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Mechanical modeling of thrust faults in the Thaumasia region, Mars, and implications for the Noachian heat flux
Icarus 186 (2007) 517–526 www.elsevier.com/locate/icarus
Mechanical modeling of thrust faults in the Thaumasia region, Mars, and implications for the Noachian heat flux M. Grott a,∗ , E. Hauber a , S.C. Werner c , P. Kronberg b , G. Neukum c a Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstraße 2, 12489 Berlin, Germany b Institute of Geology, Technical University of Clausthal, Leibnizstraße 10, 38678 Clausthal-Zellerfeld, Germany c Institute of Geological Sciences, Freie Universität Berlin, Malteser Straße 74-100, 12249 Berlin, Germany
Received 2 June 2006; revised 25 September 2006 Available online 17 November 2006
Abstract Insight into the state of the early martian lithosphere is gained by modeling the topography above surface breaking thrust faults in the southern Thaumasia region. Crater counts of key surface units associated with the faulting indicate a scarp emplacement in the late Noachian–early Hesperian periods between 4.0 and 3.7 Gyr. The seismogenic layer thickness at the time of faulting is constrained to 27–35 km and 21–28 km for the two scarps investigated, implying paleo geothermal gradients of 12–18 and 15–23 K km−1 , corresponding to heat flows of 24–36 and 30–46 mW m−2 . The heat flow values obtained in this study are considerably lower than those derived from rift flank uplift at the close-by Coracis Fossae for a similar time period, indicating that surface heat flow is a strong function of regional setting. If viewed as representative for magmatically active and inactive regions, the thermal gradients at rifts and scarps span the range of admissible global mean values. This implies dT /dz = 17–32 K km−1 , with the true value probably being closer to the lower bound. © 2006 Elsevier Inc. All rights reserved. Keywords: Mars, surface; Mars, interior; Tectonics
1. Introduction The way in which the lithosphere responds to tectonic deformation can give important clues to its thermal state at the time of structure emplacement and a variety of methods to constrain lithospheric properties have been applied to Solar System objects including icy satellites (Nimmo et al., 2003; Nimmo and Pappalardo, 2004), Mercury (Watters et al., 2002), Venus (Barnett et al., 2002) and Mars (Schultz and Watters, 2001; McGovern et al., 2004; Grott et al., 2005). In this paper we investigate the topography of lobate scarps in the southern Thaumasia region to constrain the mechanical and thermal state of the martian lithosphere in the late Noachian–early Hesperian period. The Thaumasia region of Mars is located in the south of the Tharsis province, a region which has been tectonically ac* Corresponding author.
E-mail address: [email protected] (M. Grott). 0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.10.001
tive throughout martian history (Anderson et al., 2001). The Thaumasia plateau was emplaced during the late Noachian to early Hesperian periods and its structural style is comparable to intra-continental plateaus on Earth. The geological evidence is most consistent with a formation process involving crustal underplating and subsequent uplift (Dohm and Tanaka, 1999) as the developing plateau was pushed over the adjacent foreland. Being concentric to the Tharsis rise, the fold and thrust margins considered here are part of the south Tharsis ridge belt and formed by compression and thrust faulting as a consequence of the uplift process (Schultz and Tanaka, 1994). Lobate scarps are landforms commonly encountered on the Moon, Mercury and Mars and they are characterized by a steeply rising scarp face, a gently declining back scarp and a trailing syncline (Schultz, 2000). On Mars, lobate scarps are located in Noachian terrain and they have relief of the order of a few hundred meters (Watters and Robinson, 1999; Watters, 2003), although individual scarps stand up to 1200 m above the surrounding highlands (Schultz and Watters, 2001). The way in which many lobate scarps offset the walls of impact
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craters suggests that they are compressional tectonic features, being the expressions of surface breaking thrust faults (Watters et al., 2001, 2004). The faults beneath lobate scarps are assumed to deform the entire brittle lithosphere and scarp topography is primarily controlled by the faulting geometry (Schultz and Watters, 2001; Watters et al., 2002). The distribution of vergence directions of thrust fault-related folds in the Tharsis province indicates a strong coupling between the underlying Noachian crust and the Tharsis rise, also favoring lithosphere-scale thick-skinned deformation processes (Okubo and Schultz, 2003). As the zone of seismic deformation is bounded by the onset of plasticity at depth (Scholz, 1998), the depth of faulting may be connected to an isotherm, constraining the thermal structure of the lithosphere. In this work we determine the depth of this brittle–ductile transition beneath lobate scarps in the southern Thaumasia region by forward mechanical modeling of MOLA topographic data. The time of scarp formation is constrained by applying standard crater count techniques (Neukum and Hiller, 1981) to key surface units, using images taken by the High Resolution Stereo Camera (HRSC) on board the Mars Express mission (Neukum and Jaumann, 2004) as a database. Combining these methods allows us to determine the past thermal state of the martian lithosphere and helps to constrain the mean global heat flux during the late Noachian–early Hesperian period. 2. Geology and age determination 2.1. Geology Thaumasia forms the south-eastern region of the Tharsis bulge, the major volcano-tectonic structure on Mars. Tharsis formed over a long period, encompassing most of the planet’s history, but several lines of evidence suggest that the major part of Tharsis’ elevated topography was already in place at the end of the Noachian (Banerdt and Golombek, 2000; Anderson et al., 2001; Phillips et al., 2001). The Thaumasia plateau forms a large region of elevated topography. It consists of interior plains and a surrounding highland belt to the east, south, and west. In the north, Thaumasia is bordered by the trough system of Valles Marineris. The most detailed geologic mapping was performed by Dohm and Tanaka (1999) and Dohm et al. (2001). The interior lava plains of Thaumasia, i.e., Solis, Sinai, and Thaumasia Plana, are of Hesperian age. Their tectonic structure is characterized by wrinkle ridges, which are contractional features oriented concentric to the Syria Planum center of the Tharsis bulge. The highland belt consists of ancient material of mostly Noachian age. It is heavily fractured by different extensional fault sets, e.g., Claritas, Coracis, Nectaris, Thaumasia, and Melas Fossae, which can be grouped with respect to the time of their formation into five main stages (Dohm and Tanaka, 1999; Dohm et al., 2001; Anderson et al., 2001). In general, it seems that the peak of tectonic activity occurred already in the Noachian, and declined subsequently during the Hesperian and Amazonian (Tanaka, 1986; Scott and
