Numerical slope stability simulations of the northern wall of eastern Candor Chasma (Mars) utilizing a distinct element method

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Planetary and Space Science 52 (2004) 1303–1319 www.elsevier.com/locate/pss

Numerical slope stability simulations of the northern wall of eastern Candor Chasma (Mars) utilizing a distinct element method B. Imrea,b, a

Department for Planetary Research, German Aerospace Center (DLR), RutherfordstraX e 2, 12489 Berlin, Germany b Department for Geology and Paleontology, University of Graz, HeinrichstraX e 26, 8010 Graz, Austria Received 28 July 2003; received in revised form 22 March 2004; accepted 6 September 2004

Abstract Valles Marineris offers a deep natural insight into the upper crust of Mars. The morphology of its slopes reflects the properties of the wall materials, thus constraining in models of composition and evolution of the upper layers of the Martian crust. Hence, knowledge about the lithological composition of these wall rocks is of major interest to the understanding of the geological and climatic history of Mars. This study investigates mechanical rock mass parameters of the northern wall of eastern Candor Chasma (between 2901E and 2961E longitude,
81 to
51 latitude). These are inferred from its present-day morphology and a proposed slope-forming history, applying a distinct element code to simulate the stability and the tectonic history of this slope within a parameter study. Additionally, a mathematical denudation model is applied to take into account the effect of exogenic processes on the slope. The study results show that two periods of normal faulting in conjunction with massive interim denudational scarp recess is a valid model for the evolution of the northern wall of eastern Candor Chasma. The estimated rate of scarp recess of 60 m Myr
1 is comparable with certain terrestrial scarp retreat rates. The best-fit models yield a homogenous distribution of low-level rock mass strength and deformability properties distributed over the entire stratigraphic column of the northern wall of eastern Candor Chasma. The values are 5.0 (70.7) MPa for the uniaxial compressive strength, 1.6 (70.2) MPa for the Brazilian tensile strength, 4.7 (71.5) GPa for the Young’s modulus, 0.2 (70.15) for the Poisson’s ratio, 22 (72)1 for the internal friction angle, 1.6 (70.2) MPa for the cohesion and 2200 (7500) kg m
3 for the density. This study favors columnar jointed basalt as the material that builds up the northern wall of eastern Candor Chasma and other walls within central Valles Marineris. The best-fit denudational model of the upper slope section of the northern wall of eastern Candor Chasma indicates a distinct cap rock unit of lesser susceptibility to denudation than the wall rock below. r 2004 Elsevier Ltd. All rights reserved. Keywords: Mars; Valles marineris; Wall rock; Numerical simulation; Slope stability; Rock mass strength properties

1. Introduction Valles Marineris represents a vast, approximately 4000 km long system of troughs in the Tharsis region of Mars immediately south of the Martian equator. The majority of the troughs exhibit a relief of up to 8 km. In the central parts of this system, some walls reach an even Department for Planetary Research, German Aerospace Center (DLR), RutherfordstraXe 2, 12489 Berlin, Germany. Tel.: +49 30 67055 325; fax: +49 30 67055 402. E-mail address: [email protected] (B. Imre).

0032-0633/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.09.001

higher relief of up to 11 km. The very high wall slopes of Valles Marineris offer a deep natural insight into the upper crust of Mars. The morphology reflects properties of the wall materials, thereby constraining models of structure, composition, and evolution of the upper layers of the Martian crust (Carr, 1981). Hence, knowledge of the lithological composition of these wall rocks is of major interest to the understanding of the geological and climatic history of Mars. Firstly, this study describes key features of the selected area of the northern wall of eastern Candor Chasma. Secondly, a parameter study is performed on mechanical properties

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of the wall rocks by numerical modeling of the tectonic history, stability and the resulting morphology of wall slopes, by utilizing a distinct element code. In addition, a mathematical denudation model after Scheidegger (1991) is applied to simulate the effect of denudation to complete the picture of the slope-forming history. Finally, both models are combined and evaluated by comparing their predictions to the described features of the northern wall of eastern Candor Chasma. Previous studies on Valles Marineris wall rock strength properties were performed by Clow and Moore (1988) by mathematical inversion of the at least stable topographic profile. Recent studies were performed by Caruso and Schultz (2001) and Schultz (2002) by investigating the stability of Martian slopes using the method of slices and by Me`ge and Gatineau (2003) by using Rock Mass Rating based on the angle of stable wall slopes.

2. Site selection For model calibration and interpretation, it is crucial to choose a section of the Valles Marineris wall slopes which is, on the one hand, representative and, on the other hand, structurally as simple as possible. This reduces the number of unknown variables that otherwise can lead to complex and unwieldy models of questionable validity (e.g. Starfield and Cundall, 1988). Moreover, sufficient high-quality data have to be available for this wall section. These requirements are well fulfilled by the northern wall of eastern Candor Chasma, located between 2901E and 2961E longitude and
81 to
51 latitude (Fig. 1). Based on remote sensing data and

literature used for this study, this wall segment can be described as having a straight alignment, and to be free of visible signs of tectonic ruptures except for a basal fault scarp (e.g. Peulvast et al., 2001, Fig. 3a). This wall displays a well-defined homogenous spur and gully morphology not modified by landslides. Its high relief of about 8 km exposes a significant part of the upper crust (Fig. 2). The wall rock is only partially mantled by aeolian or other materials, as layering within the wall rock is visible down to deep exposures (Figs. 3b and c; e.g. McEwen et al., 1999). Only sparse interior layered deposits are embaying the wall rock (Lucchitta et al., 1994).

3. Creation of a representative profile of the chasma wall For calibration and confirmation of a 2D numerical model, a simple but still representative 2D profile of a 3D chasma wall, which is stamped by spurs and gullies, has to be created (e.g. Oreskes et al. (1994) and Starfield and Cundall (1988). The procedure to create such a wall profile begins with the selection of the appropriate Mars Orbiter Laser Altimeter (MOLA) orbits (Heller, 2002; Smith et al., 2001; PDS, 2002). A multitude of such orbits intersects the approximated strike of the northern wall of the eastern Candor Chasma at angles of about 631 and 791, respectively (Fig. 2). Thirty-three orbits, located within the study area were chosen from the latter group (Table 1). Accuracy assessments of the MOLA data yielded an accuracy of absolute elevation measurements between 50 and 100 m. MOLA orbits are almost polar and show

Fig. 1. Digital elevation model of Valles Marineris (DLR–RIPF, 2002), merged with an orthophoto mosaic based on Viking orbiter images (DLR–RIPF, 2002). Major features in central Valles Marineris area are indicated with numbers: Candor Chasma (1), Ophir Chasma (2), Melas Chasma (3), Ius Chasma (4), Coprates Chasma (5), Juventae Chasma (6), Hebes Chasma (7), Ophir Planum (8), Lunae Planum (9), and Sinai Planum (10). The present study area on the northern wall of eastern Candor Chasma is marked by a yellow square. The section runs between 2901E (701W) and 2961E (641W) longitude and
81 to
51 latitude. Enlarged details of this area can be seen in Figs. 2 and 3a. Geoid height is in meters with zero elevation as described in Smith et al. (2001).

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strike of the chasma wall at a right angle. The projection is given by xpn ¼ xn þ sinðaÞ½
ðxn
xn¼1 Þ sinðaÞ þ ðyn
yn¼1 Þ cosðaÞ;

ð1aÞ

ypn ¼ yn þ sinðaÞ½
ðxn
xn¼1 Þ cosðaÞ
ðyn
yn¼1 Þ sinðaÞ;

Fig. 2. The enlarged detail of the study area (e.g. Fig. 1) as a digital elevation model. It reveals a terrace (t, ranging between
2000 and
1000 m altitude) as a dominant morphological feature of the northern wall of eastern Candor Chasma. Color coded elevation model (about 1 m vertical and about 1000 m pixel
1 horizontal resolution, DLR–RIPF, 2002) based on MOLA data (Smith et al., 2001; PDS, 2002). The elevation model is merged with a Viking image mosaic (DLR–RIPF, 2002) and Mars Orbiter Camera (MOC) narrow angle narrow angle images (from left) M12-02724, M13-01771, M1700261, M04-00136 and M17-00801 (resolutions between 2.5 and 5.5 m pixel
1, Malin et al., 1998; MSSS, 2002). Bright lines indicate the tracks of MOLA orbits crossing the chasma wall between 2901E and 2961E longitude. Geoid height is in meters with zero elevation as described in Smith et al. (2001). Sinusoidal projection, north to the top.

their greatest separation from one another at the equator, with gaps of 4 km on average and 15 km at a maximum (Heller, 2002). Based on the facts that the chasma wall within the study area displays a straight alignment and an almost constant relief, a computer algorithm is applied on each of these MOLA orbits to create 2D wall profile. Due to the close position to the equator and the narrowness (only approximately 1  11) of the study area, the global coordinates of the MOLA orbits are approximated to be Cartesian. For a better comparison of this wall profile with the results of the numerical simulations, the latitude coordinates are converted from degrees to km. In the present case, 11 latitude represents about 59.27 km. This ratio is based on the radii of the Martian Geoid after Seidelmann et al. (2000). The algorithm starts with the projection (Eqs. (1a) and (1b)) of each MOLA profile, whereby each measurement point is projected onto the dip direction line of the chasma wall via lines that are parallel to the approximated strike of the chasma wall. The purpose of this projection is to correct the length of the original MOLA-wall profiles which are about 2% too long due to the fact that they do not intersect the approximated

ð1bÞ

where xpn and ypn denote the projected coordinates of the original latitude coordinates xn and longitude coordinates yn, respectively. a denotes the angle between a given MOLA orbit and the dip direction of the chasma wall. The next step is to transform the coordinate system in such a way that all selected MOLA orbits are oriented parallel to the latitude axis of the coordinate system (Eqs. (2a) and (2b); Fig. 5a). This means that all measurement points of a given orbit share the same yvalue. The transformation is given by xtn ¼ ypn sin c þ xpn cos c;

(2a)

ytn ¼ ypn cos c
xpn sin c;

(2b)

where xtn and ytn are the transformed coordinates of the projected coordinates xpn and ypn. c denotes the transformation angle in a clockwise direction, which amounts to 348.51 in this case. Each transformed profile is then truncated to a constant length of 230 MOLA shots, whereby this length is divided into 80 shots in the direction of the Lunae Planum (sub-north) and 150 shots down-dip the chasma wall (sub-south). The well-developed chasma rim serves as the point of origin. After projection, transformation and truncation of each MOLA profile, it is possible to merge them all into a 3D matrix (Fig. 4a). From the resulting matrix, a mean chasma wall profile is derived by calculating the arithmetic mean of all elevations and transformed latitude coordinates (Fig. 4b). A true scale plot of this mean profile is shown in Fig. 4c. This mean profile demonstrates characteristics such as the smoothing of small-scale morphological features (heights o1000 m). This is consistent with the maximum resolution of the distinct element tectonic models used in this study. Additionally, the mean profile length and height are representative for the present wall section. Finally, the terrace is clearly visible (e.g. Fig. 2) and the distinct chasma rim is preserved (e.g. Fig. 3a).

4. General description of the distinct element code PFC-2D To model the tectonic evolution and mechanical stability of the chasma wall, the program ‘‘Particle

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Fig. 3. (a) Enlarged detail of the study area (e.g. Fig. 1). Dominant geomorphic features of this straight aligned wall are a steep rim (r), spurs and gullies (g) and a dissected basal fault scarp (s) (e.g. Peulvast et al., 2001). The floor at the base of the northern wall is the deepest section within eastern Candor Chasma and may be interpreted as a trench. Despite the occurrence of massive interior layered deposits (Lucchitta et al., 1994)., the southern flank of that trench may therefore represent an antithetic fault scarp (sa). Viking orbiter mosaic (resolution approximately 60 m pixel
1; DLR–RIPF, 2002) merged with MOC narrow angle images (from left) M12-02724, M13-01771, M17-00261, M04-00136 and M17-00801 (resolutions between 2.5 and 5.5 m pixel
1, Malin et al., 1998; MSSS, 2002) to enhance details. Full resolution enlargements of MOC narrow angle image M13-01771 are indicated by white arrows (Figs. 3b and c). Sinusoidal projection, north to the top. (b) Maximum resolution detail of MOC narrow angle image M1301771 (Malin et al., 1998; MSSS, 2002). This picture shows exposed layered wall rock. The layering on both spurs (black arrows) displays the same sub-horizontal orientation, indicating that these layering sets are neither tilted to each other nor to the general orientation of layers within Valles Marineris wall rocks (e.g. McEwen et al., 1999). The global altitude of image center is about
1000 m (image resolution 2.85 m pixel
1), sinusoidal projection, north to the top. (c) Maximum resolution detail of MOC narrow angle image M13-01771 (Malin et al., 1998; MSSS, 2002). This picture shows exposed layered wall rock. The layers on both spurs (black arrows) display different orientation indicating that these layering sets are disturbed and tilted relative to each other. The left, sub-vertically layered block shows dark lines that can be interpreted as fractures (white arrows). The global altitude of image center is about
1500 m (image resolution 2.85 m pixel
1), sinusoidal projection, north to the top.

Flow Code in 2 Dimensions—PFC-2D’’ is applied (ITASCA, 2002). This distinct element code simulates the mechanical behavior of a system comprised of a collection of disk-shaped particles (e.g. Figs. 5a and b). These distinct particles can displace independently from one another and interact only at contacts or interfaces between the particles. Newton’s laws of motion provide the fundamental relationship between the particle motion and the forces causing that motion. The behavior of massive rock is modeled by bonding the particles together at their contact points to create an artificial material. When the inter-particle forces acting at any bond exceed the bond strength, that bond will break. This allows tensile forces to develop between particles and fractures to evolve naturally within the artificial material. Most two-dimensional continuumbased codes determine three-dimensional elastic response by enforcing a condition of either plane stress or plane strain through the constitutive relations between stress and strain. A PFC-2D model, however,

invokes neither of these conditions. The out-of-plane force component and stresses and strains are simply not considered in the equations of motion or in the force–displacement laws. Thus, the out-of-plane constraint necessary to enforce a state of plane strain is not present (ITASCA, 1999). This program code already has been successfully applied to a wide range of applications (e.g. Konietzky, 2003).

5. Objectives and set up of the tectonic chasma wall modeling environment The angle of a slope is a function of the strength of the slope-forming material against failure, the forces acting on this material and the time until the slope reaches a stable state. But the reverse is also valid: the angle of a stable slope allows the mechanical rock mass parameters to be inferred that have led to deductions about the tectonic chasma wall environment. Information about

ARTICLE IN PRESS B. Imre / Planetary and Space Science 52 (2004) 1303–1319 Table 1 The Mars orbiter laser altimeter orbits used in this study, crossing the northern wall of eastern Candor Chasma between 2901E and 2961E longitude and
81 to
51 latitude (Smith et al., 2001; PDS, 2002) #

MOLA orbit name

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

ap10440i ap11113i ap11199i ap11529i ap12276i ap12594i ap12925i ap13010i ap13341i ap13757i ap13989i ap14087i ap14320i ap14406i ap14650i ap14736i ap15067i ap15299i ap15385i ap16462j ap16548j ap17049j ap17135j ap17221j ap17319j ap18456j ap18542j ap18921j ap19215j ap19410j ap19899j ap20107j ap20303j

the mechanical wall rock mass parameters is obtained by modeling the mechanical slope stability of the northern wall of eastern Candor Chasma and calibrating the results against the mean wall profile (Fig. 4c). Naturally, no unique result can be achieved, which is inherent to models of open systems such as the present one. However, it is possible to validate the model results on the observed data (Oreskes et al., 1994). An accurate analysis of a slope stability problem needs to consider the evolving strains and path dependency by a constitutive model that exceeds the capabilities of conventional limit equilibrium methods (e.g. Laouafa and Darve, 2002). The approach of the present study is to investigate mechanical rock strength and deformability properties by numerical non-linear analysis based on a distinct element method. The abilities of PFC-2D allow infinite strain and the natural development of slope failures without critical assumptions on failure geometries. In the present tectonic models, it is assumed that the chasma wall slope evolves

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naturally from an initially entirely flat plane to its final relief, only due to normal faulting along a pre-existent basement fault (Fig. 5a). This assures that the slope is always in a state of incipient failure. The assumption that normal faulting is the exclusive agent creating the relief of the slope is based on the discussion on which the northern wall of eastern Candor Chasma shows signs of diastrophic processes that led to or at least contributed to its present height (among others, e.g. Barnett and Nimmo, 2002; Peulvast et al., 2001; Schultz and Lin, 2001; Schultz, 1998; Me`ge and Masson, 1996, 1997; Tanaka, 1997; Lucchitta et al., 1994). Values for the dip of the basement fault are taken from the literature without any preference to test their influence on the wall slope development: 451 after Schultz and Lin (2001), 601 and 901 after Me`ge and Masson (1996). The basic model consists of only one fault plane (e.g. Fig. 5a). A modified model with a set of two parallel faults is used to simulate the hypothesis of the origin of a wall-terrace induced by two parallel faults (e.g. Fig. 6).

6. Set up and boundary conditions of the uniaxial/biaxial compressive strength and the Brazilian tensile strength test environment The behavior of loose sand is concerned with the movement and interaction of particles. This can be modeled correctly in PFC simply by defining microproperties of particles and its contacts (Table 2). To date, it is not possible to define material bulk properties, such as those of solid rock, directly within PFC. Consequently, the macro-mechanical (bulk) properties of a particle assemblage, representing an artificial solid material have to be determined in an additional step by performing a series of calibration tests within an uniaxial/biaxial compressive- and Brazilian tensile strength test environment implemented in PFC (for a general description about strength tests, refer to Vutukuri et al. (1974) or any general textbook on rock testing). Uniaxial- and biaxial compressive strengths, and the static elastic properties such as Young’s Modulus and Poisson’s ratio are derived from these numerical simulations for the artificial materials. Material tensile strengths are directly derived from Brazilian strength tests. The values of Poisson’s ratio obtained in PFC-2D are not strictly comparable to the Poisson’s ratio of a real material obtained from a triaxial test, because conditions in a two-dimensional PFC-2D biaxial test are neither plane strain nor plane stress— therefore, there is no out-of-plane stress and no out-ofplane deformation (ITASCA, 1999). The initial width of tested samples within the strength test environment amounts 1800 m and is therefore 20 times greater than the radius of the largest particles. Test samples intended for compressive strength tests display a width to height

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Fig. 4. (a) 3D view of 33 MOLA-profiles (Heller, 2002; PDS, 2002), which are used in this study to calculate the wall slope mean profile. The terrace is clearly recognizable (e.g. Fig. 2) as well as local peaks caused by spurs. The exaggerated profiles are back-projected, transformed and truncated as described in the text. (b) Exaggerated profile of 33 superposed MOLA-profiles plotted as the arithmetic mean of their altitude against transformed latitude coordinates (black line). The grey bars indicate the standard deviation of the altitude coordinates. The standard deviation of the latitude coordinates is not indicated graphically. It reaches a maximum of 7238 m on the right end of the mean profile. (c) Non-exaggerated arithmetic mean profile of 33 MOLA-profiles. It clearly displays the steep rim and terrace (e.g. Figs. 2 and 3a). Local peaks caused by spurs are smoothed (e.g. Fig. 4a). This profile is simple, but still representative of the northern wall of eastern Candor Chasma and is therefore suitable for calibration and validation of numerical simulations performed in the present study.

ratio of 1:2 (1800/3600 m). Both ratios follow recommendations on strength tests by Vutukuri et al. (1974). To derive the relevant material strength properties, internal friction angle j0 and cohesion c0 , from the failure envelope of an artificial material derived in biaxial compressive tests, the failure criterion after Mohr–Coulomb (Eq. (3)) is applied as described in Prinz (1997). After Mohr–Coulomb, the shear stress can be described as a linear function in terms of t ¼ c0 þ s0 tan j0 ; Fig. 5. (a) The simplified boundary conditions of a true size distinct element tectonic chasma wall model with a single predefined basement fault. vx ; vz denotes the velocity of the model boundaries. The top of the model is initially a horizontal surface formed by particles of a simulated artificial material. No boundary conditions are assigned to this free surface except that all particles within the assembly are accelerated in vertical direction by 3.71 m s
2 to simulate Martian gravity conditions (geoid after Archinal, 2003). Normal faulting is simulated by moving the lower and right boundary of the hanging wall block with a constant velocity vx ; vz (faulting rate). Faulting rate values are chosen in a way that the computed solutions produced by model remain stable. (b) Enlarged detail of the particle assembly. It is shown here that the artificial material modeled by this code consists of distinct particles. They are of unit width and display diameters ranging between 60 and 90 m with a Gaussian normal distribution.

(3)

where t denotes the shear stress, c0 the effective cohesion, s0 the effective normal stress and j0 the effective internal friction angle. This function describes a limiting condition against shear failure and is therefore referred to as a ‘‘failure envelope’’ or ‘‘limit line’’ when plotted in octahedral stress space. The advantages of this failure criterion are that it is simple, and very often successfully applied. It can be adopted that the intermediate principal stress has no influence on failure as is modeled here in PCF-2D. The present distinct element models are at true scale to minimize scale effects in terms of the strength and deformability of a generalized rock mass. At larger scales, the bulk properties of a

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Fig. 6. The tectonic chasma wall model with two predefined parallel basement faults. Fault ‘‘1’’ is activated first. After a throw of about
4200 m is reached, it stops and fault ‘‘2’’ is activated. The cumulative throw amounts to about
6200 m. Clearly visible is that both basement faults induce the formation of a terrace under intense deformation of strata within the two emerging surface fault zones.

Table 2 Best fit micro-properties for the artificial material ‘‘wall rock’’ Type

Micro-property

Value

Unit

Particle properties

Particle density Static Young’s modulus Particle normal to shear stiffness ratio Friction coefficient

1900–3300 3.9e9 0.4 0.5

kg m
3 Pa — —

Parallel bond properties

Static Young’s modulus Normal to shear stiffness ratio Normal strength Normal strength standard deviation Shear strength Shear strength standard deviation Multiplier of bond radius

3.6e9 0.4 4.8e6 1.6e6 4.8e6 1.6e6 1.0

Pa — Pa Pa Pa Pa —

rock mass not only relate to the properties of its intact rock components but also to the density, persistence, orientation, roughness and alteration of fractures as well as other forms of anisotropy, etc. (list not inclusive). Often, the strength of a rock mass can be reduced by as much a factor of 10 compared to the intact rock strength (Schultz, 1996). On account of the size of both the tectonic chasma wall model (initial width/height: 12500/37000 m) and the test samples within the numerical strength test environment, the macro- (bulk) strength properties of the tested artificial materials can be treated as strength properties of a such generalized rock mass. No efforts are made to evaluate intact rock strength and deformability values out of rock mass strength values, as this would require numerous assumptions (see previous paragraph), which can hardly be made based on actual knowledge for Valles Marineris wall rocks. The pore pressure is

implemented in the failure criterion via the effective normal stress s0 : It is mentioned for the sake of completeness because the presence of volatiles like water or ice within the wall rock of Candor Chasma cannot be excluded (among other, e.g. Carr, 1996; Clifford, 1993; Fanale et al., 1986; Peulvast et al., 2001). However, the narrow angle images from the MOC, analyzed in this study show no evidence of the presence of liquid water. Consequently the effects of enhanced pore pressure are not modeled explicitly. Furthermore, enhanced pore pressure is not required to explain the results of the tectonic chasma wall model and the strength test environment. In compressive strength tests, the artificial materials dilate slightly during failure. The amount of dilatation is not recorded in the present study. Therefore, no exact statements can be made but it is estimated that the internal friction angles j0 may be increased by up to 10% due to dilatation.

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7. The terrace in the wall profile 7.1. The terrace in the tectonic chasma wall modeling environment In this modeling environment, normal faulting is assumed to be the only slope (wall)-forming agent and care has to be taken that the resulting slope not only matches the actual wall angle but also its overall profile (e.g. Fig. 4c). To investigate the development of a terrace within the wall slope, a parameter study is performed on a double fault chasma wall model (Fig. 6). Those models indeed develop a terrace which would endorse the concept that the steeper wall segments, bounding the terrace, are the result of two parallel normal faults. Although this is a reasonable attempt, one major observation excludes this slope-forming process and also casts a different light on the evolution of the actual chasma wall itself: the best-fit models (in terms of the resulting slope angle) form two fault zones, containing tilted strata, instead of distinct fault planes. But McEwen et al. (1999) revealed ubiquitous horizontal layering to depth of at least 8 km. This observation is confirmed in this study utilizing MOC narrow angle images (Figs. 2a and 3b). Based on this finding, this type of model is not pursued further and a detailed discussion on the formation of a fault zone follows below. 7.2. The terrace in the mathematical denudation model— general remarks As discussed previously, a purely structurally controlled model of the chasma wall does not reproduce the observed flat laying strata. An additional process has to be taken into account: erosional widening of chasmata. This process is discussed in the literature in great number (among others, e.g. Barnett and Nimmo, 2002; McGovern et al., 2002; Peulvast et al., 2001; Schultz and Lin, 2001; Schultz, 1998; Tanaka, 1997; Wells and Zimbelman, 1997; Me`ge and Masson, 1996). To attempt to simulate and to discuss erosion as an agent of wall slope development, a mathematical denudation model after Scheidegger (1991) is utilized. This model has been selected because it simulates slope recession—the retreat of a stable slope from a former position without change in its (stable) angle (Bates and Jackson, 1984). Therefore this denudation mode does not disturb existing wall rock layering. The term denudation is introduced instead of erosion because the formulation combines all exogenical agents affecting slopes, whereas, by definition, erosion only includes processes of slope material transport by intermediaries such as wind, water or ice (Scheidegger, 1991). To simulate denudation acting normal to a slope, Scheidegger (1991) developed a non-linear hyperbolic

partial differential equation given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi qz qz qz ¼
aðzÞ 1þ ; qt qx qx

(4a)

where z and x denotes height (global altitude) and distance (transformed latitude) of the slope and t the unit time. The function a(z) takes into account the influence of differing susceptibility to denudation by lithological variations within the slope. It is reasonably assumed that denudation acts proportional to the steepness of a slope. The steeper the slope, the faster the debris will be removed. Eq. (4a) also assumes that all debris is completely removed from the slope during its development. Although this is an oversimplification, it appears to be valid for the northern wall of eastern Candor Chasma, since wall-derived deposits are remarkably scarce (e.g. Fig. 3a and Lucchitta et al., 1994). Eq. (4a) does not take into account any endogenic movements. Thus it fits into the Davisian concept of a geomorphic cycle: it assumes that an original slope is somehow created by a diastrophic process and that thereafter, the denudation proceeds at a steady rate (Scheidegger, 1991). If both processes occur at once, this assumption could still be valid if denudation processes act at high rates in a short time period relative to the rates of endogenic movements. Since analytical solutions cannot be obtained easily for Eq. (4a), it is useful to solve this equation within an approximation procedure. Therefore, Eq. (4a) can be approximated by the difference equation sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   zn
zn
1 zn
zn
1 2 ztmþ1
ztm ¼
a 1þ xn
xn
1 xn
xn
1 ðtmþ1
tm Þ;

ð4bÞ

where n and m are the coordinate and time step numbers, respectively. 7.3. Denudation acting on the entire wall The attempt of this model is to simulate the evolution of a terrace within a parameter study, as seen in the mean profile (Fig. 4c), by denudation acting on the entire wall. It assumes that denudation sets in, after some diastrophic process has created a slope profile as high as the present northern wall of eastern Candor Chasma. Various materials, with differing susceptibility to denudation in various positions within the stratigraphic column, are tested. The best-fit model (Fig. 7) yields a profile very much comparable to the mean profile (Fig. 5c) after time step m ¼ 400: It is based on a tripartite stratigraphic column consisting of a 0.4 km thick cap unit, a 4.7 km thick intermediate unit and a 3.0 km thick base unit. The thickness of the cap unit corresponds to the thickness of

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the ‘‘cap rock’’, a prominent cliff-forming unit throughout Valles Marineris, which seems to be more resistant to denudation than directly underlying units (e.g. McEwen et al., 1999). The thickness of the other units is based on the altitude of the terrace within the mean profile. The most resistant unit against denudation is the base unit, followed by a 10% weaker cap unit and a 28% weaker intermediate unit. Despite the correspondences between the result of this best-fit denudational model and the shape of the mean profile, the morphology of the lower slope section quite clearly indicates at least in part, an endogenic origin for the wall profile (Fig. 3a and, e.g. Peulvast et al., 2001). Based on these findings, this type of model is not pursued further. 7.4. Combination between a tectonic chasma wall model and a denudation model of the upper slope section As previously discussed, endogenic or exogenic processes alone do not explain the morphological features of the northern wall of eastern Candor Chasma. However, a combination of both processes, such as a slope evolution controlled by two tectonic movements with interim scarp recess seems reasonable (e.g. Hamblin, 1976 in Peulvast et al., 2001, Fig. 7e). This type of slope evolution is modeled by manually combining a distinct element single fault chasma wall model to simulate the endogenic process and a denudation model to simulate the exogenic process. A scope for future work would be an attempt to implement a denudation model directly within the program of the distinct element code. 7.5. Initial situation (Fig. 8) Initially, a 12.5 km thick block of the upper Martian crust is assumed at the position of the present-day Candor Chasma. This block will form the future southern rim of the Lunae planum and the northern

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wall of eastern Candor Chasma. It is also assumed that this block consists of horizontally layered material—the future wall rock and cap rock. 7.6. The first ‘‘ancient’’ faulting period (Fig. 9a) It is assumed in a first phase that normal faulting creates a slope with an ‘‘ancient’’ (Peulvast et al., 2001) relief of about 4.5 km, the approximate height of the slope section above the terrace. This process is simulated within the tectonic chasma wall modeling environment invoking a single basement fault model. Again numerous simulations with varying strength and density properties of both the wall rock mass and the cap rock mass are performed as a parameter study. The modeling focuses on the evaluation of rock mass strength values necessary to support a circa 201 dipping slope which is equivalent to the upper section of the mean profile. Maintaining the properties of the rock mass constant, the influence of different initial basement fault dips on the development of the wall slope and surface fault geometry is tested as well. As expected, basement fault dips of 451, 601 or 901 have only a slight influence on the morphology of wall slopes higher than 3 km. The dip of

Fig. 8. A sketch of a 12.5 km thick block of the upper Martian crust at the position of present-day Candor Chasma defines the initial situation of the combined tectonic and denudational chasma wall models. This block will form the future southern rim of the Lunae planum and the northern wall of eastern Candor Chasma. Within the block horizontal layering is indicated by thin black lines and a ‘‘cap rock’’ unit is indicated by a bold black line, which are assumed to be pre-existent. Beneath that block a pre-existent, so far inactive basement fault is defined (451 dip).

Fig. 7. Mathematical model after Scheidegger (1991) to simulate the evolution of the wall terrace, alone due to the action of denudation processes. Different m-values indicate individual stages in the iteration process. m ¼ 0 indicates the initial slope, m ¼ 400 the best-fit final one. The color bar represents the stratigraphic column; the altitudes of the unit boundaries are indicated. Dark grey—cap unit, resistant factor a ¼ 1:0; light grey— intermediate unit, resistant factor a ¼ 1:25; black—base unit, resistant factor a ¼ 0:9:

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Fig. 9. (a) Sketch of the end of the first phase of the combined tectonic and denudational chasma wall models. Movement at the basement fault induces a synthetic surface fault which initially dips at about 701. Due to counterclockwise rotation this fault reaches a final dip of about 451, which causes the development of a fault zone and the tilting of layering. Additionally, this basement movement induces an antithetic surface fault displaying a constant dip of about 551. In total, these simulated tectonic movements form an ‘‘ancient’’ (e.g. Peulvast et al., 2001) relief of about 4.5 km, with a wall slope dipping about 201. The same result is yielded for a pre-existent basement fault displaying a dip of 601. (b) The best-fit tectonic chasma wall model showing that the first phase of wall slope development after normal faulting created a slope with an ‘‘ancient’’ (Peulvast et al., 2001) relief of about 4.5 km. This corresponds to the approximated height of the slope section above the today’s terrace. The relief is higher than the indicated fault throw, as the hanging-wall block undergoes horizontal extension. It can be clearly seen that faulting induces within the relatively weak best-fit material a fault zone with tilted strata (indicated by white marker particles) rather than a distinct fault plane.

such high slopes is primarily controlled by the lithostatic stresses behind the slope, which are a function of the weight of the overburden. The surface faults and their development indicate an additional mechanism. In the case of the basement faults with dips of 451 or 601, a steep planar synthetic surface fault evolves with an initial inclination of circa 701, finally reaching a dip of about 451. Hence the inclination d of the synthetic fault zone (zone of maximum shear displacement) decreases with time depending on the throw of the normal fault. This behavior can be described mathematically where the inclination, d; of the fault with respect to the orientation of the maximum principal stress s01 is given by the following equation:   j0 d ¼ 45
; (5) 2

where j0 is the effective internal friction angle of the rock mass (modified after Mandl, 1988). Initially, the maximum lithostatic principal stress is vertically oriented. As the wall evolves, the orientation of the principal stress rotates under the control of gravity and the morphology of the overburden which causes the surface fault to rotate and a broad fault zone to develop (e.g. Dresen et al., 1991, p. 221). Such behavior is clearly shown in the present model where faulting induces a fault zone with tilted strata rather than a distinct fault plane (Fig. 9b). Additionally, a planar antithetic fault evolves with a constant dip of about 551. In the case of a basement fault which is inclined at 901, surface faults develop as expected in the form of ‘‘palm tree structures’’. However, this behavior does not agree with the observations made in this study.

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The best-fit result of the parameter study to evaluate rock mass strength values necessary to support a circa 201 dipping slope is shown in Fig. 9b. This model reveals that the stratigraphic column may consist mechanically of only one, massive wall rock unit (indicated by dark grey particles in Fig. 9b). Other stratigraphies are also modeled including about 400 m thick cap rock unit. Regardless of its the mechanical strength, the cap rock unit has only very minor influence on the overall slope evolution. The main reason may be found in the fact that the present tectonic chasma wall models show a maximum resolution of about 1000 m caused by their large particle diameters. The proposed thickness of the ‘‘cap rock’’ of about 400 m (e.g. McEwen et al., 1999; Treiman et al., 1995) as a unit of distinct mechanical properties, lies therefore beneath the model resolution. This is especially valid for the layers within the chasma walls of Valles Marineris, where thicknesses vary between about 5 and 50 m (McEwen et al., 1999). The assumption, that at such a scale the chasma walls are mechanically homogeneous, can also be implied from the vertically fairly uniform erosional patterns (e.g. Schultz, 2002). As mentioned previously, the mechanical properties of an artificial material are defined by the microproperties of its constitutive particles and particle-toparticle bonds. The best-fit micro-properties of the wall rock are displayed in Table 2. The bulk-properties or macro-properties of this unit are determined as described above by performing a series of numerical strength tests on the considered artificial material. Their results are summarized in Table 3. The latter are discussed below in detail, together with the lithology of the wall rock. 7.7. Scarp recession (Fig. 10a) In the second phase, it is assumed that denudation sets in at high rates causing the slope to recess forming a fault-line scarp (e.g. Keller and Rockwell, 1984). To implement the results of the denudation model, the corresponding particles are deleted manually within the final state of the first phase of the best-fit tectonic

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chasma wall model. The best-fit denudation model is based on a bipartite stratigraphic column consisting of a 0.4 km thick cap rock unit (e.g. McEwen et al., 1999; Treiman et al., 1995) and a 4.1 km thick intermediate unit. Their combined thickness represents an ‘‘ancient’’ slope height (Fig. 9a). The vertical resolution of this model is about 26 m, which allows the cap rock unit to be taken into account. Layering within the wall rock is

Fig. 10. (a) A sketch of the end of the second phase of the combined tectonic and denudational chasma wall models. During this phase denudation is simulated, which causes the tectonically induced slope to recess forming a fault-line scarp. The slope recession leads to the exposure of undisturbed, horizontal layers within the chasma wall. Denudation acting on the antithetic fault scarp is not modeled but may have in fact happened on Mars. During that phase the basement fault is assumed to be inactive. (b) The mathematical model after Scheidegger (1991) to simulate the evolution of the upper section of the northern wall of eastern Candor Chasma (located above presentday terrace). Different m-values indicate individual stages in the iteration process. m ¼ 0 indicates the initial slope, m ¼ 400 the best-fit final one. The color bar represents the stratigraphic column; the altitudes of the unit boundaries are indicated. Dark grey—cap unit, resistant factor a ¼ 1:0; light grey—intermediate unit, resistant factor a ¼ 1:25:

Table 3 Best fit rock mass properties for the material ‘‘wall rock’’ Rock type

Macro properties (rock mass properties)

Value

Unit

Wall rock

Uniaxial compressive strength Brazilian tensile strength Static Young’s modulus Poisson’s ratio Internal friction angle Cohesion Density

5.0 (70.7) 1.6 (70.2) 4.7 (71.5) 0.2 (70.15a) 22 (72) 1.6 (70.2) 2200 (7500)

MPa MPa GPa — Degrees MPa kg m
3

a

The values of Poisson’s ratio obtained in PFC 2D are not strictly comparable with the Poisson’s ratio of a real material obtained from a triaxial test (ITASCA, 1999, Augmented Fishtank, p. 61).

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again not modeled. MOC narrow angle images analyzed in the present study, do not give evidence that bands of differing albedo indicate sufficient differences from each other with respect to their competence against denudation. Interpretations concerning materials and processes, which formed the cap rock unit, are still uncertain. Proposed arguments are, e.g. a massive unit of lava flows (McEwen et al., 1999) or wall rock material altered by diagenetic processes as described in Treiman et al. (1995). After time step m ¼ 400; the best-fit model (Fig. 10b) yields an amount of slope recess, which is based on geometrical considerations necessary to create a terrace such as that of the mean profile (Fig. 4c). The slope recession is sufficient to cut through the fault zone and to expose undisturbed layered wall rock. The best-fit model (Fig. 10b) confirms that the most resistant unit against denudation is the cap unit, followed by the 20% weaker wall rock unit. Under these conditions, the slope retreats without major change to its dip. However, the toe slope becomes shallower and the head slope is steepened due to the resistant of the cap rock. Thus the slope develops an overall concave appearance, as seen on the upper section of the mean profile (Fig. 4c). Detailed information on the model properties are presented in Table 4. The basement fault is assumed inactive during this phase. This period of massive slope recession may correspond to a ‘‘wet’’ period where volatiles or interstitial ice were involved in the massive widening of troughs within the central Valles Marineris, which has later been followed by a ‘‘dry’’ period of very minor denudational activity (Peulvast et al., 2001). According to the present model, the total scarp retreat amounts to about 30 km (Fig. 10a). Should this ‘‘wet’’ phase have continued through the Late Hesperian Period (e.g. Lucchitta et al., 1992) for about 0.5 Gyr (Hartmann and Neukum, 2001), then the retreat rate can be estimated at about 60 m Myr
1. This value is comparable, e.g. with post early Eocene scarp retreat rates for the southwest margin of the Colorado Plateau (Young, 1985).

7.8. The second ‘‘recent’’ faulting period (Fig. 11) The third phase is again simulated within the distinct element code by reactivating the same set up as in phase one. During this phase, the denudation processes are assumed to stop and faulting to set in again throughout a reactivation of the existing fault plane. To implement the results of the denudation model, the corresponding particles are deleted manually as if they would have been removed by denudation. During this phase, the ‘‘recent’’ (Peulvast et al., 2001) fault scarp and a corresponding ‘‘recent’’ level of the chasma floor evolve. In addition, within this distinct element model a second planar antithetic fault evolves with a constant dip of about 551. Within the fault zone, layering remains recognizable but tilted. Following or simultaneously to the most ‘‘recent’’ faulting, a minor period of denudation can be assumed to set in causing the basal fault scarp to dissect (e.g. Fig. 7E in Peulvast et al., 2001, p. 339). This causes an overall ‘‘rounding’’ of the profile (e.g. Fig. 12a). 7.9. Comparison between the simulation results and the mean chasma wall profile (Fig. 12a) The presented model of a combination of tectonic and a denudational processes shows that a wall profile

Fig. 11. A sketch of the end of the third phase of the combined tectonic and denudational chasma wall models. During this phase the denudation rate is assumed to have ceased. Movement at the basement fault sets in again, which reactivates the existing fault zone forming the ‘‘recent’’ (e.g. Peulvast et al., 2001) relief of about 8 km. It also induces within the tectonic chasma wall model the formation of a new, second antithetic surface fault and seems to reactivate the exiting one to a lesser degree.

Table 4 Initial and boundary conditions of the best-fit denudation model simulating recession of the ‘‘ancient’’ fault scarp Constants, variables

Value

Unit

Description

tmþ1
tm m n

0.024 400 162

Unit time — —

Time increment Number of iterations steps Number of x values

acap

1.0

—

awall

1.25

—

20 4.1

Degrees km

Factor describing the resistance against denudation Factor describing the resistance against denudation Initial slope angle Slope height

Note

Both ends of the slope are bounded by horizontal planes Resistance of the cap unit Resistance of the wall rock unit

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created by two periods of normal faulting and a major interim period of scarp recession due to denudation fits the observed mean profile strikingly well (Fig. 4c). Furthermore, this combined model is capable of explaining a number of observations. As discussed previously, normal faulting with displacements of the order of kilometers within relatively weak material can produce a fault zone with incorporated tilted blocks rather than a high, sharp fault scarp. Hence, exposed and more or less undisturbed layering of the foot wall block would only be expected over a small section at the crest of a fault zone. This stands in contrast to observations of the present study, which confirm layering. This is especially the case for the wall

Fig. 12. (a) A sketch of the result of the third phase of the combined tectonic and denudational chasma wall models (Fig. 11) overlain by the mean profile (Fig. 4c). It can be seen that the result of the combined models matches the mean profile very well. Furthermore, the result of the combined models displays undisturbed layering in the upper slope sections and a debris slope with incorporated tilted blocks in the lower slope section, as is seen in this study on MOC narrow angle images (Fig. 3c). According to this simulation result, the slope is interpreted as consisting of two parts: an ‘‘ancient’’ fault-line scarp with its base forming the present-day terrace and a ‘‘recent’’ degraded fault scarp. The chasma floor at the base of the northern wall may be interpreted as consisting of ‘‘cap rock’’ material. This area is the deepest section within eastern Candor Chasma and forms a chasma within the chasma. According to the result of the tectonic chasma wall models it may be interpreted as a trench. The southern flank of that trench is therefore not only formed by thick interior layered deposits (Lucchitta et al., 1994) but may also be raised due to antithetic normal fault movements. (b) Details showing the toe section of the 33 MOLA profiles used in this study. Many of them display a tripartite profile. Firstly, there is a moderately steep section at the base of the profiles: the present study interprets this as a fault zone consisting of tilted blocks (TB) covered with debris. Secondly, at an elevation of around
2 km, a steeply dipping zone can be observed. The present study interprets this as the EFS. Finally, an almost flat zone which represents the lower part of the terrace, which is interpreted by the present study as being an ‘‘ancient’’ chasma floor level.

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sections above the terrace utilizing MOC narrow angle images (Figs. 3a and b). The denudation model applied in the present study can explain undisturbed layering through slope recession (Fig. 10a). The mathematical denudation model also can explain the steep chasma rim. The basal fault scarps suggest ‘‘recent’’ tectonic deformation (Peulvast et al., 2001). Fig. 12b displays the toe section of the 33 MOLA orbits used in this study. Many of them show a tripartite profile. Firstly there is a moderately steep section at the base of these profiles: the present study interprets these as a fault zone consisting of tilted blocks covered with debris (Fig. 11, TB). This may be confirmed by the present study utilizing MOC narrow angle images. In all probability, some images show fractured blocks, whose layering exhibit varying dip directions (Fig. 3c). Above this section, at an elevation of around -2 km, follows a steeply dipping zone. The present study interprets this zone as the exposed footwall of the fault scarp (Fig. 11, EFS). Within this zone, the profiles display a dip of between 301 and 401. These dips are comparable to the fault dips measured photogrammetrically by Chadwick and Lucchitta (1992) but are significantly lower than those presented subsequently by Chadwick and Lucchitta (1993). Taking into account the degrading effect of minor, post faulting denudational activity on the fault scarp, the dips of these profiles within this second zone would correlate quite well with the circa 451 dip of the final surface fault that is invoked by the best-fit tectonic chasma wall model (Fig. 11). The footwall of this final surface fault zone displays (as expected) layering that is not significantly disturbed (e.g. Fig. 11). This may to be confirmed by the present study utilizing MOC narrow angle images (Fig. 3b). Above this middle section a third, almost flat zone can be observed. This zone represents the lower part of the terrace, which is interpreted by the present study as being an ‘‘ancient’’ chasma floor level (e.g. Hamblin, 1976 in Peulvast et al., 2001, Fig. 7e). It is expected that the High-Resolution Stereo Camera onboard the ongoing European ‘‘Mars Express’’ mission, will provide additional high-quality remote sensing data of the lower sections of the walls of eastern Candor Chasma. This would be critical for future attempts of the investigation of the development of these wall slopes. The floor at base of the northern wall is the deepest section within eastern Candor Chasma and seems to form a chasma within the chasma (e.g. Figs. 2 and 3a). According to the result of the best-fit tectonic chasma wall model (e.g. Fig. 12a), it may be interpreted as a trench (Fig. 3a). The southern flank of that trench may therefore not only be formed by thick interior layered deposits (Lucchitta et al., 1994). It may also be raised due to antithetic normal fault movements.

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8. Discussion on the lithology of the wall rock unit The very high wall slopes of Valles Marineris offer a deep natural insight into the upper crust of Mars. They are thought to expose the record of the geological history of Mars. A key of great importance for the understanding of this history would be a knowledge of the lithological composition of this wall rock unit. 8.1. Mineral surface spectra A first approach is to interpret infrared surface spectra: data from the Mars Global Surveyor Thermal Emission Spectrometer (TES) do not match terrestrial high-silica igneous rocks such as granite and rhyolite, ultramafic igneous rocks, limestone, or quartz- and clayrich sandstone and siltstone (Christensen et al., 2001). Such rock types can be generally excluded to make up the northern wall of eastern Candor Chasma. On the other hand TES data closely match the surface spectra of basaltic sands for dark regions in the southern highlands (Christensen et al., 2001). Also, Gaddis et al. (2002) interpreted layered dark deposits within the walls of Valles Marineris as to be of volcanic origin based on TES data. Similar results for dark regions have been obtained by the Imaging Spectrometer ISM aboard the Soviet Phobos 2 probe, indicating a basaltic mineralogy (Bibring and Erard, 2001; Erard et al., 1991). 8.2. Wall rock mass density A second approach to gain knowledge about wall rock lithology is to discuss possible wall rock densities. Both McKenzie et al. (2002) and McGovern et al. (2002) calculated the relationship between gravity and topography for Valles Marineris (in addition other areas) and compared them to those predicted from models of the Martian crust. In the model of McKenzie et al. (2002) a low crustal density of 2350 kg m
3 fits best the observed admittance spectra for Valles Marineris. The authors stated that such low crustal density may be caused by differences in composition between the denser Tharsis volcanoes and the walls of Valles Marineris. Another proposed alternative is that the density is reduced by the presence of a large proportion of interstitial ice within the stratigraphic column. McGovern et al. (2002) proposed two models as a best-fit for their admittance spectra of Candor Chasma: one of even lower crustal densities than McKenzie et al. (2002) between 2000 and 2200 kg m
3 or a high-density crust of somewhat less than 2900 kg m
3 in combination with a significant amount of subsurface loading by intrusion of dense mafic dykes. Each scenario would have a major impact on the mechanism of the evolution of Valles Marineris troughs. In the first of these models, McGovern et al. (2002) saw a consistency with ideas

that the troughs had been cut into a low-density crust, which might consist either of compacted sedimentary deposits, ash deposits or altered, originally denser basaltic material. In the second of these models McGovern et al. (2002) saw a consistency with the idea that the chasmata of Valles Marineris were formed by a combination of collapse and extensional faulting. Wall rock mass densities (Table 3) from 1700 to 2700 kg m
3 are consistent with the best-fit rock mass strength properties of the tectonic chasma wall model in terms of the resulting stable slope angle. The present study is not able make a conclusive comment to this discussion. Also, the question of the existence of significant amounts of interstitial ice can not be answered. The content of ice is not modeled explicitly. However, its presence is not compelling to explain any of the results of the present study. Only implications on the evolution of the northern wall of eastern Candor Chasma made in the present study, combined with the model discussed in McGovern et al. (2002) in which Valles Marineris chasmata are formed by a combination of collapse and extensional faulting, may give a clue to this ‘‘density question’’. These scenarios of both the models for the proposed formation of the northern wall of eastern Candor, presented in this study and the ‘‘second’’ model of McGovern et al. (2002) are comparable, since both models include tectonic and erosional components for the trough formation. If both models are assumed to be right, this would suggest that for the present study a density of 2700 kg m
3 would reflect the present, and to a possibly large degree the past, wall rock mass density of the northern wall of eastern Candor Chasma. 8.3. Wall rock mass strength A third approach to gain knowledge about wall rock lithology is to find terrestrial analogs of rocks which match the gained information on rock mass strength properties that are consistent with the best-fit tectonic chasma wall model. Additionally, the properties of these analogs must match TES, ISM data and the previous discussion on rock mass densities. Values of 1.6 (70.2) MPa for cohesion and 221 (72) for internal friction angle derived in the best-fit model of the present study are of the same order of magnitude as strength properties proposed in previous studies for Valles Marineris. Recent models of slope stabilities by Schultz (2002) yielded wall rock strength properties of 0.1–0.2 MPa for cohesion and an internal friction angle of 19–251. Wall rock tensile strength properties of 1.6 (70.6) MPa derived in the present study are comparable to tensile strength values postulated by Golombek et al. (1995) and Tanaka and Golombek (1989) for shallow crustal materials on Mars. Based on analytical slope stability considerations, Clow and Moore (1988) proposed wall rock strength properties of about 0.4 MPa

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for cohesion and 201 as internal friction angle for the Tithonium-Ius Chasma region. In reference to this and other studies, Lucchitta et al. (1992) suggested that the chasma walls in Noctis Labyrinthus and Ius and Tithonium Chasmata where comprised by volcanic tuff or rocks similar to tuff produced as impact ejecta of volatile target rocks. However the formation of impact ejecta deposits is possibly not consistent with the relatively thin layering of wall rocks observed in the present study. Based on TES and ISM data, these voluminous tuff deposits appear to be of basaltic origin. Such voluminous basaltic tuff deposits are not known on Earth but could indeed be possible on Mars as discussed by Hynek et al. (2002), Mitchell et al. (2002), Schott and van den Berg (2002), Weitz and Hort (1998), Wilson et al. (1998), and Geissler et al. (1990). A second material which matches all, the density considerations by McGovern et al. (2002) or McKenzie et al. (2002), the spectral data by TES and ISM and the mechanical rock mass properties, as derived in the present study, is columnar jointed basalt (e.g. Schultz, 1993, 1995, 2002; Caruso and Schultz, 2001). This result is however still highly speculative, as input data display large variances. It seems that only a future lander mission within Valles Marineris itself would allow a final judgment to be made. However on the scale of the entire chasma wall a distinction between tuff and basalt may not be necessary since both may be present as alternating relatively thin layers of (dark colored) lava flows (e.g. McEwen et al., 1999) and (light colored) pyroclastic deposits, such as those seen for terrestrial stratovolcanoes.

9. Extension of the study results for the Northern wall of Eastern Candor Chasma to other trough walls of the Valles Marineris system The erosional and tectonic history of Valles Marineris is very complex and will continue to be a subject of debate. The aim of the present study is to gain insight of the possible mechanical rock mass parameters of a suitable Valles Marineris wall section by inference from the slope morphology. Extending the results of the present study by comparing the proposed history of the northern wall of eastern Candor Chasma to other walls within the system of Valles Marineris would be of interest but exceeds by far the scope of the present study. Within the central Valles Marineris, the composition of the wall rock seems to be remarkably uniform (e.g. McEwen et al., 1999; Treiman et al., 1995; Lucchitta et al., 1992, 1994). It is therefore not surprising that studies which have investigated present wall rock strength properties within Valles Marineris so far (Me`ge and Gatineau, 2003; Schultz, 2002; Caruso and Schultz, 2001; Clow and Moore, 1988) yielded quite similar results. Due to this, the rock mass strength results of the

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present study compare remarkably well with the studies mentioned above. Thus it is reasonable to conclude that the rock mass strength results of the present study are representative for actual mechanical properties of all walls within the central Valles Marineris.

10. Conclusions This study investigates mechanical rock mass parameters of the northern wall of eastern Candor Chasma by inference from its present-day morphology and an assumed slope-forming history. A distinct element code is applied to simulate the tectonic element of the slope evolution and a parameter study performed, to investigate mechanical rock mass parameters consistent with the assumed past and observed present slope morphology. Additionally, a mathematical denudation model is applied to simulate the effect of denudation to complete the picture of the slope-forming history. This study proposes that two periods of normal faulting together with a massive interim denudational scarp recess are valid combined models for the evolution of the northern wall of eastern Candor Chasma. It is also shown that the rate of the interim scarp recess is comparable to certain terrestrial scarp retreat rates. The best-fit tectonic model yields a homogenous distribution of low-level wall rock mass strength and deformability properties distributed over the entire stratigraphic column of the northern wall of eastern Candor Chasma (at a maximum resolution of approximately 1000 m), which is reasonably representative for the entire present-day central Valles Marineris. This study favors columnar jointed basalt as the material that makes up the northern wall of eastern Candor Chasma and the other walls within the central Valles Marineris. However, it must be stated that this result is highly speculative as input data display large variances. The best-fit denudational model of the upper slope section of the northern wall of eastern Candor Chasma recognizes a distinct cap rock unit of lesser susceptibility to denudation than the wall rock below.

Acknowledgements This study was performed at the German Aerospace Centre (DLR), Berlin, Germany. The author is very grateful to Tim Vietor and Erik Rybacki both from the Geoforschungszentrum (GFZ), where he was able to perform simulations on PFC-2D. He is also grateful to Ernst Hauber and Marita Waehlisch (DLR-Adlershof), Marcel Naumann (GFZ Potsdam), Heinz Konietzky (ITASCA Germany), Manfred Buchroithner (Technical University Dresden), Sarah Springman (ETH Zurich), Richard Longden and Adele Inferrera for thorough comments and constructive reviews of this manuscript.

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