1. Possible Temperature-Related Slope and Surface Roughness Differences Between the North and South Walls of Coprates Chasma, Mars joern@jernsletten.name http://joern.jernsletten.name/ Tirsdag, 15. Juni 2004 Universitetet i Bergen Universitetet i Bergen Det Matematisk-Naturvitenskapelige Fakultet Det Matematisk-Naturvitenskapelige Fakultet Institutt for Geovitenskap Institutt for Geovitenskap Doctor Philosophiae Doctor Philosophiae Disputas Jørn Atle Jernsletten Jørn Atle Jernsletten

2. Outline Questions? Geology and stratigraphy of Valles Marineris / Coprates Chasma Creep of ice-rich geologic materials – – Deformation mechanisms – – Temperature dependence in material strength – – Earth / Mars analogs MOLA data Topographic architecture of Coprates Chasma Topographic profiling methods Data and statistics Conclusions

3. Questions? Effect of temperature on topography of the near-equatorial trough of Coprates Chasma? Presence of ground ice and its role in landscape evolution? Over geologic time, surface temperature factor in: – – Rheology and stability of ice-rich geologic materials – – Evolution and morphology of the trough walls – – Controlling the distribution of ground ice Do expected temperature differences result in: – – Measurable differences in slope angles? – – Measurable differences in surface roughness?

4. Chronology Based on Crater Counts ( Adapted from McKee, 2003, after: Hartman and Neukum, 2001; Jakosky and Phillips, 2001; Zuber, 2001; Tanaka et al., 1992 )

5. Global Map of Mars ( Modified from Eötvös Lornd University, 2001 ) ( Modified from Eötvös Loránd University, 2001 )

6. Geologic Map Legend √ √ √ √ ( Created from GIS tabular data from Scott and Tanaka, 1986 ) √ √

7. Valles Marineris Geologic Map ( Modified from Scott and Tanaka, 1986 )

8. Coprates Chasma Layering and Spur-and-Gully Morphology b. This close-up is centered at 14.5° South, 55.8° West; Image covers an area of approximately 9.8 km by 17.3 km; North is up ( MOC images courtesy of NASA/JPL/Malin Space Science Systems ) a. Context imageb. Central ridge close-up

9. Stress / Strain Relationships μ = ε 1 /ε 3 Equation 4.3 Poisson ’ s ratio, μ, ratio of unit strain perpendicular and parallel to applied stress: Poisson ’ s ratio describes the ability of a solid to shorten parallel to σ 1 without elongation in the σ 3 direction, and can vary from 0 (compressible) to 0.5 (incompressible) In the case of ideally viscous (Newtonian) materials, strain rate is related in a linear fashion to applied stress: σ = ηέ Equation 4.4 where η is the viscosity, a material property constant During steady state creep, the stress and strain rate are related in a power law: έ = A exp –(Q/RT)σN Equation 4.5 where T is the absolute temperature; A is a temperature-dependent constant, the frequency factor; Q is a constant, the activation energy for creep; R is the universal gas constant; and N is the stress exponent, typically varying from 1-2 when σ is < 20 MPa, and from 2-4 when 20 < σ < 200 MPa

10. Map of the Deformation Mechanisms of Ice As a function of temperature, applied stress, and strain rate ( from Carr, 1996, after Shoji and Higashi, 1978 )

11. Constitutive Relation for Ice Glen's Flow Law is widely accepted as the constitutive relation for ice when shear stress acts on its basal plane: where έ is the strain rate; A is a temperature-dependent constant; τ b is the basal shear stress; and n is a power law exponent (Glen, 1958) έ = A τ b n Equation 4.15   Regards ice as a plastic substance with a yield stress τ of 1 bar (Paterson, 1981)   Value of n generally taken as 3 (Paterson 1981; Johnston, 1981)   Shear strain rate (flow velocity) is lower for colder ice as a function of A   A varies with temperature, and is equal, for example, to 6.8 x 10 -15 s -1 kPa -3 at 273 K, 4.9 x 10 -16 at 263 K, 1.7 x 10 -16 at 253 K, and 5.1 x 10 -17 at 243 K   n varies with applied stress, taking a value of 1 for Newtonian deformation, and 3 for non-Newtonian deformation (Paterson, 1994)   Available evidence indicates that n = 3 for most situations (Russell-Head and Budd, 1979)

12. Deformation of Frozen Ground The total strain in deforming frozen ground is the sum of an instantaneous strain, ε (i), and a creep strain, ε (c). The primary creep of frozen ground (and ice) in a state of constant stress can be described by the creep law (Andersland et al., 1978): ε (c) = Kσ n t b Equation 4.17 where K, n, and b are temperature-dependent material constants The steady state creep strain is governed by the creep law (Hult, 1966): έ (c) = G(σ, T) Equation 4.18 where έ (c) is the steady state (secondary) creep rate; and the function G(σ,T) is found by plotting the slope dε (c) /dt against the applied stress for various temperatures

13. Temperature Dependence in the Creep Law where έ c is the creep rate selected for the laboratory experiment - for frozen soils is often taken as 10 -5 min -1 (Andersland et al., 1978); σ c is the uniaxial stress for the selected creep rate; σ c (T) and n(T) are temperature-dependent creep parameters The creep law can be rewritten in the form of a power expression (Hult, 1966; Ladanyi, 1972): έ (c) = έ c [σ/σ c (T)] n(T) Equation 4.19   The equations for both primary and secondary creep emphasize the temperature-dependence of creep deformation

14. Dependence on Temperature of Compressive Strength for Ice and Various Frozen Soils ( From Andersland et al., 1978; after Sayles, 1966 )

15. Debris-Ice Feature Terminology ( Adapted from Whalley and Azizi, 2003 )

16. Typical Rock Glaciers in Wrangell Mountains, Alaska Rock glacier “a” has a single lobe, and rock glacier “b” has a second lobe that appears to have advanced on top of another lobe that advanced at an earlier time ( Adapted from Whalley and Azizi, 2003 )

17. Two Possible Rock-Ice Systems in Candor Chasma, Mars Feature “A” resembles a rock glacier, and feature “B” resembles a protalus rampart ( Adapted from Whalley and Azizi, 2003; After Malin et al., 2000 )

18. Enlargements of Candor Chasma Features Feature “A” resembles a rock glacier, and feature “B” resembles a protalus rampart ( Adapted from Whalley and Azizi, 2003; After Malin et al., 2000 ) Enlargement of feature A Enlargement of feature B

19. Mars Orbiter Laser Altimeter (MOLA) Data Polar orbit Nadir measurements ±30 cm vertical accuracy ~150 m spot size ~330 m along-track spacing (along orbital track) Good coverage in Valles Marineris region

20. 1/64° Gridded MOLA Elevation Data 1/64° resolution ≈ 926 m/pixel Elevation: ±30 cm vertical accuracy Steepest gradient slope angle Steepest gradient slope aspect (slope orientation) Measures of surface roughness: –Curvature (slope of slope) –Surface area ratio (ratio of total surface area to planimetric surface area) Intermediate products: –Cosine (aspect) –North-South component of slope angle –Local incidence angles Temperatures

21. 247 Profiles Across Coprates Chasma Coprates Chasma Trough Wall Cutout marked on this map is the location of the trough wall segment in Figure 6.2. The points marked in green are the starting points for each profile, while the points in red are correspondingly the end points for each profile. From west to east, the two profiles marked in bright red are Coprates Chasma profile number 100 and Coprates Chasma profile number 200, respectively

22. Basic Topographic Architecture of Coprates Chasma Extends from 54º to 70º West longitude 10º to 17º South latitude ~1,000 km long Trough trends 100º-104º Elevations at trough rims range from 0.5 km below datum to 5.5 km above datum –Highest elevations along the segment of the trough extending from 64º to 67º West longitude Width of trough ranges from 70 km to 125 km Trough wall heights vary from ~4.5 km to ~10.5 km –Deepest segment of the trough extending from 64º to 67º West longitude

23. Structural Cross-Section of Coprates Chasma ( Adapted from Schultz, 1991 )

24. Steepest Gradient Slope Angles and Aspects   Arrow on trough wall points in direction of steepest gradient   Slope angle is calculated in this direction   Slope aspect is the horizontal direction (bearing) in which the arrow points

25. Topographic Profiling Rules 1)The trough rim, coming in either direction (~north or ~south) is the first point steeper than 5° where it and the next 14 points (15 points total) average > 8.75° 2)Points selected for analysis must: a)Be located between the rim and the first point at which elevation is <= rim elevation minus 50% of the difference between the rim elevation at that side of the trough (north or south) and the absolute lowest elevation anywhere along the profile (inclusive) b)Have slope aspects within +/- 60° (non-inclusive) of profile trend (for most Coprates profiles, ~194° trend coming from north, correspondingly ~14° trend coming from south) c)Have slope angles > 5° 3)Each of the 5 topographic parameters (elevation, slope angle, slope aspect, curvature, surface area ratio) is averaged in a "selective average" over the wall segment extracted according to 2) as follows: a)The sum of values of the parameter at all points satisfying 2) rules b)The count of points satisfying 2) rules c)a) divided by b) for north and south trough walls, respectively 4)Going downslope, find the first 5 points averaging < 3.7º, last of the 5 is the trough wall bottom

26. Valid Points for Analysis Along Coprates Chasma Profile Number 200   Vertical exaggeration = 6x   Profile aspect = 187.2 º (North wall) / 7.2 º (South wall)

27. Cryosphere and Thermal Equations Equation 3.1 T ms = 64 K cos i + 154 KEquation 6.2 where z is depth, K is the thermal conductivity of the Martian crust, T mp is the melting point of ground ice, T ms is the (latitude-dependent) mean annual surface temperature, and Q g is the value of the geothermal heat flux. Nominal values cited for Mars are Q g = 30 mW m -2, K = 2.0 W m -1 K -1, and T mp = 252 K (Clifford, 1993) Steady state one-dimensional heat conduction equation: Simplified surface energy balance equation (Equation 6.1): where i is the local incidence angle; assuming an albedo of A b = 0.25, a thermal conductivity of k = 2.0 W m -1 K -1, and ignoring the latent heat of CO 2 sublimation ( L ); works well equatorward of approximately 45 º north or south latitude

28. Thermal Equations Equation 6.1 i = abs (l - β)Equation 6.3 β = s cos aEquation 6.4 Surface energy balance equation: where S 0 is the solar constant at 1 AU, R is the mean distance of Mars from the sun, A b is the bolometric albedo, i is the local incidence angle of sunlight, k is the thermal conductivity of the regolith, F a is the downward component of atmospheric radiation, L is the latent heat of CO 2 sublimation, m is the mass of CO 2 condensate per unit area, ε is the surface emissivity, σ is the Stephan-Boltzmann constant, and T is temperature (Kieffer et al., 1977; Clifford, 1993) Local incidence angle: where i is the local incidence angle, l is latitude, and β is the north-south component of slope North-south component of slope: where β is the north-south component of slope s is slope angle, and a is slope aspect (slope orientation)

29. Temperature vs. Incidence Angle

30. Coprates Chasma Temperature Data

31. Temperature vs. Longitude Temperature was calculated using Equation 6.2, Equation 6.3, and Equation 6.4

32. Temperature Along Coprates Chasma Profile Number 200   Vertical exaggeration of elevation profile = 5x

33. Calculated Possible Depths to the Base of the Martian Cryosphere ( Adapted from tabular data, Clifford, 1993 ). The thermal model used Equation 3.1, and with the following values for parameters: Minimum: Q g = 45 mW m -2, K = 1.0 W m -1 K -1, and T mp = 210 K; Nominal: Q g = 30 mW m -2, K = 2.0 W m -1 K -1, and T mp = 252 K; Maximum: Q g = 15 mW m -2, K = 3.0 W m -1 K -1, and T mp = 273 K

34. Coprates Chasma Profile Number 200 with Hypothetical Cryosphere Calculated using Equation 3.1; Nominal values cited for Mars are Q g = 30 mW m -2, K = 2.0 W m -1 K -1, and T mp = 252 K (Clifford, 1993); T ms was calculated using Equation 6.2, Equation 6.3, and Equation 6.4 a. 6x vertical exaggeration b. No vertical exaggeration 3.6 km 2.2 km

35. Coprates Chasma Slope Angle vs. Longitude for North and South Walls

36. Coprates Chasma Slope Angle Differences

37. Coprates Chasma Curvature vs. Longitude

38. Coprates Chasma Surface Area Ratio vs. Longitude

39. Paired Differences Between North and South Wall Data

40. Elevations of Coprates Chasma Floor and Surrounding Plateaus

41. Coprates Chasma Trough Rim Elevation vs. Longitude

42. Coprates Chasma Trough Wall Height vs. Longitude

43. Coprates Chasma Trough Wall Bottom Elevations for North and South Walls

44. Coprates Chasma Trough Wall Bottom Elevations There is NO significant difference in elevation between the North and South trough wall bottoms The place is FLAT!

45. Slope Angle Correlations With Morphological and Structural Patterns Morphologic and structural patterns are from Peulvast et al. (2001) Morphology Key (1) Cornice with smooth talus slope; (2) Cornice with spurs and gullies; (3a) Crest with spurs and gullies on both sides; (3b) Crest with spurs and gullies on one side and smooth talus slope on the other side; Structure Key (4a) Fault; (4b) Conjectured fault; (5a) Normal fault; (5b) Conjectured normal fault

46. Coprates Chasma Trough Wall Height vs. Slope Angle ( Results of Schultz, 2002 Superimposed on Results from this Study; Mége and Gatineau, 2003: RMR = 50-70 )

47. Conclusions North walls of Coprates Chasma 1.33º ± 0.49º steeper than South walls No significant difference in curvature between North walls and South walls Surface area ratios 0.011 ± 0.004 higher in the North walls than in the South walls Cryosphere thickness – – ~3.7 km in North walls – – ~2.3 km in South walls ~10 K temperature difference Similarities between walls – – Horizontal stratigraphic layers – – Spur-and-gully morphology – – Apparently similar materials – – Geology Extremely flat trough floor Tectonic symmetry