Dohm, 1990; Dohm and Tanaka, 1999; Dohm et al., 2001; Anderson et al., 2001). Besides the lobate scarps, several other tectonic and magmatic structures are of particular interest for our study. Immediately adjacent to the lobate scarps is the elevated area of the Warrego rise (Fig. 1). It is an area of crustal thickening (Neumann et al., 2004), and sets of narrow grabens that intersect at the Warrego rise are deflected (Dohm and Tanaka, 1999). The Warrego rise is also a late Noachian–early Hesperian center of tectonic activity identified through vector and beta analyses of a comprehensive fault data base by (Anderson et al., 2001). Based on these observations, Dohm et al. (2001) suggest that the Warrego rise has a history of prolonged intrusive activity, with a peak of magmatic-driven tectonic activity at the end of the Noachian. The dense pattern of dendritic valleys of probably fluvial origin at the southern flanks of the Warrego rise (cf. Fig. 2) might be in agreement with such a scenario, since hydrothermal activity associated with the Warrego magmatism might have melted snow, which was preferentially precipitated at the high topography of the rise, and produced surface runoff (Gulick, 1998; Gulick, 2001). It has to be noted, though, that Ansan and Mangold (2006) question magmatic processes near the Warrego Valles. The Warrego rise is the dominant, but not the only possible magmatic center in the region. Several ancient volcanic edifices of Noachian to early Hesperian age were recognized by Scott and Tanaka (1981) and Scott (1982). They are heavily dissected and often associated with tectonic structures. At least two of them are clearly associated with the double rift system of Coracis Fossae (Kronberg et al., 2005), and according to the mapping of Dohm et al. (2001), another one is situated north of the western lobate scarp of this study. The Coracis Fossae rifts resemble terrestrial continental rifts. They trend in a NW–SW direction and have been investigated in detail by Grott et al. (2005). 2.2. Age determination The determination of the age of the thrust faulting at the lobate scarps is critical to our study. We use HRSC images with a resolution of about 20 m pixel−1 to measure the crater size-frequency distribution of key geologic units to derive their absolute ages. HRSC images are ideally suited for such an approach, since they combine a large areal coverage with relatively high ground resolution. We use standard crater count techniques (Neukum and Hiller, 1981) and apply the new cratering model described by Hartmann and Neukum (2001) and the polynomial description of crater production function given in Ivanov (2001). The HRSC imagery allows for reliable crater counts in the size range of craters with a diameter of >200 m. These counts were used for deriving the cratering model ages in a crater diameter range avoiding the potential problem that small secondary craters affect the original sizefrequency distribution (McEwen et al., 2005; Hartmann, 2005). The crater counts for four key units are given in Fig. 3. The deviation from the crater production function (Ivanov, 2001; Werner, 2005) indicate subsequent resurfacing, which is confirmed in the morphology. We made use of the fact that the
Thaumasia thrust faults
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Fig. 1. Topographic image map of the southern Thaumasia region (altimetry data derived from the MOLA 1/128◦ digital elevation model). Solid white lines indicate locations of topographic profiles, letters denote areas of crater counts.
lobate scarps form geologic contacts (Dohm et al., 2001). In these cases, the lobate scarp should have formed after the formation of the older surface, usually at the elevated back scarp, and before the younger surface extending from the scarp base towards the foreland. The geologic units bordering the western lobate scarp are an ancient, heavily eroded volcano in the north, at the elevated back scarp (marked by letters “AV” in Fig. 1), thus the formation of the geologic unit can be reliably determined only through a fit in the largest diameter range. The cratering model age of this edifice is about 4.0 Ga (Fig. 3a; Ncum (1 km) = 4.08 × 10−2 , Ncum (1 km) is the cumulative number of impact craters greater than or equal to 1 km diameter per surface unit of 106 km2 ), followed by resurfacing. Towards the southwest, the lobate scarp is embayed by younger plains (“Pl” in Fig. 1). We obtain a cratering model age of 3.4 Ga (Fig. 3b; Ncum (1 km) = 2.03 × 10−3 ). Therefore, the lobate scarp appears to have formed between 4.0 and 3.5 Ga before present. This age is in good agreement with previous age assignments by Dohm et al. (2001), who ascribe the thrust faults at the southern margin of Thaumasia to their tectonic stages 1–2, and believe that the formation of these lobate scarps has declined at the end of stage 2 in the early Hesperian. The definition of geologic units that are clearly older and younger, respectively, as the faulting is more difficult for the eastern scarp. In particular, we could not define a surface that is clearly older than the scarp (unit “HNPld” in Fig. 1 is as young as 3.7 Ga
(Fig. 3d; Ncum (1 km) = 5.21 × 10−3 )). A plains unit towards the south of the scarp (“HNf” in Fig. 1), which seems to be younger than the faulting, has a cratering model age of 3.65 Ga (Fig. 3 c; Ncum (1 km) = 4.72 × 10−3 ). The eastern scarp would have, therefore, an age of more than 3.7 Ga. A further constraint on the age of these scarps comes from the western Coracis Fossae rifts. Their age, according to crater statistics, is between 3.5 and 3.9 Ga (Grott et al., 2005). This would imply that the lobate scarps and the Coracis Fossae rifts formed almost simultaneously. However, one and the same stress field cannot produce extensional and contractional tectonic features by shear failure of the lithosphere at the same location and the same time (e.g., Anderson, 1951). Given the considerable spread in our age determinations, we conclude that the lobate scarps formed before the Coracis Fossae rifts. This notion is supported by morphostructural observations. The easternmost part of the western lobate scarp is downfaulted by the western Coracis Fossae rift (see center of Fig. 1) and, therefore, must be older. Again, this relationship is in agreement with the results of Dohm et al. (2001), who report a formation of the Coracis Fossae rifts in their tectonic stages 1–3, i.e., coeval with, or slightly younger than the lobate scarps. Based on our crater counting results, structural mapping, and comparison with previous studies, we believe that the lobate scarps formed in the late Noachian or very early Hesperian, after 4.0 Ga and before about 3.7 Ga.
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Fig. 2. Structural map showing the locations of surface breaking thrust faults and main extensional fault systems in the study area. The locations of topographic profiles are indicated by lines. The contour interval is 250 m.
3. Modeling approach 3.1. Mechanical modeling We have taken sets of topographic profiles across two lobate scarps along the lines indicated in Fig. 1. The data is derived from the MOLA 1/128◦ digital elevation model and shown in Figs. 4a1 and 4a2, where subsequent profiles have been offset by 500 m for better visibility. The main topographic features are the steeply rising scarp faces, having slopes of ∼10◦ , the gently declining back scarps, having slopes of ∼1◦ , and the trailing synclines 50–60 km behind the surface break. The mean topography, calculated by stacking and averaging of individual profiles, is shown as solid lines in Figs. 4b1 and 4b2. The regional topographic slope has been subtracted and the spread of one standard deviation is indicated by broken lines. Lobate scarps are the topographic expressions of surface breaking thrust faults and their morphology is controlled by slip along a deeply rooted fault-plane (Schultz, 2000). Given faulting geometry and slip distribution, the associated surface deformation may thus be calculated. This forward modeling approach has been widely applied to a variety of different tectonic settings, including thrust faults on Mercury (Watters et al., 2002) and Mars (Schultz and Watters, 2001), wrinkle ridges (Schultz, 2000; Watters, 2004) and normal faulting in the Valles Marineris (Schultz and Lin, 2001). A comparison
between modeled and measured topography then allows for a determination of the faulting geometry. The approach adopted here is similar to the dislocation method (e.g., Cohen, 1999) and we calculate the displacements in an elastic half-space transected by a model fault using the plane strain application mode of the commercial finite element package FEMLAB (http://www.femlab.com). The model setup is schematically shown in Fig. 5a and the faulting geometry is specified by angle θ and depth D. The half-space is represented by a 1000 km wide and 300 km deep box, sufficient to minimize boundary effects. The automatically generated mesh is shown in Fig. 5b and consists of approximately 18,000 elements which are refined at the surface and the fault plane, the resolution there being 1 km and 500 m, respectively. The fault is implemented as a gap whose boundaries are restricted to movement in the tangential direction. The calculated topography is very sensitive to the distribution of slip on the fault surface and simple crack models suggest an elliptical slip distribution. To avoid stress singularities at the rupture ends, tapered distributions having minimum slip at the fault tips are usually prescribed (Toda et al., 1998). However, a recent compilation of data on slip distributions by Manighetti et al. (2005) suggests that many terrestrial faults have triangular shaped slip profiles both along strike and dip. These characteristics appear to arise from the physical fault properties and are independent of fault scale, age, kinematics and loca-
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Fig. 3. Crater size-frequency distributions of four key areas, for the location compare Fig. 2: (a) the ancient eroded volcano (AV), (b) the lobate scarp embaying plains (Pl), (c) plains south of the eastern scarp (HNf), and (d) plains north of the eastern scarp (HNPld).
Fig. 4. (a) Topographic profiles of the western (1) and eastern (2) scarps, taken along the lines indicated in Fig. 1. For better visibility subsequent profiles have been offset by 500 m. (b) Mean profiles (solid lines) and spread of one standard deviation (broken lines) calculated by stacking of individual profiles. The mean profiles have been detrended by subtracting the regional topographic gradient.
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Fig. 5. (a) A sketch of the model geometry indicating the fault plane by a broken line. The depth and angle of faulting D and θ are indicated. (b) Finite element mesh used for calculating the deformation induced by slip on the fault. The mesh has been refined at the fault and the surface, reducing the maximum element size there to 0.5 and 1 km, respectively.
tion. Terrestrial examples for thrust faults exhibiting triangular slip profiles include blind thrusts (Mendoza and Hartzell, 1988; Salichon et al., 2003) as well as surface breaking thrust faults (Chi et al., 1999). We therefore use a triangular taper to calculate the surface displacements. The misfit between simulated and measured topography is calculated by aligning the positions of the scarp faces and comparing the positions of the trailing synclines. This approach is very robust and nonsensitive to regional slope and the detrending carried out during data processing. The displacements are calculated for a given faulting geometry and slip distribution while increasing the total amount of slip until the modeled relief matches the observed topographic offset. The simulations are carried out for D = 20–40 km and θ = 20–40◦ , the step sizes being 1 km and 2◦ , respectively. This allows for a systematic study of the trade off effects between θ and D and is achieved by use of the MATLAB (http://www.mathworks.com) interface to FEMLAB, which allows for a complete automatization of the calculations once the initial model has been set up. We assume a Young’s modulus of 100 GPa and Poisson’s ratio of 0.33. The method has been verified by reexamining the Amenthes Rupes thrust fault, which has previously been studied by (Schultz and Watters, 2001). Using the presented approach, the angle and depth of faulting are constrained to 25◦ –35◦ and 32–40 km, respectively. (Schultz and Watters, 2001) report best fitting parameters of 30◦ –35◦ and 35–40 km, values withing the error margins determined here.
once stresses exceed σB = fρgZ,
(1)
where f is the frictional coefficient and ρgZ is the lithostatic pressure, i.e., ρ is crustal density and g is gravitational acceleration. Ductile deformation is governed by σD =
1/n ε˙ eQ/nRT , A
(2)
where ε˙ is strain rate, R is the universal gas constant and A, n and Q are rheological parameters. Equating σB and σD and solving for T then yields the temperature at the brittle ductile transition (BDT) Q f gρZA1/n −1 . ln TBDT = nR ε˙ 1/n
(3)
Here we assume a diabase composition of the crust (Caristan, 1982) and strain rates between 10−15 and 10−17 s−1 . The crustal density is taken to be 2700–3100 kg m−3 (Nimmo and Tanaka, 2005). To a good degree of approximation the frictional parameter is independent of rock type and we adopt f = 0.65, suitable for dry friction (Byerlee, 1978). Using these parameters, the temperature at the base of a 30 km thick seismogenic layer is 630–700 K, comparable to the isotherm controlling intraplate seismicity in Earth’s crust (Chen and Molnar, 1983). Once the depth and the temperature at the BDT are known, the heat flow may be calculated using Fourier’s Law: dT , dz
3.2. Thermal modeling
F = −k
On Earth’s continents the maximum depth of intraplate earthquakes is bounded by the transition from the frictionally unstable to the conditionally stable regime, a transition which coincides with the onset of plasticity of the corresponding rock (Scholz, 1998). This transition occurs when the stresses necessary to initiate sliding along preexisting cracks (seismic slip) become larger than those needed for ductile deformation (aseismic slip). Given the rheology of the rocks and the depth of the transition Z, the isotherm corresponding to Z may be calculated by equating the relevant stresses. Brittle failure initiates
where k is the thermal conductivity. Large uncertainties are connected to the value of k, which strongly depends on material properties like porosity and water content. (McGovern et al., 2004) assume k = 2.5 W m−1 K−1 , while (Schultz and Watters, 2001) assume a conductivity of 3.2 W m−1 K−1 . Taking the presence of a top layer of poorly conducting megaregolith into account we adopt a rather low column averaged thermal conductivity of k = 2 W m−1 K−1 (Squyres et al., 1992; Clifford, 1993). Due to the uncertainties connected to k, we prefer to use thermal gradients for the comparison with previous studies.
(4)
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4. Results 4.1. Mechanical and thermal modeling Fig. 6 shows the sensitivity of the calculated surface deformation with respect to changes of the faulting angle (a) and depth of faulting (b), while keeping all other parameters constant. As a reference, the topographic data for the western lobate scarp and the spread of one standard deviation are also given. Starting with a faulting angle of 30◦ and a depth D = 30 km, an
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increase of θ by 10◦ removes the syncline. A decrease of θ by 10◦ moves the syncline 20 km away from the scarp. A similar sensitivity can be observed for changes of the depth of faulting D, while θ is kept constant at 30◦ . Decreasing D to 20 km moves the syncline 17 km closer to the scarp, while the syncline is removed for D = 40 km. This sensitivity forms the basis of our modeling approach. Fig. 7a shows contour plots of the misfit (in meters) between the positions of the synclines of simulated and measured mean topography for the western (1) and eastern (2) scarps
Fig. 6. Variation of simulated profiles with respect to the measured data when varying depth (a) and angle of faulting (b) for the western scarp while keeping all other parameters constant.
Fig. 7. (a) Contour plot of the misfit between simulated and measured mean topography for the western (1) and eastern (2) scarps as a function of faulting angle and depth. The lines represent the misfit between the measured and simulated position of the trailing syncline in meters. Acceptable fits are obtained for a misfit of less than 2 km. (b) The mean topographic profile (broken line) and best fit simulated profile obtained for a faulting angel of 30◦ for the western (1) and eastern (2) scarps. The mean spread of the measured profiles is indicated by the dotted lines.
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as a function of faulting angle and depth. For faulting angles between 25◦ and 35◦ , corresponding to f = 0.35–0.85 (Anderson, 1951), acceptable fits with misfit below 2 km are obtained for D = 27–35 km and 21–28 km for the western and eastern scarp, respectively. Clearly, there is a trade-off between faulting angle and depth. Fig. 7b shows the mean topographic profiles (broken lines) and best fit simulated profiles (solid lines) obtained for a faulting angle of 30◦ for the western (1) and eastern (2) scarps. The spread of one standard deviation of the measured profiles is indicated by dotted lines. The method produces good fits to the observed surface deformation. The steeply sloping scarp face, gently dropping back scarp as well as the position of the trailing depression are satisfactorily reproduced. The offset of the base of the syncline with respect to the reference level depends on the faulting angle, with low angles giving smaller offsets. However, since the level of offset is strongly depending on regional slope, it cannot serve as a further constraint to the faulting geometry. The range of seismogenic layer thicknesses determined for the two scarps investigated places bounds on the respective thermal environments at the time these structures formed. Using Eq. (3), the temperatures at the BDT may be calculated. For D = 27–35 km and 21–28 km we obtain TBDT = 620–700 and 630–710 K. Assuming a surface temperature of 220 K, the thermal gradient at the time of scarp emplacement can be constrained to 12–18 and 15–23 K km−1 at the western and eastern scarps, respectively. Using Fourier’s Law (Eq. (4)) and assuming k = 2 W m−1 K−1 , this implies heat fluxes in the range of 24–36 and 30–46 mW m−2 . The determination of heat fluxes from elastic and seismogenic layer thicknesses is sensitive to the adopted crustal rheology. Assuming a dry diabase flow law for the crust (Mackwell et al., 1998) the temperatures at the BDT increase to 850–950 K, implying heat fluxes of 36–54 and 44–68 mW m−2 . However, the strength of martian faults suggests that they are in contact with liquid water below the surface, indicating a wet rheology to be more appropriate (Barnett and Nimmo, 2002; Grott et al., 2005). Furthermore, weaker rheologies lead to considerably lower heat flow values. We have here assumed that the bulk of the martian crust is basaltic, as is indicated by geochemical evidence (e.g., Nimmo and Tanaka, 2005). The values chosen for Young’s Modulus and Poisson ratio differ slightly from those adopted by (Schultz and Watters, 2001) and (Watters et al., 2002), who assume E = 80 GPa and ν = 0.25. However, changing E and ν has only minor effects on the results. Adopting E = 80 GPa and ν = 0.25 the range of acceptable depths of faulting for the western scarp is shifted to 26–32 km, as compared to 27–35 km obtained using 100 GPa and 0.33. Our choice of Poisson ratio is motivated by the fact that higher ν leads to more pronounced trailing synclines. This greatly improves the reliability of the fitting procedure while leading to negligible changes of thermal gradient and heat flux. The detrending performed in the data analysis may slightly affect the position of the trailing syncline, moving it away from the surface break. This implies that the thermal gradients determined here are upper limits, since a shorter distance between
scarp face and syncline implies a lower depth of faulting, which in turn requires higher gradients. 4.2. Displacement and strain For a faulting angle of θ = 30◦ the total amount of slip corresponding to the best fit is 2100 m for the eastern and western scarps. This is slightly larger than the measured kinematic offset d = h sin(θ ) of 1900 m, where h is the height of the scarp with respect to its surroundings. The displacement falls within the slip ranges observed for other martian scarps, being larger than the mean slip observed for the Amenthes–Northern Cimmeria thrust fault population, which is ∼1 km, but smaller than that determined for Amenthes Rupes, which accommodates 3 km of displacement (Watters and Robinson, 1999; Watters, 2003). On Earth’s continents, the maximum displacement D on faults scales with their planimetric length L (Cowie and Scholz, 1992a, 1992b; Kim and Sanderson, 2005) D = γ L,
(5)
where γ is a constant related to material properties and tectonic setting and 100 > γ > 10−3 . This relationship also holds for planetary faults (Schultz, 1997; Watters and Robinson, 1999; Watters et al., 2000), with γMercury = 6.5 ± 3.2 × 10−3 and γMars = 5.9 ± 2.0 × 10−3 (Watters et al., 2000). The planimetric length of the two faults investigated here is ∼250 km for the western and ∼150 km for the eastern scarp, giving displacement–length ratios γ of 8.4 × 10−3 and 1.4 × 10−2 , respectively. These values are typical for martian scarps and fall within the range derived by Watters (2003) for the Amenthes and Arabia Terra thrust fault populations. Given the age determinations derived from crater statistics, the timespan it took the scarps to form may have been as long as 300 Myr. This implies very low displacement rates of ∼10−3 mm yr−1 , much slower than typical displacement rates for terrestrial intraplate thrust faults, which range from 0.01 to 1 mm yr−1 (Wesnousky, 1999). Assuming these higher rates, the scarps considered might have formed within as little as ∼2 Myr. 5. Discussion and conclusions We have modeled the topography above two surface breaking thrust faults in the southern Thaumasia region to constrain the faulting geometry and thus the thickness of the seismogenic layer thickness at the time of scarp emplacement. The faults accommodate 2100 m of displacement and extend to a depth of D = 27–35 and 21–28 km, respectively, implying thermal gradients of 12–18 and 15–23 K km−1 . The ratio between accommodated displacement and planimetric fault length found for the two scarps is typical for martian conditions (Watters, 2003), being 8.4 × 10−3 and 1.4 × 10−2 , respectively. Evaluating the crater size-frequency distribution of key surface units connected to the faulting, the time of scarp formation was constrained to 3.5–4.0 Gyr for the western and >3.7 Gyr for the eastern scarp.
Thaumasia thrust faults
As a consistency check for the thermal gradients determined here we consider the strength envelope formalism of McNutt (1984), an approach that connects the lithospheric flexure to its thermal environment. For the investigated scarps, the lithospheric curvature is 2.5–4 × 10−7 m−1 . On Earth’s continents the seismogenic layer thickness Ts is similar to the effective elastic thickness Te (McKenzie and Fairhead, 1997; Maggi et al., 2000), with Ts usually being slightly larger than Te . Assuming Te = Ts , the minimum thermal gradient at the time of faulting can be constrained to 11–17 K km−1 , a value consistent with the results presented here. The thermal gradients at the time of scarp emplacement determined here are comparable to the values obtained by Schultz and Watters (2001) and McGovern et al. (2004) for other Noachian structures in the southern highlands, their values being dT /dz = 14–20 at Amenthes Rupes and >20 K km−1 in Noachis Terra, respectively. The seismogenic layer thickness of 21–35 km is also roughly consistent with elastic thickness estimates by Williams et al. (2006), who analyzed line-of-sight gravity data from the Mars Global Surveyor mission and obtained Te < 20 km in the Thaumasia Highlands at the time of load emplacement. However, the thermal gradient determined by the analysis of rift flank uplift at the nearby Coracis Fossae for a similar time period is higher by almost a factor of two, being 27–33 K km−1 (Grott et al., 2005). This implies a change of the magmatectonic and thermal environment after the formation of the thrust margin, which is consistent with the observation that rifting on Mars is connected to magmatic activity (Hauber and Kronberg, 2001; Grott et al., 2005; Kronberg et al., 2005). Heat flow values obtained near active rifts may therefore be viewed as elevated with respect to the background values in magmatically inactive areas. In this context, we interpret the heat flow values determined here to be close to the global background. The thermal gradients and heat flow values presented here have been derived on the assumption of a linear temperature profile within the seismogenic layer (Eq. (4)), an assumption only strictly valid if there is no crustal heat production. A concentration of radioactive elements within the crust would lead to a deviation from the linear temperature profile assumed here and result in a more parabolic shape. Thus, the temperature gradient within the seismogenic layer would no longer be constant. Rather, steeper gradients and higher heat flows near the surface and lower values at the BDT would be expected. However, crustal heat production is probably low (Nimmo and Tanaka, 2005) and we do not expect its influence to be significant. To serve as meaningful constraints on thermal evolution models, the true global mean thermal gradient needs to be known. This is difficult to estimate and the best guess so far is that it was contained within a 17–32 K km−1 interval during the late Noachian–early Hesperian period. This problem should be addressed in more detail in the future, possibly by weighting the mean value by the appropriate surface shares of active and inactive areas. Since we would presume that inactive areas dominate, the global mean is probably closer to the lower bound.
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Acknowledgments We thank the HRSC Experiment Teams at DLR Berlin and Freie Universität Berlin as well as the Mars Express Project Teams at ESTEC and ESOC for their successful planning and acquisition of data as well as for making the processed data available to the HRSC Team. We acknowledge the effort of the HRSC Co-Investigator Team members and their associates who have contributed to this investigation in the preparatory phase and in scientific discussions within the Team. S.C.W. acknowledges financial support from the German Research Foundation (DFG) within the priority program SPP 1115 Mars and the Terrestrial Planets. This work was also financially supported by the Federal Ministry of Economics and Technology (BMWI) under contract 50 QM 0404. References Anderson, E.M., 1951. The Dynamics of Faulting and Dyke Formation with Applications to Britain, second ed. Oliver & Boyd, Edinburgh. 206 pp. Anderson, R.C., Dohm, J.M., Golombek, M.P., Haldemann, A.F., Franklin, B.J., Tanaka, K.L., Lias, J., Peer, B., 2001. Primary centers and secondary concentrations of tectonic activity through time in the western hemisphere of Mars. J. Geophys. Res. 106 (E9), 20563–20586. Ansan, V., Mangold, N., 2006. New observations of Warrego Valles, Mars: Evidence for precipitation and surface runoff. Planet. Space Sci. 54, 219–242. Banerdt, W.B., Golombek, M.P., 2000. Tectonics of the Tharsis region of Mars: Insights from MGS topography and gravity. Lunar Planet. Sci. 31. Abstract 2038. Barnett, D.N., Nimmo, F., 2002. Strength of faults on Mars from MOLA topography. Icarus 157, 34–42. Barnett, D.N., Nimmo, F., McKenzie, D., 2002. Flexure of venusian lithosphere measured from residual topography and gravity. J. Geophys. Res. 107 (E2), doi:10.1029/2000JE001398. 2-1. Byerlee, J.D., 1978. Friction of rocks. Pure Appl. Geophys. 116, 615–626. Caristan, Y., 1982. The transition from high temperature creep to fracture in Maryland diabase. J. Geophys. Res. 87, 6781–6790. Chen, W.-P., Molnar, P., 1983. Focal depths of intracontinental and intraplate earthquakes and their implications for the thermal and mechanical properties of the lithosphere. J. Geophys. Res. 88, 4183–4214. Chi, W.-C., Dreger, D., Kaverina, A., 1999. Finite-source modeling of the 1999 Taiwan (Chi-Chi) earthquake derived from a dense strong-motion network. Bull. Seismol. Soc. Am. 91 (5), 1144–1157. Clifford, S.M., 1993. A model for the hydrologic and climatic behavior of water on Mars. J. Geophys. Res. 98, 10973–11016. Cohen, S.C., 1999. Numerical models of crustal deformation in seismic zones. Adv. Geophys. 41, 133–231. Cowie, P.A., Scholz, C.H., 1992a. Physical explanation for the displacement– length relationship of faults using a post-yield fracture mechanics model. J. Struct. Geol. 14 (10), 1133–1148. Cowie, P.A., Scholz, C.H., 1992b. Displacement–length scaling relationship for faults: Data synthesis and discussion. J. Struct. Geol. 14 (10), 1149–1156. Dohm, J.M., Tanaka, K.L., 1999. Geology of the Thaumasia region, Mars: Plateau development, valley origins, and magmatic evolution. Planet. Space Sci. 47, 411–431. Dohm, J.M., Tanaka, K.L., Hare, T.M., 2001. Geologic, paleotectonic, and paleoerosional maps of the Thaumasia Region, Mars (scale 1:5,000,000). In: Geologic Investigations Series I-2650, US Geological Survey. Grott, M., Hauber, E., Werner, S.C., Kronberg, P., Neukum, G., 2005. High heat flux on ancient Mars: Evidence from rift flank uplift at Coracis Fossae. Geophys. Res. Lett. 32, doi:10.1029/2005GL023894. L21201. Gulick, V.C., 1998. Magmatic intrusions and a hydrothermal origin for fluvial valleys on Mars. J. Geophys. Res. 103, 19365–19388. Gulick, V.C., 2001. Origin of the valley networks on Mars: A hydrological perspective. Geomorphology 37, 241–268.
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Mechanical modeling of thrust faults in the Thaumasia region, Mars, and implications for the Noachian heat flux M. Grott a,∗ , E. Hauber a , S.C. Werner c , P. Kronberg b , G. Neukum c a Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstraße 2, 12489 Berlin, Germany b Institute of Geology, Technical University of Clausthal, Leibnizstraße 10, 38678 Clausthal-Zellerfeld, Germany c Institute of Geological Sciences, Freie Universität Berlin, Malteser Straße 74-100, 12249 Berlin, Germany
Received 2 June 2006; revised 25 September 2006 Available online 17 November 2006
Abstract Insight into the state of the early martian lithosphere is gained by modeling the topography above surface breaking thrust faults in the southern Thaumasia region. Crater counts of key surface units associated with the faulting indicate a scarp emplacement in the late Noachian–early Hesperian periods between 4.0 and 3.7 Gyr. The seismogenic layer thickness at the time of faulting is constrained to 27–35 km and 21–28 km for the two scarps investigated, implying paleo geothermal gradients of 12–18 and 15–23 K km−1 , corresponding to heat flows of 24–36 and 30–46 mW m−2 . The heat flow values obtained in this study are considerably lower than those derived from rift flank uplift at the close-by Coracis Fossae for a similar time period, indicating that surface heat flow is a strong function of regional setting. If viewed as representative for magmatically active and inactive regions, the thermal gradients at rifts and scarps span the range of admissible global mean values. This implies dT /dz = 17–32 K km−1 , with the true value probably being closer to the lower bound. © 2006 Elsevier Inc. All rights reserved. Keywords: Mars, surface; Mars, interior; Tectonics
1. Introduction The way in which the lithosphere responds to tectonic deformation can give important clues to its thermal state at the time of structure emplacement and a variety of methods to constrain lithospheric properties have been applied to Solar System objects including icy satellites (Nimmo et al., 2003; Nimmo and Pappalardo, 2004), Mercury (Watters et al., 2002), Venus (Barnett et al., 2002) and Mars (Schultz and Watters, 2001; McGovern et al., 2004; Grott et al., 2005). In this paper we investigate the topography of lobate scarps in the southern Thaumasia region to constrain the mechanical and thermal state of the martian lithosphere in the late Noachian–early Hesperian period. The Thaumasia region of Mars is located in the south of the Tharsis province, a region which has been tectonically ac* Corresponding author.
E-mail address: [email protected] (M. Grott). 0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.10.001
tive throughout martian history (Anderson et al., 2001). The Thaumasia plateau was emplaced during the late Noachian to early Hesperian periods and its structural style is comparable to intra-continental plateaus on Earth. The geological evidence is most consistent with a formation process involving crustal underplating and subsequent uplift (Dohm and Tanaka, 1999) as the developing plateau was pushed over the adjacent foreland. Being concentric to the Tharsis rise, the fold and thrust margins considered here are part of the south Tharsis ridge belt and formed by compression and thrust faulting as a consequence of the uplift process (Schultz and Tanaka, 1994). Lobate scarps are landforms commonly encountered on the Moon, Mercury and Mars and they are characterized by a steeply rising scarp face, a gently declining back scarp and a trailing syncline (Schultz, 2000). On Mars, lobate scarps are located in Noachian terrain and they have relief of the order of a few hundred meters (Watters and Robinson, 1999; Watters, 2003), although individual scarps stand up to 1200 m above the surrounding highlands (Schultz and Watters, 2001). The way in which many lobate scarps offset the walls of impact
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craters suggests that they are compressional tectonic features, being the expressions of surface breaking thrust faults (Watters et al., 2001, 2004). The faults beneath lobate scarps are assumed to deform the entire brittle lithosphere and scarp topography is primarily controlled by the faulting geometry (Schultz and Watters, 2001; Watters et al., 2002). The distribution of vergence directions of thrust fault-related folds in the Tharsis province indicates a strong coupling between the underlying Noachian crust and the Tharsis rise, also favoring lithosphere-scale thick-skinned deformation processes (Okubo and Schultz, 2003). As the zone of seismic deformation is bounded by the onset of plasticity at depth (Scholz, 1998), the depth of faulting may be connected to an isotherm, constraining the thermal structure of the lithosphere. In this work we determine the depth of this brittle–ductile transition beneath lobate scarps in the southern Thaumasia region by forward mechanical modeling of MOLA topographic data. The time of scarp formation is constrained by applying standard crater count techniques (Neukum and Hiller, 1981) to key surface units, using images taken by the High Resolution Stereo Camera (HRSC) on board the Mars Express mission (Neukum and Jaumann, 2004) as a database. Combining these methods allows us to determine the past thermal state of the martian lithosphere and helps to constrain the mean global heat flux during the late Noachian–early Hesperian period. 2. Geology and age determination 2.1. Geology Thaumasia forms the south-eastern region of the Tharsis bulge, the major volcano-tectonic structure on Mars. Tharsis formed over a long period, encompassing most of the planet’s history, but several lines of evidence suggest that the major part of Tharsis’ elevated topography was already in place at the end of the Noachian (Banerdt and Golombek, 2000; Anderson et al., 2001; Phillips et al., 2001). The Thaumasia plateau forms a large region of elevated topography. It consists of interior plains and a surrounding highland belt to the east, south, and west. In the north, Thaumasia is bordered by the trough system of Valles Marineris. The most detailed geologic mapping was performed by Dohm and Tanaka (1999) and Dohm et al. (2001). The interior lava plains of Thaumasia, i.e., Solis, Sinai, and Thaumasia Plana, are of Hesperian age. Their tectonic structure is characterized by wrinkle ridges, which are contractional features oriented concentric to the Syria Planum center of the Tharsis bulge. The highland belt consists of ancient material of mostly Noachian age. It is heavily fractured by different extensional fault sets, e.g., Claritas, Coracis, Nectaris, Thaumasia, and Melas Fossae, which can be grouped with respect to the time of their formation into five main stages (Dohm and Tanaka, 1999; Dohm et al., 2001; Anderson et al., 2001). In general, it seems that the peak of tectonic activity occurred already in the Noachian, and declined subsequently during the Hesperian and Amazonian (Tanaka, 1986; Scott and
Dohm, 1990; Dohm and Tanaka, 1999; Dohm et al., 2001; Anderson et al., 2001). Besides the lobate scarps, several other tectonic and magmatic structures are of particular interest for our study. Immediately adjacent to the lobate scarps is the elevated area of the Warrego rise (Fig. 1). It is an area of crustal thickening (Neumann et al., 2004), and sets of narrow grabens that intersect at the Warrego rise are deflected (Dohm and Tanaka, 1999). The Warrego rise is also a late Noachian–early Hesperian center of tectonic activity identified through vector and beta analyses of a comprehensive fault data base by (Anderson et al., 2001). Based on these observations, Dohm et al. (2001) suggest that the Warrego rise has a history of prolonged intrusive activity, with a peak of magmatic-driven tectonic activity at the end of the Noachian. The dense pattern of dendritic valleys of probably fluvial origin at the southern flanks of the Warrego rise (cf. Fig. 2) might be in agreement with such a scenario, since hydrothermal activity associated with the Warrego magmatism might have melted snow, which was preferentially precipitated at the high topography of the rise, and produced surface runoff (Gulick, 1998; Gulick, 2001). It has to be noted, though, that Ansan and Mangold (2006) question magmatic processes near the Warrego Valles. The Warrego rise is the dominant, but not the only possible magmatic center in the region. Several ancient volcanic edifices of Noachian to early Hesperian age were recognized by Scott and Tanaka (1981) and Scott (1982). They are heavily dissected and often associated with tectonic structures. At least two of them are clearly associated with the double rift system of Coracis Fossae (Kronberg et al., 2005), and according to the mapping of Dohm et al. (2001), another one is situated north of the western lobate scarp of this study. The Coracis Fossae rifts resemble terrestrial continental rifts. They trend in a NW–SW direction and have been investigated in detail by Grott et al. (2005). 2.2. Age determination The determination of the age of the thrust faulting at the lobate scarps is critical to our study. We use HRSC images with a resolution of about 20 m pixel−1 to measure the crater size-frequency distribution of key geologic units to derive their absolute ages. HRSC images are ideally suited for such an approach, since they combine a large areal coverage with relatively high ground resolution. We use standard crater count techniques (Neukum and Hiller, 1981) and apply the new cratering model described by Hartmann and Neukum (2001) and the polynomial description of crater production function given in Ivanov (2001). The HRSC imagery allows for reliable crater counts in the size range of craters with a diameter of >200 m. These counts were used for deriving the cratering model ages in a crater diameter range avoiding the potential problem that small secondary craters affect the original sizefrequency distribution (McEwen et al., 2005; Hartmann, 2005). The crater counts for four key units are given in Fig. 3. The deviation from the crater production function (Ivanov, 2001; Werner, 2005) indicate subsequent resurfacing, which is confirmed in the morphology. We made use of the fact that the
Thaumasia thrust faults
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Fig. 1. Topographic image map of the southern Thaumasia region (altimetry data derived from the MOLA 1/128◦ digital elevation model). Solid white lines indicate locations of topographic profiles, letters denote areas of crater counts.
lobate scarps form geologic contacts (Dohm et al., 2001). In these cases, the lobate scarp should have formed after the formation of the older surface, usually at the elevated back scarp, and before the younger surface extending from the scarp base towards the foreland. The geologic units bordering the western lobate scarp are an ancient, heavily eroded volcano in the north, at the elevated back scarp (marked by letters “AV” in Fig. 1), thus the formation of the geologic unit can be reliably determined only through a fit in the largest diameter range. The cratering model age of this edifice is about 4.0 Ga (Fig. 3a; Ncum (1 km) = 4.08 × 10−2 , Ncum (1 km) is the cumulative number of impact craters greater than or equal to 1 km diameter per surface unit of 106 km2 ), followed by resurfacing. Towards the southwest, the lobate scarp is embayed by younger plains (“Pl” in Fig. 1). We obtain a cratering model age of 3.4 Ga (Fig. 3b; Ncum (1 km) = 2.03 × 10−3 ). Therefore, the lobate scarp appears to have formed between 4.0 and 3.5 Ga before present. This age is in good agreement with previous age assignments by Dohm et al. (2001), who ascribe the thrust faults at the southern margin of Thaumasia to their tectonic stages 1–2, and believe that the formation of these lobate scarps has declined at the end of stage 2 in the early Hesperian. The definition of geologic units that are clearly older and younger, respectively, as the faulting is more difficult for the eastern scarp. In particular, we could not define a surface that is clearly older than the scarp (unit “HNPld” in Fig. 1 is as young as 3.7 Ga
(Fig. 3d; Ncum (1 km) = 5.21 × 10−3 )). A plains unit towards the south of the scarp (“HNf” in Fig. 1), which seems to be younger than the faulting, has a cratering model age of 3.65 Ga (Fig. 3 c; Ncum (1 km) = 4.72 × 10−3 ). The eastern scarp would have, therefore, an age of more than 3.7 Ga. A further constraint on the age of these scarps comes from the western Coracis Fossae rifts. Their age, according to crater statistics, is between 3.5 and 3.9 Ga (Grott et al., 2005). This would imply that the lobate scarps and the Coracis Fossae rifts formed almost simultaneously. However, one and the same stress field cannot produce extensional and contractional tectonic features by shear failure of the lithosphere at the same location and the same time (e.g., Anderson, 1951). Given the considerable spread in our age determinations, we conclude that the lobate scarps formed before the Coracis Fossae rifts. This notion is supported by morphostructural observations. The easternmost part of the western lobate scarp is downfaulted by the western Coracis Fossae rift (see center of Fig. 1) and, therefore, must be older. Again, this relationship is in agreement with the results of Dohm et al. (2001), who report a formation of the Coracis Fossae rifts in their tectonic stages 1–3, i.e., coeval with, or slightly younger than the lobate scarps. Based on our crater counting results, structural mapping, and comparison with previous studies, we believe that the lobate scarps formed in the late Noachian or very early Hesperian, after 4.0 Ga and before about 3.7 Ga.
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Fig. 2. Structural map showing the locations of surface breaking thrust faults and main extensional fault systems in the study area. The locations of topographic profiles are indicated by lines. The contour interval is 250 m.
3. Modeling approach 3.1. Mechanical modeling We have taken sets of topographic profiles across two lobate scarps along the lines indicated in Fig. 1. The data is derived from the MOLA 1/128◦ digital elevation model and shown in Figs. 4a1 and 4a2, where subsequent profiles have been offset by 500 m for better visibility. The main topographic features are the steeply rising scarp faces, having slopes of ∼10◦ , the gently declining back scarps, having slopes of ∼1◦ , and the trailing synclines 50–60 km behind the surface break. The mean topography, calculated by stacking and averaging of individual profiles, is shown as solid lines in Figs. 4b1 and 4b2. The regional topographic slope has been subtracted and the spread of one standard deviation is indicated by broken lines. Lobate scarps are the topographic expressions of surface breaking thrust faults and their morphology is controlled by slip along a deeply rooted fault-plane (Schultz, 2000). Given faulting geometry and slip distribution, the associated surface deformation may thus be calculated. This forward modeling approach has been widely applied to a variety of different tectonic settings, including thrust faults on Mercury (Watters et al., 2002) and Mars (Schultz and Watters, 2001), wrinkle ridges (Schultz, 2000; Watters, 2004) and normal faulting in the Valles Marineris (Schultz and Lin, 2001). A comparison
between modeled and measured topography then allows for a determination of the faulting geometry. The approach adopted here is similar to the dislocation method (e.g., Cohen, 1999) and we calculate the displacements in an elastic half-space transected by a model fault using the plane strain application mode of the commercial finite element package FEMLAB (http://www.femlab.com). The model setup is schematically shown in Fig. 5a and the faulting geometry is specified by angle θ and depth D. The half-space is represented by a 1000 km wide and 300 km deep box, sufficient to minimize boundary effects. The automatically generated mesh is shown in Fig. 5b and consists of approximately 18,000 elements which are refined at the surface and the fault plane, the resolution there being 1 km and 500 m, respectively. The fault is implemented as a gap whose boundaries are restricted to movement in the tangential direction. The calculated topography is very sensitive to the distribution of slip on the fault surface and simple crack models suggest an elliptical slip distribution. To avoid stress singularities at the rupture ends, tapered distributions having minimum slip at the fault tips are usually prescribed (Toda et al., 1998). However, a recent compilation of data on slip distributions by Manighetti et al. (2005) suggests that many terrestrial faults have triangular shaped slip profiles both along strike and dip. These characteristics appear to arise from the physical fault properties and are independent of fault scale, age, kinematics and loca-
Thaumasia thrust faults
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Fig. 3. Crater size-frequency distributions of four key areas, for the location compare Fig. 2: (a) the ancient eroded volcano (AV), (b) the lobate scarp embaying plains (Pl), (c) plains south of the eastern scarp (HNf), and (d) plains north of the eastern scarp (HNPld).
Fig. 4. (a) Topographic profiles of the western (1) and eastern (2) scarps, taken along the lines indicated in Fig. 1. For better visibility subsequent profiles have been offset by 500 m. (b) Mean profiles (solid lines) and spread of one standard deviation (broken lines) calculated by stacking of individual profiles. The mean profiles have been detrended by subtracting the regional topographic gradient.
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Fig. 5. (a) A sketch of the model geometry indicating the fault plane by a broken line. The depth and angle of faulting D and θ are indicated. (b) Finite element mesh used for calculating the deformation induced by slip on the fault. The mesh has been refined at the fault and the surface, reducing the maximum element size there to 0.5 and 1 km, respectively.
tion. Terrestrial examples for thrust faults exhibiting triangular slip profiles include blind thrusts (Mendoza and Hartzell, 1988; Salichon et al., 2003) as well as surface breaking thrust faults (Chi et al., 1999). We therefore use a triangular taper to calculate the surface displacements. The misfit between simulated and measured topography is calculated by aligning the positions of the scarp faces and comparing the positions of the trailing synclines. This approach is very robust and nonsensitive to regional slope and the detrending carried out during data processing. The displacements are calculated for a given faulting geometry and slip distribution while increasing the total amount of slip until the modeled relief matches the observed topographic offset. The simulations are carried out for D = 20–40 km and θ = 20–40◦ , the step sizes being 1 km and 2◦ , respectively. This allows for a systematic study of the trade off effects between θ and D and is achieved by use of the MATLAB (http://www.mathworks.com) interface to FEMLAB, which allows for a complete automatization of the calculations once the initial model has been set up. We assume a Young’s modulus of 100 GPa and Poisson’s ratio of 0.33. The method has been verified by reexamining the Amenthes Rupes thrust fault, which has previously been studied by (Schultz and Watters, 2001). Using the presented approach, the angle and depth of faulting are constrained to 25◦ –35◦ and 32–40 km, respectively. (Schultz and Watters, 2001) report best fitting parameters of 30◦ –35◦ and 35–40 km, values withing the error margins determined here.
once stresses exceed σB = fρgZ,
(1)
where f is the frictional coefficient and ρgZ is the lithostatic pressure, i.e., ρ is crustal density and g is gravitational acceleration. Ductile deformation is governed by σD =
1/n ε˙ eQ/nRT , A
(2)
where ε˙ is strain rate, R is the universal gas constant and A, n and Q are rheological parameters. Equating σB and σD and solving for T then yields the temperature at the brittle ductile transition (BDT) Q f gρZA1/n −1 . ln TBDT = nR ε˙ 1/n
(3)
Here we assume a diabase composition of the crust (Caristan, 1982) and strain rates between 10−15 and 10−17 s−1 . The crustal density is taken to be 2700–3100 kg m−3 (Nimmo and Tanaka, 2005). To a good degree of approximation the frictional parameter is independent of rock type and we adopt f = 0.65, suitable for dry friction (Byerlee, 1978). