crater. The surface is covered
with a 2 km thick megaregolith (gray). Impacts produce
both breccias (gray) and fractures (white) beneath the crater.
an updated data set of all locatable moonquakes, found a
steady increase in the P wave velocity from the base of the
megaregolith at a depth of 1 km, down to the base of the
crust at a depth of 40 km. They found no evidence for an
intracrustal seismic discontinuity at 20 km. Longonné et al.
[2003] found a 30 km thick crust, with increasing seismic
velocity with depth. Looking at the VP/VS ratio, Longonné
et al. [2003] found evidence that the crust is heavily
fractured throughout its thickness, and that the fractures
may even extend somewhat deeper than the 30 km crustal
thickness. However, it is not possible to calculate hydrologically useful parameters such as fracture frequency and
aperture based on seismic data alone, as the seismic wave
velocity is affected by a number of unknown parameters
including the along-strike dimension and the aspect ratio of
the fractures [O’Connell and Budiansky, 1974]. In addition,
the elastic properties, and thus the effect on seismic wave
velocities, of simple spherical pores and elongated fractures
differ substantially [Walsh, 1965], complicating the matter
further when both pores and fractures are present.
[16] The proposed elastic decrease in porosity with depth
does not correlate with the low compressibility actually
measured for the lunar breccias [Warren and Trice, 1975].
The demonstration of substantial crustal permeability at
depths of 9 km on the Earth [Huenges et al., 1997],
corresponding by a simple pressure scaling to a depth of
24 km on Mars and 56 km on the Moon, contradicts the
interpretation of the elastic closure of the lunar pore space at
20 km. In section 4.5, we demonstrate that the closure of
pore space is more likely caused by either plastic deformation or pressure solution.
[17] The Clifford [1993] study did not predict the permeability based on the model of porosity, since there is no
unique relationship between porosity and permeability in a
fractured porous medium. Clifford and Parker [2001]
modeled the permeability of the Martian crust after the
study by Manning and Ingebritsen [1999] of the average
permeability in the terrestrial crust as a function of depth,
which they again scaled to Mars gravity:
logðk Þ ¼ 14 3:2 logð z gMars =gEarth Þ
¼ 12:65 3:2 logð zÞ;
ð10Þ
where z is the depth in km, and k is the permeability in m2.
The Manning and Ingebritsen [1999] model was based on
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indirect evidence for the permeability obtained from heat
flow data and metamorphic reaction rates.
[18] The permeability in the Earth’s crust is influenced
by a number of different factors, including rock type,
fracture frequency, fracture aperture, heat flow, degree of
metamorphism, age, and tectonic history. A simple gravitational scaling of the terrestrial permeability function to
Mars is likely an oversimplification. For the same reason,
this model also does not allow for the variation of
permeability with changing pore pressure. Note that as
the depth approaches zero, or alternatively as the pore
pressure approaches the lithostatic pressure, equation (10)
would predict infinite permeability. This unphysical result
occurs simply because the model was intended only to
apply to greater depths within the Earth’s crust. Thus the
Manning and Ingebritsen [1999] model is of only limited
applicability and does not allow for the modeling of
shallow aquifers or deep aquifers with large pore pressures, both of which are integral parts of the Martian
hydrologic system.
[19] Another drawback of these models is that the
parameters of interest were not modeled self consistently.
The porosity and permeability models were based on
hydrologic models of different geologic environments on
different planets. Furthermore, they did not consider the
compressibility of the crust, thus precluding the modeling
of time-dependant flows. What is needed is a single selfconsistent and physically realistic model of the porosity,
permeability, and compressibility of the Martian crust for
any combination of depth and pore pressure.
4. Megaregolith Aquifer Model
4.1. General Characteristics
[20] We assume, as a starting condition, that the crust
of Mars at the time of its formation was composed of a
crystalline basement rock [Harper et al., 1995], which
was subsequently modified by impacts (Figure 1). On the
basis of the effect of a single impact on the porosity and
fracture frequency induced in the host rock, it should be
possible to calculate the hydraulic properties of a planetary surface with a given crater distribution. Since the
southern highlands of Mars are near crater-saturation, any
preferential radial or circumferential orientation of the
impact-induced damage should average out and the
resulting porosity, permeability and compressibility are
considered to be isotropic. We assume that the impacts
during and after the period of heavy bombardment
resulted in a heavily fractured and partially brecciated
basement overlain by a megaregolith breccia layer of
consolidated impact ejecta [Clifford, 1981; MacKinnon
and Tanaka, 1989; Woronow, 1988]. For Noachian-aged
surfaces, the thickness of this upper megaregolith layer
would likely be between 1 and 3 km [Hartmann et al.,
2001; MacKinnon and Tanaka, 1989; Ward, 2002; Woronow,
1988]. Since cratering and megaregolith production are
contemporaneous processes, the megaregolith is subject to
impact modification as well. This megaregolith layer is
capped by a thin (tens of m up to 1 km) layer of aeolian
and aqueous sediments [Malin and Edgett, 2000b], Vikingtype ‘‘soil’’ [Moore et al., 1977], and unconsolidated regolith
from the perpetual impact gardening [Hartmann et al.,
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HANNA AND PHILLIPS: HYDROLOGICAL MODELING OF THE MARTIAN CRUST
2001; Shkuratov and Bondarenko, 2001; Watkins and
Kovach, 1973]. However, this upper thin veneer of
materials will not be hydrologically active under the cold
climate conditions that have persisted for much of Mars’
history.
4.2. Impact-Induced Breccias
[21] As impact-generated breccias are thought to be a
significant component of the ancient heavily cratered
portions of the Martian crust, it is thus necessary to
estimate the distribution, abundance, and hydraulic properties of breccias in Martian aquifers. As previously
stated, the accumulation of impact ejecta on the Martian
surface likely produced a megaregolith breccia layer
between 1 and 3 km thick. Furthermore, breccias are
produced in the bedrock beneath craters both during the
initial passage of the shockwave after impact, and during
the subsequent decompression and modification phases
[Dressler et al., 1996]. In this latter stage, large breccia
bodies and anastamozing breccia dykes form as blocks of
bedrock slide past one another during the modification of
the transient cavity, providing a mechanism for the
acoustic fluidization of the target material [Ivanov,
2002; Melosh and Ivanov, 1999].
[22] The distribution and abundance of breccia beneath
impact craters can be inferred from a combination of
gravity studies and drill core data. Early studies of
terrestrial impact craters revealed that they are often
associated with negative gravity anomalies [Innes, 1961;
Pilkington and Grieve, 1992]. In a study of young lunar
craters, Dvorak and Phillips [1977] found that the gravity
data was best explained by a brecciated layer extending
to a depth of one third of the crater diameter and laterally
to the crater rim, with a density contrast of 0.3 g/cm3.
The deep drilling project into the 40 km diameter
Puchezh-Katunki impact crater found that the crust beneath
the crater consists of blocks of bedrock, 100 to 400 m
across, separated by zones of breccia [Ivanov et al., 1996;
Kocharyan et al., 1996]. The average ratio of breccia to
competent rock was 1:3 down to a depth of about 4 km.
Combining these two lines of evidence, we suggest that the
crust beneath large craters is composed of a mixture of
breccia and bedrock, in a ratio of 1:3, down to a depth of
1/3 the crater diameter.
[23] The hydraulic properties of breccias can be estimated on the basis of observations of terrestrial and lunar
breccias. Porous fault breccias have porosities of around
0.1 [Antonellini and Mollema, 2000]. MacKinnon and
Tanaka [1989] calculated that Martian ejecta should have
porosities in the range of 0.1 to 0.2. The porosities of
lunar breccia samples lie in the range of 0 to 0.4 with a
mean of 0.17, and with the most representative sample of
highlands breccia having a porosity of 0.15 [Warren and
Rasmussen, 1987]. We adopt a value of 0.15 as representative
of the uncompressed porosity of breccias, including both
lithified impact ejecta and breccias intermixed with the
bedrock at greater depth.
[24] Laboratory studies of the compressibility of fault
breccia yield values of approximately 109 Pa1 [Seront
et al., 1982]. Similarly, the compressibility of lunar
breccias is approximately 109 Pa1 at low effective
stresses, while at higher effective stresses it can be fit
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by a power law with a change in slope at 10 MPa
[Warren and Trice, 1975]:
bbrec ¼ c1 sceff2
c1 ¼ 7:94 1010
for 0:1 < seff < 10 MPa
c1 ¼ 2:81 109
for 10 seff 1000 MPa
c2 ¼ 0:1
c2 ¼ 0:65
for 0:1 < seff < 10 MPa
for 10 seff 1000 MPa;
ð11Þ
where the effective stress is in MPa and the compressibility
is in Pa1. The breccia porosity as a function of the effective
stress can then be calculated using equations (8) and (11).
[25] Breccias have low permeability relative to their porosity due to the poor degree of sorting and the presence of
small clast sizes. Gudmundsson [2001] measured the permeability of fault breccias to be in the range of 1017 to 1020 m2,
much lower than the upper limit of 1014 m2 calculated by
MacKinnon and Tanaka [1989]. As will be seen in the next
section, the permeability of intact breccia is orders of magnitude lower than the permeability of the superimposed fracture
network, and thus can be neglected. Both seismic observations of the lunar megaregolith [Watkins and Kovach, 1973],
as well as geomorphic observations of fault scarps in the top
kilometer or so of the Martian megaregolith suggest that the
breccia is likely a coherent, lithified unit. We assume that
breccia is subject to impact fracturing to the same degree as
competent rock, so fractured breccia is treated in the same
manner as fractured bedrock with regards to the permeability.
The observation of hydraulically conducting fractures within
the breccia filled cores of fault zones [Gudmundsson et al.,
2001] supports this assumption.
[26] In summary, we assume that the heavily cratered
Noachian-aged crust is composed of a 2 km thick megaregolith overlying the partially brecciated basement rock, in
which the ratio of breccia to bedrock is 1:3. The breccias in
the upper megaregolith and intermixed within the bedrock
are assumed to have similar hydraulic properties, with an
uncompressed porosity of approximately 0.15, a compressibility given by equation (11), and negligible permeability.
The permeability within the breccia units will be determined
by the presence of the superimposed fracture network, if one
exists.
4.3. Impact-Induced Fractures
[27] The permeability resulting from the presence of
fractures beneath an impact crater is determined by the
fracture frequency (N, expressed in terms of the number of
fractures per unit distance) and the fracture aperture (b), as
described by the cubic law [Domenico and Schwartz,
1990]:
kfrac ¼
Nb3
:
12
ð12Þ
The fracture porosity in the host rock can be calculated as
the product of the fracture frequency and the fracture
aperture:
nfrac ¼ N b:
ð13Þ
Thus, to calculate the impact-induced permeability and
fracture porosity, it is necessary to estimate the frequency
and aperture of fractures beneath a crater.
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[28] Seismic data indicate that the zone of fractures
around a crater with diameter D extends radially a
distance of D/2 beyond the crater rim and down to a
depth of D/2 [Ackermann et al., 1975]. This is supported
by both impact experiments [Ahrens and Rubin, 1993]
and numerical modeling studies [Ivanov, 2002]. The
fracture frequency in the 218 m deep drill hole in the
Lappajarvi crater in Finland [Kukkonen et al., 1992] is
approximately 20 m1. Similarly, the fracture frequency
in outcrops of the intensely fractured and shattered
bedrock in the Acraman crater in Australia is between
20 and 100 m1 [Williams, 1994]. These values are
significantly greater than the fracture frequency of typical
terrestrial crust, which lies in the range of 0.1 to 5 m1
[Seeburger and Zoback, 1982], but are roughly consistent
with the fracture frequency of about 10 m1 in active
fault zones [Gudmundsson et al., 2001]. The increased
fracture frequency is in agreement with the observation of
a large zone of crushed rock in the vicinity of underground nuclear explosions in which the density of joints
increases up to hundreds of times above the initial value
[Kocharyan et al., 1996]. For this work we adopt a
fracture frequency of 20 m1.
[29] A number of both theoretical and experimental
studies have been performed on the compression of
fractures. Experimental studies measure the change in
aperture and permeability with changing confining pressure for small samples of actual fractures [Cook, 1992].
Theoretical studies, on the other hand, produce complicated integral formulations for the aperture as a function of pressure, based on the statistical distribution of
asperities along the fracture faces [Brown and Scholz,
1986]. The theoretical studies base the geometry of the
fracture face on measurements of small samples of
actual fractures, thus both the experimental and theoretical approaches rely on laboratory-scale fracture samples. However, it has been demonstrated that the
permeability of the Earth’s crust is very strongly scale
dependant [Brace, 1984]. Permeability on the scale of a
laboratory sample is often orders of magnitude less
than the large-scale permeability in the same region.
Furthermore, it has been demonstrated that flow within
fractures is focused along discrete channels between the
fracture faces [Wang et al., 1988]. Hence the fractallike nature of the fracture face topography and the
nonuniformity of the flow within fractures make it
unlikely that the hydraulic behavior of small-scale
laboratory samples of natural fractures will be representative of the average behavior of large-scale in situ
fractures.
[30] We model fracture apertures using a novel approach in which we use data on near-surface fracture
apertures to calculate the fracture aperture and compressibility at low effective stresses. We then extrapolate these
values to high effective stresses using data on the
permeability and fracture frequency at greater depths.
[31] Snow [1970] calculated the effective fracture apertures in the near-surface on the basis of permeability and
fracture frequency measurements in wells to depths in
excess of 100 m in a variety of rock types, and found
that the apertures decrease regularly with depth and are
essentially independent of host rock type. We plot these
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Figure 2. Fracture aperture as a function of depth for a
variety of rock types (data of Snow [1970]).
data together on one graph (Figure 2), and fit the data
with an exponential function:
1
bð zÞEarth 2 104 ðmÞ e0:0087ðm Þz ;
ð14Þ
where b and z are both expressed in meters. The exponential
decrease in aperture implies a constant compressibility of
the fractures in the near surface. The fracture compressibility is then calculated as
bfrac;0 ¼
brock ¼
1 dVfrac
1
dbð zÞ
¼
2:9 107 Pa1
Vfrac dseff
rr g bð zÞ dz
1
Vrock
dVrock
1 dVfrac
¼
¼ bfrac Nfrac bfrac ;
dseff
Vrock dseff
ð15Þ
where bfrac,0 is the compressibility of an individual fracture
under low effective stresses, brock is the whole rock
compressibility due to the presence of the fractures, rr is
the rock density, and Vfrac is the volume of the fracture.
[32] We estimate fracture apertures at depths greater than
100 m on the Earth based on permeability data by assuming
a typical fracture frequency. Seeburger and Zoback [1982]
measured fracture frequencies to depths in excess of 1 km in
three geologically distinct areas. On the basis of their data,
we consider a range of 0.1 to 1 m1 as being representative
of the fracture frequency of the Earth’s crust at depths of a
kilometer or more. Permeabilities obtained in the KTB drill
hole of the German Continental Deep Drilling Program are
on the order of 1016 to 1017 m2 for depths ranging from
0.5 to 5 km [Huenges et al., 1997]. Using this range in
permeabilities with the above range in fracture frequencies,
equation (12) allows us to calculate the typical fracture
aperture at large depths to be on the order of 105 to 5 106 m. These minimum effective apertures are in agreement with laboratory experiments on the compression of
fractures [Cook, 1992]. While an aperture of 10 mm seems
exceptionally small to be considered an open fracture, it
must be remembered that this is an effective hydraulic
aperture. The actual fracture would have a larger aperture
in places and be completely closed at the contact points
between the two faces.
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equation (16) depend only upon the effective stress state
of the aquifer, making these results directly applicable to
Mars.
Figure 3. Conceptual diagram of the compression of a
fracture. Individual contact points are drawn as (left)
asperities on the fracture surface, or (right) springs,
demonstrating the increased resistance to further compression
as more asperities come into contact.
[33] Fracture compressibility must decrease markedly
with depth, approaching zero so as to agree with the
relatively constant permeability at large depths found by
Huenges et al. [1997]. This can be justified conceptually by
considering that on the microscopic level fracture surfaces
have a fractal-like roughness [Wang et al., 1988]. Thus the
aperture is just an average value, while the fracture is held
open by the asperities on the fracture surface. As the
fracture is compressed, the opposing faces come into
contact in more places and the resistance to further compression is increased proportionately (Figure 3). We apply
this conceptual model by assuming a simple exponential
decrease in the fracture compressibility as a function of
confining pressure, and fitting it to the surface compressibility and the inferred minimum fracture aperture at large
depths:
bfrac seff ¼ bfrac;0 exp seff =sfrac;0
2 seff
3
Z
bfrac seff ¼ b0 exp4
bfrac seff ds5
ð16Þ
0
h
i
¼ b0 exp sfrac;0 bfrac;0 eseff =sfrac;0 1 ;
where sfrac,0 is the scale stress of the exponential decrease
in fracture compressibility. Assuming a minimum fracture
aperture of 105 m at large depth, we find that sfrac,0 is
approximately 10.3 MPa. This aperture function fits both
the near surface aperture data as well as the deep
permeability data. The general character of the plot of the
fracture aperture as a function of effective stress in this
study (Figure 4) agrees well with both the theoretical and
laboratory studies, while avoiding the limitations of smallscale samples. This approach, while more empirical in
nature, is likely a better representation of the net behavior of
real fractures within the crust.
[34] In summary, we assume that heavily cratered crust
has a fracture frequency of approximately 20 m1. The
fracture apertures decrease exponentially with increasing
effective stress at low values of the effective stress, from
an uncompressed value of approximately 2 104 m.
Under conditions of high effective stress, the fracture
apertures plateau at a value of approximately 105 m,
while the fracture compressibility decreases to zero. The
fracture aperture and compressibility as expressed in
4.4. Megaregolith Aquifer Model Synthesis
[35] We use the above description of the hydrologic
properties of impact-induced breccias and fractures to
synthesize an aquifer model based on the record of
impacts on the surface. As stated earlier, we assume that
the top 2 km of the crust is composed of a lithified and
fractured breccia. Beneath this megaregolith, the crust is
composed of an equally fractured mixture of bedrock and
breccia. We assume that the effects of superimposed
impacts do not add, as preexisting fractures and faults
would likely be reactivated by subsequent impacts. Thus
we assume that the fracture frequency and breccia distribution beneath the crater-saturated Noachian-aged crust is
the same as that found beneath a single isolated crater.
Since the largest fraction by area of the crater population
on Noachian aged surfaces is composed of craters with
radii in excess of 15 km, there will likely be no
significant decrease in the fracture frequency and breccia
abundance in the top 15 km of the crust. As will be seen
in section 4.5, this likely constitutes the bulk of the
hydrologically active crust of Mars. Crater saturation will
also lead to an averaging out of any preferred radial and
circumferential orientations of the impact-induced damage
beneath individual craters. It is thus assumed that cratersaturated terrains are underlain by a uniform and isotropic
distribution of fractures and breccia to a depth of 15 km
or more, with a breccia fraction of 0.25 and a fracture
frequency of 20 m1. The hydraulic properties of less
densely cratered terrains could be calculated using the
crater density, though at low crater densities the assumptions of uniform and isotropic hydraulic parameters would
break down.
[36] The porosity in the crust is largely a result of the
presence of breccias, but it also includes smaller components due to the fracture porosity and the primary porosity
of the crystalline rocks:
ntotal z; seff
0 seff
1
#
Z
¼ fbrec ð zÞ n0;brec 1 exp@ bbrec dsA þ 1
"
0
þ Nfrac bfrac seff þ ð1 fbrec ð zÞÞ
n0;primary 1 exp bprimary seff þ 1 ;
ð17Þ
where fbrec is the breccia fraction within the crust as a
function of depth (defined as 1.0 in the megaregolith, and
0.25 in the partially brecciated bedrock at greater depths),
n0,primary is the uncompressed bedrock primary porosity
(assumed to be 0.02 [Domenico and Schwartz, 1990]),
bprimary is the compressibility of the primary pore space in
the bedrock (assumed to be 1010 Pa1 [Domenico and
Schwartz, 1990]), and all other parameters are as previously
defined. The permeability is determined by the fracture
frequency and aperture as described by equations (12) and
(16). The net compressibility of the crust depends on the
fracture compressibility, the fracture frequency, the compressibility of the breccia, the volumetric breccia fraction in
the crust, the primary pore space compressibility in the rock,
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Figure 4. Hydrologic parameters of the Martian crust based on the impact generation of fractures and
breccia within the megaregolith (solid black line), for the sandstone model (gray line) and for the model
of Clifford [1993] and Clifford and Parker [2001] (dashed black line). The estimated one-sigma
uncertainty in the megaregolith aquifer model is represented by the shaded gray region.
and the compressibility of the water within the pore space
(bwater):
btotal ¼ bfrac Nfrac bfrac þ fbrec bbrec þ ð1 fbrec Þ bprimary
þ n bwater :
ð18Þ
A summary of all parameters used in the equations is
presented in Table 1.
[37] The megaregolith aquifer model of this study is
presented in Figure 4 alongside the model of Clifford
[1993] and Clifford and Parker [2001], as well as the
sandstone model to be developed in section 6. The parameters for the megaregolith model in Figure 4 are calculated
on the basis of the assumption of hydrostatic pore pressure,
though similar plots can be produced for any amount of
excess pore pressure.
[38] In an attempt to quantify the uncertainty in the
megaregolith hydrologic model, we calculate the likely
range of parameter space using a Monte Carlo analysis.
We consider the likely range of values for the key input
parameters for which the uncertainty can be estimated
(Table 1). Note that for the fracture model, uncertainty is
considered in the uncompressed fracture aperture and fracture frequency only. The fracture compressibility function
arrived at above is constrained by the minimum fracture
aperture at great depth, and thus is not independent of the
assumed uncompressed aperture. The adopted range in
uncompressed fracture aperture leads to the likely range in
minimum fracture aperture discussed above without varying
the fracture compressibility function. We represent the uncertainty in the breccia compressibility function expressed in
equation (11) by a scaling factor ranging from 0.3 to 3,
encompassing the range in the data of Warren and Trice
[1975]. The range in values for each parameter is assumed
to correspond to the two-sigma variation. These parameters
are then varied normally using a random number generator, and the mean values and standard deviations are
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Table 1. Summary of Parameters Used in Modelsa
Parameter
Symbol
Value
Uncompressed fracture aperture
Surface fracture compressibility
Scale-stress of exponential decrease in fracture compressibility
Fracture frequency
Regolith thickness
Breccia fraction within crust
Bedrock compressibility
Water compressibility
Uncompressed bedrock porosity
Uncompressed breccia porosity
Rock density
Water density
b0
bfrac,0
sfrac,0
Nfrac
zreg
fbrec
bprimary
bwater
n0,primary
n0,brec
rrock
rwater
2 104 m
2.9 107 Pa1
10.3 MPa
20 m1
2 km
1.0 for z < zreg, 0.25 for z > zreg
1 1010 Pa1
4.4 1010 Pa1
0.02
0.15
2700 kg m3
1000 kg m3
Range
1 – 3 104 m
10 – 30 m1
1 – 3 km
0.15 – 0.35
0.5 – 3 1010 Pa1
0.05 – 0.25
a
The likely range in values is given for the parameters varied in the Monte Carlo analysis.
calculated for the fracture aperture, porosity, permeability
and compressibility as a function of depth. Values of the
permeability and compressibility are varied and averaged
logarithmically. The one-sigma variations in the hydraulic
parameters are represented in Figure 4 by the shaded gray
regions.
4.5. Closure of Pore Space and the Base of the Aquifer
[39] Previous studies [Clifford, 1981, 1993] emphasized
the depth of the base of the aquifer as a means of
calculating the total volume of fluid that could be
contained within the pore space of the Martian crust,
and thus constraining the total water storage capacity of
the crust and the amount of water available for surface
processes. Clifford [1993] assumes that it is the elastic
closure of the pore space with increasing pressure that
determines the base of the aquifer. However, using the
actual compressibilities of breccias and fractures, we find
that a significant amount of pore space and permeability
extends to depths much greater than the 8 km depth
assumed in that study. Considering elastic compression
alone, the porosity decreases slowly with depth beyond
the base of the megaregolith, and will remain at values of
around 0.04 to 0.03 until a depth is reached at which the
impacts into the surface had little effect. Similarly,
fracture apertures reach a minimum value of approximately
105 m, and thus continue to be hydraulically conducting
even under conditions of extremely large overburden
pressures.
[40] Instead, we propose that an upper limit to the
thickness of aquifers on Mars is imposed by the rheology
of the rocks. The brittle to ductile transition is defined as the
depth at which the stress required to form a new fracture is
equal to the frictional resistance on existing fractures
[Byerlee, 1968]. The ductile flow in this case is still
cataclastic in nature, and is not relevant to the closure of
the pore space. The brittle to plastic transition (BPT),
which is more relevant to the closure of pore space and
fractures within an aquifer [Brace and Kohlstedt, 1980],
occurs approximately when the differential stress necessary for plastic flow is equal to the effective confining
pressure [Kohlstedt et al., 1995]. We calculate the maximum differential stress that could be supported in the
Martian crust at the end of the heavy bombardment using
a combined thermal and rheological model of the Martian
crust based on the megaregolith model developed above.
[41] The thermal conductivity of the Martian crust is
calculated for both dry and wet conditions. For dry breccias,
the thermal conductivity is given by
k ¼ 2:0 en=n0 W m1 K1 ;
ð19Þ
where k (W m1K1) is the thermal conductivity, n is the
porosity, and n0 is 0.0738 [Warren and Rasmussen, 1987].
For saturated breccias, the thermal conductivity is calculated
by the harmonic mean of the thermal conductivities of rock
and water:
k¼
kr kw
;
n kr þ ð1 nÞ kw
ð20Þ
where kr and kw are the thermal conductivities of rock and
water, taken to be 3 W m1K1 and 0.57 W m1K1
respectively [Demming, 2002]. In the partially brecciated
basement crust, the thermal conductivity is likely intermediate between the harmonic and arithmetic means of the
conductivities of the breccia component and solid rock. For
the saturated crust, the harmonic and arithmetic means yield
essentially the same result due to the similar thermal
conductivities of rock and saturated breccia. At depths
greater than the depth of the BPT, it is assumed that the pore
space has closed and the thermal conductivity is set equal to
that of solid rock.
[42] The heat flux into the base of the lithosphere at the
end of the heavy bombardment is taken to be 65 mW m2
[Hauck and Phillips, 2002], and the surface temperature is
set to be 273 K on the basis of the assumption of a warmer
and wetter early Mars. If surface temperatures were cooler,
as is suggested by some [e.g., Squyres and Kasting, 1994],
the brittle to plastic transition would be pushed deeper
within the crust, increasing the thickness of potential
Martian aquifers.
[43] The rheology of the Martian crust is modeled after
studies of the rheology of diabase in dislocation creep:
e_ ¼ A sn expðEa =RT Þ;
ð21Þ
where A, n, and Ea are constants that take on different
values for dry [Mackwell et al., 1998] or wet [Caristan,
1982] diabase. For the case of a dry crust, it is clearly
appropriate to use the rheology of dry diabase, but it is
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Figure 5. Models of yield stress, temperature, and thermal conductivity for the Martian crust at the end
of the heavy bombardment, assuming a surface temperature of 273 K and a heat flux of 65 mW/m2 for
(top) dry and (bottom) saturated pore space. Shown on the stress plots are (1) the effective stress, seff, the
lithostatic pressure minus the pore pressure, and (2) and the ductile yield stress for diabase under various
conditions and a strain rate of 1015 s1. For the dry case, only the dry diabase rheology is used
[Mackwell et al., 1998], and thermal conductivities of rock/breccia mixtures are calculated using the
harmonic (h) and arithmetic (a) means. For the wet case, both dry and wet [Caristan, 1982] diabase
rheologies are used, and thermal conductivities of rock/breccia mixtures are calculated with the harmonic
mean. The intersection of seff with the ductile yield stress defines the brittle-plastic transition (BPT;
indicated by arrows) [Kohlstedt et al., 1995], here used to define the depth of pore space closure.
unclear which rheology is more appropriate for the case of
water saturated pore space. For pore pressures greater than
the hydrostatic pressures, the water fugacity is likely to be
large and the wet rheology may be appropriate. However,
experiments on wet diabase experienced partial melting
upon release of the water, which would have resulted in an
overly weak rheology [Mackwell et al., 1998]. Thus the
rheologies of both dry and wet diabase are plotted for the
case of the saturated crust, while only the dry rheology is
plotted for the case of unsaturated crust.
[44] Figure 5 shows that the BPT occurs between depths
of 6 and 10 km for the dry crust case, and between depths of
17 and 26 km for the case of saturated crust. The 26 km
depth is likely an overestimate, as the dry rheology assumed
is probably stronger than the wet Martian crustal rocks.
Furthermore, even for the case of a wet early Mars, an upper
dry layer of regolith may have formed an insulating blanket
on the surface, thus decreasing the depth to the BPT.
However, hydrothermal circulation of groundwater in the
Martian crust [Travis et al., 2003] would lead to a substantial advective heat flux, thereby decreasing the conductive
temperature gradient and increasing the depth to the BPT.
Similarly the 6 km depth is likely an underestimate, as it is
unlikely that no water existed in the crustal pore space on
early Mars. The unrealistic assumption of a fully dry
Martian crust results in excessively low thermal conductivities and high temperatures at shallow depth, leading to
partial melting at depths as shallow as 30 km under
Noachian conditions. The approximate range of likely
depths for the BPT at the end of the heavy bombardment,
and thus the upper limit for the thickness of ancient Martian
aquifers, is between 10 and 20 km. However, in regions of
continued geologic activity and beneath young impact
craters it is possible that open pore space has been created
at greater depths later in Mars history when the BPT was
pushed deeper by the lower surface temperatures and
decreased heat flux.
[45] While the brittle to plastic transition imposes an
upper limit on the thickness of aquifers on Mars, other
processes can act to close off the pore space at shallower
depths. Terrestrial observations demonstrate the importance
of pressure solution in the closure of both fractures and
primary pore space in the presence of a fluid [Renard et al.,
2000]. In short, this results from preferential dissolution at
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the contact points of grains and fracture surfaces, followed
by preferential precipitation in the void spaces. This is a
time dependent process that is strongly sensitive to the
temperature, pressure, rock composition, and the microscopic geometry of both the contacts and void spaces.
Furthermore, fractures and fault breccias exhibit markedly
different behaviors with regards to their susceptibility to
pressure solution. The process is poorly constrained in
terrestrial systems, and cannot be reliably applied to Mars.
Additionally, hydrothermal circulation within the crust
[Travis et al., 2003] could facilitate dissolution and mineral
precipitation, closing off the pore space and emplacing
veins within the fractures.
[46] Claims regarding the total water storage capacity of
the Martian crust will be limited by this uncertainty in the
depth of closure of the pore space. We use the megaregolith
model above to estimate the total pore volume of the
Martian crust for a range of aquifer thicknesses. For aquifer
thicknesses of 5, 10, and 20 km we calculate total pore
volumes of 6.1, 9.8, and 17 107 km3 respectively. The
pore space present in basaltic aquifers within the Tharsis
rise and the northern plains must also be considered. The
total volume of Tharsis basalts has been estimated at 3 108 km3 [Phillips et al., 2001]. Taking an average basalt
porosity of 0.1 (see section 5.1), this would give a total pore
volume of 3 107 km3. For a more conservative estimate,
we also consider cases in which there is significant porosity
only in the top 2 to 5 km of the crust in this region, as could
result from closure of the pore space at depth or if a
significant amount of low-porosity volcanic intrusions contributed to the Tharsis rise, leading to total pore volumes of
2.5 to 6.3 106 km3. Representing the northern plains as a
1 km thick layer of porous basalt, we find a total pore
volume of 4.8 106 km3 above the underlying megaregolith. Using the above ranges in values, we get low and high
estimates of the total pore volume of 6.8 107 and 2.0 108 km3, with an intermediate estimate of 1.1 108 km3.
These values are in agreement with the estimates of Clifford
[1981], despite the differences in the hydrologic model
used. However, we again caution the reader with respect
to the great uncertainties in these estimates.
5. Alternative Aquifer Types
5.1. Basaltic Aquifer Model
[47] While the megaregolith aquifer model is likely
representative of much of the Noachian-aged highlands,
the younger surfaces that predominate in other areas of the
planet have not been significantly modified by impacts. The
Tharsis and Elysium volcanic provinces are composed of
thick sequences of basalt flows, the upper portions of which
are young enough to have escaped the heavy bombardment
of the early Noachian era. The northern plains, as well as a
number of other areas across the planet, are likely composed
of layers of basaltic lava flows and sediments overlying
more ancient cratered terrain beneath [Frey et al., 2002;
Head et al., 2002].
[48] Terrestrial basaltic aquifers are characterized by both
high porosity and high permeability. While there is great
variability in the hydraulic properties of terrestrial basalts, it
is likely that the average properties of terrestrial and Martian
basalts are similar. Over small spatial scales, it is necessary to
E01004
model basaltic aquifers using a stochastic approach to represent the significant heterogeneity of the aquifers [Welhan et
al., 2002]. However, over the large spatial scales commonly
of interest on Mars, this lateral heterogeneity averages out and
it is appropriate to use the bulk properties.
[49] The hydraulic properties of the Snake River Plains
aquifer summarized in studies by Gego et al. [2002] and
Welhan et al. [2002] are reviewed here. A basaltic aquifer is
made up of a large number of individual lava flows,
typically on the order of 1 to 10 meters thick. Each flow
is composed of a thick layer of massive basalt (
84% by
volume), overlain by a thinner interflow zone (
12% by
volume) [Gego et al., 2002]. These interflow zones are both
very porous and heavily fractured, as a result of thermal
cooling of the outer surface of the flow and rotational
stresses at the lava flow front. The interflow zones have
an average porosity of 0.22 and an average permeability of
approximately 108 to 1010 m2. The intervening layers of
massive basalt, on the other hand, have an average porosity
of 0.09 and permeability of approximately 1011 to 1013 m2.
The average porosity of a basaltic aquifer is then calculated to
be 0.10. The average horizontal and vertical permeabilities
can be calculated using the arithmetic and harmonic means,
yielding values of approximately 109 to 1011 m2 and 1011
to 1013 m2 respectively. If there is sufficient time between
individual eruptions, a layer of sediments will accumulate
above each lava flow, which on Mars could include impact
ejecta as well as aeolian and fluvial sediments. These sediments can act to further increase the porosity and permeability, or alternatively they may fill the fractures in the
underlying interflow zone and result in a net decrease in the
porosity and permeability.
[50] There is not enough data to accurately constrain the
behavior of basaltic aquifers under varying conditions of
confining stress and pore fluid pressure, making the basaltic
aquifer model of limited applicability. While some of the
permeability is due to simple fractures, much of it is due to
the presence of larger interconnected cavities within the
interflow zones. The permeability is likely less sensitive to
the effective stress than was found for the megaregolith
model due to the presence of these larger cavities, though it
is unlikely that the high values measured at the surface
persist to depths of several kilometers as some compression
is inevitable.
[51] In a study of basaltic aquifers in the Oregon
Cascades, Saar and Manga [2004] modeled the permeability as a function of depth based on a number of indirect
approaches, including spring discharges, thermal profiles,
magmatic intrusion rates, and seasonal seismicity. They
represent the permeability as following an exponential
decrease with depth in the top 800 m, followed by a power
law relationship similar to that of Manning and Ingebritsen
[1999] at greater depths. The horizontal permeability ranges
from 109 to 1013 m2 at the surface, to 1015 to 1018 m2
at a depth of 10 km. They propose that the decrease in
permeability with depth is exclusively due to mineral
precipitation, though we would suggest that the elastic
compression of the fractures plays a significant role as well.
Manga [2004] suggests that lower water to rock ratios on
Mars would lead to negligible mineral precipitation and the
maintenance of the high surface permeability values even at
great depth. However, as discussed earlier, pressure solution
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and hydrothermal circulation are likely important in the
closure of pore space and the decrease in permeability with
depth on Mars. While the Saar and Manga [2004] study
sheds some light on the variation of permeability with depth
in basaltic aquifers, the methods of calculating the permeability were indirect and there are large uncertainties in the
numbers. There still remains much work to be done to fully
understand the dependence of the permeability, porosity,
and compressibility on the depth and pore pressure in
basaltic aquifers on both Earth and Mars.
particles [Nelson, 1994]. It is commonly assumed that the
permeability is proportional to the log of the porosity
[Archie, 1950; Demming, 2002], but no one relationship
between permeability and porosity can be said to be
representative of all sandstones or shales. On the basis of
the data of Nelson [1994], we represent the log of the
permeability as being proportional to the porosity:
5.2. Sedimentary Aquifers
[52] A number of studies have emphasized the possibility
of extensive sedimentary deposits on Mars [Goldspiel and
Squyres, 1991; Malin and Edgett, 2000b]. Sedimentary
rocks can display a wide range of hydraulic behaviors,
and a comprehensive treatment of the topic is beyond the
scope of the present study. We here aim only to outline the
basic properties and behavior in such a way as to allow for
the production of a generalized model.
[53] The porosity of sandstone at the surface is generally
in the range of 0.05 to 0.3 [Domenico and Schwartz, 1990],
and is commonly modeled as decreasing exponentially with
depth [Athy, 1930; Chapman et al., 1984]:
where k is the permeability in m2, and n is the porosity. The
porosity, permeability, and compressibility of the sandstone
aquifer model are represented in Figure 4 alongside the
megaregolith aquifer model. An important difference
between the sandstone and megaregolith aquifers is now
apparent. In the megaregolith model the permeability is
dependent on the elastic closure of the fractures and scales
directly with the effective stress state, whereas in the
sandstone model the porosity and thus the permeability are
much less sensitive to the effective stress state.
nð zÞ ¼ n0 ez=z0 ;
ð22Þ
where n0 is the surface porosity and z0 is the scale depth.
Chapman et al. [1984] used values of 0.25 for n0, and 3 km
for z0. It is significant that this exponential decrease in
porosity cannot be attributed to the simple elastic compression of the pore space. Laboratory studies indicate that the
porosity in sandstone decreases elastically much more slowly
with increasing effective stress than would be predicted on
the basis of the observed variation of the porosity with depth
[Demming, 2002; Neuzil, 1986]. The rapid decrease in
porosity with depth observed in sandstones is likely due to
mineral precipitation within the pore space or perhaps to a
long-term viscoelastic response, and is more dependent upon
the thermal history than the effective stress [Neuzil, 1986].
The elastic response of the pore space to changes in the fluid
pressure is much less significant than the variation of the
porosity with depth, amounting to an increase in porosity of
0.015 with an increase in pore pressure of 10 MPa. As a
model of sandstone aquifers on Mars, we adopt the formula
of Chapman et al. [1984] and neglect the change in porosity
with changing effective stress state. We do not scale the value
of z0 to Mars gravity, since the decrease in porosity with depth
is not due to elastic compression. While it is unknown exactly
what processes are responsible for the decrease in porosity
with depth in terrestrial sandstones and how this would scale
to Mars, the above relationship should capture the basic
behavior of Martian sandstones. On the basis of the summary
of Neuzil [1986], we represent the compressibility as an
exponentially decreasing function of the effective stress:
b seff ¼ b0;sed exp seff =s0;sed ;
ð23Þ
where we assume values for b0,sed of approximately
109 Pa1, and s0,sed of 25 MPa.
[54] The permeability of a sedimentary rock is dependent
upon the porosity, grain size, and degree of sorting of the
log10 ðk Þ ¼ 17:3 þ 25 n;
ð24Þ
5.3. Mixed-Media Aquifers
[55] Single component aquifer models may be reasonable
representations of certain regions of the Martian crust. For
example the upper portion of the Tharsis region is composed largely of basalts, while the deep crust in the heavily
cratered southern highlands can be represented by the
megaregolith model. However, in many cases it may be
necessary to consider the effects of a mixture of two
components, such as sediments or basaltic lava flows
interlayered within or overlying a megaregolith.
[56] For the case of isotropic, intimate mixtures of different components, the permeabilities can be averaged using
the geometric mean [Demming, 2002]:
keff ¼
Y f ki i ;
ð25Þ
where ki and fi are the permeability and volumetric fraction
of the ith component, respectively. Alternatively, for the
case of horizontal layering of aquifer components, the
permeability is anisotropic. The horizontal permeability is
found by the arithmetic mean, while the vertical permeability is calculated using the harmonic mean:
khor ¼
kvert
X
ðfi ki Þ
hX
i1
¼
ðfi =ki Þ :
ð26Þ
The effective compressibility for mixed media aquifers can
be found by a simple arithmetic mean of the compressibilities of the components.
6. Application: Aquifer Pressurization Through
Climate Change
6.1. Background
[57] The outflow channels are commonly thought to have
formed when the fluid pore pressure within a confined
aquifer reached or exceeded the lithostatic pressure [Carr,
1979]. Various studies ascribe these fluid pressures to be the
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result of (1) a perched aquifer [Carr, 1979, 1996], (2) a
confined aquifer pressurized by a downward propagating
freezing front [Carr, 1979], (3) artesian pressures caused by
the proposed uplift of Tharsis [Clifford and Parker, 2001],
(4) the intrusion of magma into ice rich crust [McKenzie and
Nimmo, 1999; Squyres et al., 1987], (5) the decomposition
of gas hydrates [Milton, 1974], and (6) the coalescence of
groundwater flow in the tectonic fractures surrounding
Tharsis [Baker et al., 1991]. While many of these ideas
are conceptually valid, it has not been possible to adequately
test them without a complete hydrologic model of the
Martian crust.
[58] We here apply our hydrologic model to investigate the
possibility that the fluid pressures necessary to form the
outflow channels could be generated beneath a downward
propagating freezing front as the result of a rapid cooling of
the climate, as proposed by Carr [1979]. As the aquifer
progressively freezes, the volumetric expansion of water
accompanying the phase change would pressurize the
remaining aquifer beneath. The premise of this hypothesis
relies on a dramatic cooling of the Martian climate to its
current cold state. Mars’ climate evolution is still poorly
understood, but there is clear evidence that the surface of
Mars was both warmer and wetter during the Noachian
epoch, including the high drainage densities of the valley
networks [Baker, 1982; Hynek and Phillips, 2003] and the
inferred high erosion rates [Carr, 1992]. The climatic evolution was likely driven, to a large degree, by the loss of an early
thick greenhouse atmosphere to impact erosion, solar wind
sputtering, adsorption of CO2 onto the regolith, and the
possible precipitation of carbonates [Brain and Jakosky,
1998; Melosh and Vickery, 1989]. Alternatively, other workers propose that the Martian climate may have been subject to
more rapid, episodic climate changes associated with redistribution of the volatile inventory [Baker et al., 1991].
[59] For perfectly confined aquifers, arbitrarily large pressures could be generated by the growth of the cryosphere,
potentially leading to catastrophic breakout and the formation
of the outflow channels [Carr, 1979]. However, over
large spatial and temporal scales, all aquifers are likely
interconnected to some degree [Clifford, 1993]. This interconnectedness would be even more pronounced in the highly
fractured megaregolith of the Martian southern highlands, as
well as in the thick sequences of basalt in the Tharsis rise.
Thus it seems likely that the entire circum-Chryse region was
underlain by an extensive aquifer that would have been
continuous with the high topography of both the Tharsis rise
and the southern highlands. It is highly unlikely that this large
regional aquifer was fully confined. Rather, it would have
been locally confined from above by the cryosphere, but
laterally continuous with unconfined aquifers in the Tharsis
region and the southern highlands. Such a partially confined
aquifer can be brought about by means other than topographic variations as well, as illustrated in Figure 6. In the
absence of significant topographic relief (Figure 6a),
locally confined aquifers that are laterally continuous with
unconfined aquifers can be produced by variations in the
thickness of the cryosphere (Figure 6b) as a result of
lateral variations in either the thermal conductivity of the
surface materials or the local heat flux. The same outcome
could also be produced by variations in the height of the
water table (Figure 6c), which could result, for example,
E01004
Figure 6. Aquifer and cryosphere geometries that can lead
to locally confined aquifers in lateral continuity with
unconfined aquifers, viewed in cross section. Local
confinement of the aquifer can be brought about by
variations in (a) the topography, (b) the cryosphere
thickness, or (c) the elevation of the water table, as
described in the text.
from hydrothermal convection or a localized pressurization
mechanism operating within or beneath the aquifer.
[60] Thus the thickening cryosphere is not simply compressing a closed aquifer. Rather, as pressure is generated
beneath the freezing front, it simultaneously diffuses away
toward the edges of the confined portion of the aquifer. The
actual pressure generated depends upon the rate at which the
freezing front advances, the area over which the aquifer is
confined, and the hydraulic properties of the aquifer. If
either the confined portion of the aquifer is small or the
thickening of the cryosphere is a slow process, the pressure
should diffuse away essentially as fast as it is generated.
Alternatively, if the confined portion of the aquifer is
sufficiently large or the cryosphere thickens rapidly, significant pressures should be generated, possibly approaching
those generated within a fully confined aquifer.
6.2. Pressurization of Aquifers: Model Description
[61] In order to test the feasibility of the thickening of the
cryosphere as a means of producing high pressures in
Martian aquifers, we consider the hydrologic response to
the cryospheric thickening for a number of climate change
scenarios and aquifer geometries. The time dependant
thickening of the cryosphere is modeled using a fully
explicit finite difference code. The temperature evolution
within the crust is modeled using the 1-D heat equation:
@T
1 @
@T
;
¼
k
@t
rc @z
@z
ð27Þ
where k is the thermal conductivity and c is the specific
heat. The rate of change of the depth of the melting isotherm
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HANNA AND PHILLIPS: HYDROLOGICAL MODELING OF THE MARTIAN CRUST
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(zm) is calculated using the difference between the
temperature gradient above and beneath the freezing front:
@zm
1
@T @T ¼
k1 k2 ;
@t
nrL
@z þ
@z 1
D dz þ n dzðav 1Þ
ln
b
D dz
1 n dzðav 1Þ
;
b
D dz
DP ¼
ð29Þ
where b is the combined compressibility of the aquifer
matrix and water.
[63] Since the freezing front moves slowly relative to
the vertical diffusion of the excess hydraulic head, and
since the vertical length scale of the aquifer is several
orders of magnitude less than the horizontal, the aquifer
properties are vertically averaged and diffusion is considered in the horizontal direction only (i.e., @h/@z = 0). The
evolution of the hydraulic head produced by this excess
pressure in the confined portions of the aquifer is
calculated using a finite difference code representing the
elastic response of the aquifer as governed by the
consolidation equation (equation (5)) expressed in axisymmetric cylindrical coordinates with a pressure source term:
@h 1 1 @
@h
1 @P
þ
;
¼
Kr
@t Ss r @r
@r
rw g @t cryos
head is taken with respect to the base of the aquifer, such
that it is equal to the unconfined aquifer thickness, then flow
is modeled by
@h
1 @
@h
¼
Khr
;
@t r ntop @r
@r
ð28Þ
where n is the porosity, L is the latent heat of fusion of
water, r is the density of water, k1 is the thermal
conductivity above the freezing front, and k2 is the
thermal conductivity below the freezing front. For
simplicity, we assume a fully ice-saturated cryosphere,
though it is likely that the ice content of the pore space
will decrease to zero toward the surface at a steady state
ice table [Mellon et al., 1997]. The thermal conductivities
are modeled as in Section 4.5.
[62] Once the thickness of the cryosphere as a function
of time is computed, we model the pressure that would be
generated beneath the growing cryosphere as a function of
time for a given aquifer geometry. The pressure generated
at the freezing front is found by considering a finite-radius
aquifer of thickness D beneath the freezing front. As the
freezing front moves an incremental distance dz into this
aquifer, the expansion of the water as it freezes to form ice
expels an amount of water equivalent to a layer of
thickness n(av 1) dz, where av, the coefficient of
volumetric expansion of water upon freezing, is approximately 1.09, and n is the porosity. This water is forced
into the aquifer beneath the freezing front, resulting in a
pressure increase of DP:
ð30Þ
where (@P/@t)cryo is the rate of pressurization at the freezing
front from equation (29). In the unconfined portions of the
aquifer, the net flow of water into a column of aquifer
results in an increase in the hydraulic head through a direct
increase in the water table height, rather than through a
confined pressurization. It is also necessary to account for
the fact that the aquifer thickness now varies with radius due
to the increase in the water table height. If the hydraulic
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ð31Þ
where ntop is the porosity at the water table.
6.3. Pressurization of Aquifers: Model Results
[64] We consider instantaneous climate changes from
270 K to 220 K, and from 250 K to 220 K, representing a
transition from the warm wet climate conditions on early
Mars to the cold conditions of today in a single rapid event.
We also consider more plausible gradual climate change
scenarios, with the temperature changing from 270 K to
220 K over the course of 60 ka and 1 Ma. The former case
corresponds to half of the period of an obliquity oscillation,
while the latter case is a somewhat more conservative
timescale for climate change. The resulting cryosphere
thickness as a function of time for the four scenarios is
shown in Figure 7. The cryosphere thickness is sensitive to
the thickness of ice-free regolith above the permafrost, here
assumed to be negligible, and the geothermal heat flow, here
assumed to be 50 mW/m2. This heat flux is appropriate for
the Hesparian epoch on Mars [Hauck and Phillips, 2002], in
which most of the outflow channels formed [Baker, 1982;
Carr and Clow, 1981; Masursky et al., 1977].
[65] We use a generic aquifer geometry in which a
circular region of the aquifer is confined from above by
the thickening cryosphere, but the adjacent aquifer is
unconfined. Our nominal model consists of an aquifer with
a confined region radius (R) of 1000 km and an aquifer
thickness (D) of 3 km. This aquifer thickness is roughly
equal to the total change in cryosphere thickness during the
simulation. We also consider confined regions with radii
ranging from 500 to 3000 km, as well as initial aquifer
thickness ranging from 1 to 5 km. The megaregolith aquifer
model is representative of several of the outflow channel
source regions to the east of Tharsis, while those further up
on the Tharsis rise may be better represented by the basaltic
aquifer model. Due to the difficulty constraining the hydraulic behavior of basaltic aquifers under varying conditions of lithostatic and fluid pore pressure, we limit the
following investigation to the megaregolith aquifer model.
Lower pore pressures would be expected for basaltic aquifers due to their higher permeability relative to megaregolith
aquifers, thus the pore pressures generated in our models are
likely upper limits.
[66] Figure 8 plots the aquifer pore pressure at the base of
the cryosphere in the center of the confined region as a
function of time for the aquifer geometries and climate
change scenarios described above. Also included in the
figure is the lithostatic pressure at the base of the cryosphere, which increases with time as the cryosphere thickens. For all scenarios, the pore pressure rises steeply with
time during the early period of rapid cryosphere thickening.
As the rate of propagation of the freezing front slows, the
pore pressures plateau out. After the freezing front passes
through the base of the megaregolith, a smaller volume of
water is expelled from the freezing front per unit increase in
cryosphere thickness due to the decrease in porosity. As a
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Figure 7. Model of the depth of the base of the cryosphere
as a function of time as the average surface temperature
changes from 270 to 220 K either instantaneously (solid
black line) or linearly over a course of 1 Ma (solid gray line)
or 60 ka (dashed black). Dashed gray line shows response
for an instantaneous change from 250 to 220 K.
result, the rate of pressurization decreases dramatically
relative to the rate of diffusion within the aquifer, and the
pore pressure drops.
[67] For the instantaneous climate change from 270 K to
220 K, most scenarios result in maximum pore pressures
approaching, but not exceeding, the lithostatic pressure
(Figures 8a and 8b). As the fluid pore pressure approaches
the lithostatic pressure, the fracture apertures rapidly increase
(equation (16)), resulting in a sharp rise of the permeability
(equation (12)). This allows for a more rapid lateral diffusion
of the pressure away from the confined portion of the aquifer,
producing a negative feedback cycle that prevents fluid
pressures from exceeding the lithostatic pressure. For the
confined aquifers with radii up to 2000 km, the pore pressures
approach the lithostatic pressure during the early period of
rapid cryospheric thickening, before plateauing at lower
values as the rate of thickening decreases. For the locally
confined aquifer with a radius of 3000 km, pore pressures
exceed the lithostatic pressure during this early period by
approximately 0.4 MPa. However, as the rate of thickening of
the cryosphere decreases, the pressure diffuses away more
rapidly than it builds up and the aquifer quickly returns to
sublithostatic pore pressures.
[68] For more plausible climate change scenarios, the
pore pressure at the base of the cryosphere never exceeds
E01004
the lithostatic pressure. For the change in surface temperature from 270 to 220 K over the course of 60 ka, the pore
pressure for the 3000 km radius confined aquifer reaches,
but does not exceed, the lithostatic pressure (Figures 8c and
8d). Smaller confined aquifers result in lower pore pressures. For the change in surface temperature from 270 K to
220 K over the course of 1 Ma, the pore pressure remains
well below the lithostatic pressure for all confined aquifer
sizes (Figure 8e). During these slower climate changes, the
pore pressure has ample time to diffuse away from the
slowly advancing freezing front toward the unconfined
portions of the aquifer. For an instantaneous change from
250 K to 220 K, the greater initial cryosphere thickness
results in a greater thermal diffusion timescale at the base of
the cryosphere and a slower initial rate of cryospheric
thickening, leading to the generation of significantly lower
pressures within the aquifer (Figure 8f). These more plausible scenarios produce pore pressures significantly less
than the lithostatic pressure at all times.
[69] The pressures generated are highly sensitive to the
original thickness of the aquifer (Figures 8g and 8h). For an
initial aquifer thickness of 5 km and confined region radius
of 1000 km, the pore pressures generated are only slightly
less than those for the 3 km thick aquifer. The water being
expelled by the freezing front is being injected into a thicker
aquifer beneath, thus significantly lower pressures might be
expected. However, since the compressibility and permeability decrease with depth, the ability of the aquifer to
accommodate and transport the additional water decreases
with depth as well. On the other hand, when the aquifer is
thinner, such that the freezing front passes through the base
of the aquifer, significantly higher pressures are generated.
During the early stage of rapid cryosphere thickening, the
pore pressures for a 2 km thick aquifer approach, but do not
exceed, the lithostatic pressure, while those for a 1 km thick
aquifer exceed the lithostatic pressure by nearly 1 MPa.
Then, when the freezing front approaches and passes
through the base of the aquifer, the pore pressures rise
asymptotically as the volume of the pore space into which
the excess water is being injected decreases to zero. For
both the 1 and 2 km thick aquifers, the pore pressures don’t
begin the final asymptotic rise until the freezing front passes
within a few tens of meters to 100 m of the base of the
aquifer. Large outflow events in these cases would be
impossible, since the large volumes of water inferred for
the outflow channel floods could not be stored in such thin
aquifers.
[70] In order to highlight the importance of the dependence of the hydraulic parameters on the fluid pore pressure,
we have included one scenario in which the aquifer properties are artificially held constant in time and not allowed to
Figure 8. Aquifer pore pressure and lithostatic pressure at the base of the cryosphere as a function of time for several
different climate change scenarios and aquifer geometries, including (a and b) an instantaneous change from 270 to 220 K
for 3 km thick confined aquifers with radii between 500 and 3000 km; (a and b, dotted curve) a 1000 km radius confined
area in which the aquifer properties are modeled as being insensitive to the pore pressure; (c and d) a linear change from
270 to 220 K over the course of 60 ka for a 3 km initial aquifer thickness and radii between 500 and 3000 km; (e) a linear
change from 270 to 220 K over the course of 1 Ma for a 3 km initial aquifer thickness and radii between 500 and 3000 km;
(f) an instantaneous change from 250 to 220 K for a 3 km initial aquifer thickness and radii between 500 and 3000 km;
(g and h) an instantaneous change from 270 K to 220 K for a 1000 km radius confined region with initial aquifer
thicknesses between 1 km and 5 km.
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HANNA AND PHILLIPS: HYDROLOGICAL MODELING OF THE MARTIAN CRUST
Figure 8
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HANNA AND PHILLIPS: HYDROLOGICAL MODELING OF THE MARTIAN CRUST
adjust to the changing fluid pore pressure (dotted line in
Figures 8a and 8b). In this case, the pore pressure rises
much more rapidly and exceeds the lithostatic pressure by a
substantial margin. Similarly large pressures could be
achieved in an unfractured sedimentary aquifer of sufficient
vertical and horizontal extent, however there is no evidence
that such an aquifer exists in the region of the outflow
channel source regions.
[71] Similar simulations have been run investigating the
climate change scenarios and aquifer geometries described
above over a wider range of parameter space in the
hydrologic model. Model results are most sensitive to the
uncertainty in the fracture aperture, due to the cubic
dependence of the permeability on this parameter. Using
an uncompressed fracture aperture of 104 m, at the lowest
end of the plausible range, super-lithostatic pore pressures
can be generated for several of the model scenarios,
including the temperature changes from 270 to 220 K both
instantaneously and over 60 ka for confined aquifer radii
greater than 1000 km. However, the high discharges inferred for the outflow channel floods are suggestive of
higher than average permeability, rather than lower.
[72] The circum-Chryse region, in which most of the
outflow channels occur, is similar in size to the 2000 km
radius confined aquifer modeled above. Thus it would seem
that if the aquifer in the region were confined over an area
somewhat greater than the area of the Chryse basin (e.g.,
over a 3000 km radius area), it would be possible to produce
super-lithostatic pore pressures during an instantaneous
change in surface temperature from 270 K to 220 K.
However, the model pore pressures peak in the center of
the confined region and decrease toward the periphery,
while the outflow channel source regions are all along the
margin of the circum-Chryse region. Thus for such a
hypothetical confined aquifer in this region, the superlithostatic pore pressures would be generated in the center
of the Chryse basin, and not where the outflow channel
source regions are located.
[73] If the effects of topographic variations were to be
considered, then an extra component of hydrostatic pressure
would be added to the pore pressure in the aquifer beneath
topographic lows. However, many of the source regions of
the circum-Chryse outflow channels are relatively high up
on the Tharsis bulge and show no evidence for a preferential
occurrence in local topographic lows. If the aquifer pressurization mechanism acted over the entire circum-Chryse
region, the maximum hydrostatic component of the pressure would occur in the topographically lower center of
the Chryse basin, enhancing the higher pressures being
produced there. Thus the location of the outflow source
regions at higher elevations on the margins of the Chryse
basin suggests a more localized pressurization mechanism
focused at the individual source regions.
[74] A further argument against a climatic mechanism as
the driving force behind the outflow channel floods lies in
the observations that the channels have ages ranging from
Hesparian to early Amazonian, a time period spanning
roughly 1 billion years [Carr and Clow, 1981; Tanaka
and Skinner, 2004], and that several of the outflow channels
show evidence for multiple episodes of flow [Hanna and
Phillips, 2003; Williams et al., 2000]. Thus it would be
necessary to have repeated near-instantaneous climate
E01004
changes from 270 to 220 K recurring over a period of
roughly 1 Ga to explain the temporal distribution of outflow
channel events. While a number of workers have argued for
the importance of episodic climate changes on Mars [Baker
et al., 1991; Head et al., 2003], temperature swings as large
and rapid as are required to form the outflow channels
through this mechanism seem unlikely. Mechanisms commonly invoked for secular climate change, such as erosion
of the atmosphere by impacts and solar wind stripping
[Brain and Jakosky, 1998] act over longer timescales.
Gulick et al. [1997] found that the injection of 1 to 2 bars
of CO2 into the Martian atmosphere resulted in a temperature increase to only 250 K, however the subsequent
cooling took place over hundreds of Ma. Rapid climate
changes attributed to obliquity oscillations will be limited
by the CO2 content of the polar caps, which has been shown
to be on the order of tens to hundreds of mbar [Mellon,
1996], much less than that required for a strong greenhouse
effect.
[75] In summary, the difficulty with producing superlithostatic pore pressures through a climate change lies both
in the slow diffusion of the thermal wave into the crust and
in the negative feedback cycle between the pore pressure
and the permeability. This effect would be magnified for
basaltic aquifers, which have a significantly higher permeability than that in the megaregolith model. These results
have implications for any mechanism of aquifer pressurization that relies upon processes acting over timescales of tens
of thousands to millions of years. The work presented here
suggests that a more rapid, repeatable, and localized mechanism for pressure generation would be favored as a driving
force behind the formation of the outflow channels, such as
a magmatic intrusion into the aquifer or a tectonic event.
[76] Due to the unconstrained nature of the problem, it is
of course not possible to fully prove or disprove the theory
that the outflow channels were generated by the pressurization of an aquifer beneath a downward propagating
freezing front. However, this study sheds some light on
the details and problems of this theory. It does not appear
possible to produce super-lithostatic pore pressures solely
through the freezing of a megaregolith-type aquifer for
plausible climate change scenarios and aquifer geometries.
This does not rule out the possibility that this pressurization
mechanism could have produced the requisite pressures in
concert with another mechanism. For example, this mechanism may have played a secondary role by causing a
general increase in aquifer pore pressures to sublithostatic
levels over a large region, thereby allowing a more localized
and rapid pressurization mechanism to push pore pressures
to super-lithostatic levels at the outflow channel sources.
7. Conclusions
[77] We have presented here a generalized hydrologic
model of the Martian crust based on a combination of
terrestrial and lunar analogs, in which the relevant hydraulic
properties are represented in a physically realistic and selfconsistent manner. Much of the hydrologically active crust
of Mars can be represented by the megaregolith aquifer
model, based on the inferred effects of impacts on the
hydrologic properties of the crust. Younger terrains are
better represented as either basalts, such as the topmost
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layers in the Tharsis rise, or sediments, such as the surface
materials within craters and elsewhere [Malin and Edgett,
2000b]. The hydrologic properties of all of these crustal
materials will vary with both depth and pore pressure.
[78] The sensitivity of the hydraulic properties to the pore
pressure was highlighted in the study of the pressurization of
a partially confined aquifer beneath a thickening cryosphere.
We found that even for an unrealistically rapid climate
change, the diffusion of the excess pressure toward the
unconfined portions of the aquifer precluded the attainment
of super-lithostatic pore pressures for almost all cases considered. This lateral diffusion was accentuated by the increase
in permeability at high pore pressures, resulting in a negative
feedback cycle between pore pressure and permeability. This
feedback will be important for any hydrologic process
involving large and widely varying pore pressures.
[79] Hydrological modeling of groundwater processes on
Mars is essential for understanding the many observed
water-related features on the surface. While the nature and
hydraulic properties of the materials in the subsurface are
poorly constrained, the model developed here provides a
baseline with which we can begin to quantitatively test
current hypotheses regarding Martian hydrological processes, as has been done here for the origin of the
outflow channels. The parameters contained in this study
are best estimates based on our current understanding, but
will be subject to revision as more data become available.
The forthcoming data from the SHARAD and MARSIS
radar sounders will likely shed new light on the distribution and abundance of Martian groundwater, thereby
providing a much-needed constraint on the aquifer model.
[80] Acknowledgments. We would like to thank Daniel Nunes and
Andrew Dombard for many insightful discussions. We especially thank
Jules Goldspiel and an anonymous reviewer for their thorough and
thoughtful reviews. This work was supported by grant NAG5-13243 from
the NASA Planetary Geology and Geophysics Program and grant NAG511202 from the NASA Mars Data Analysis Program.
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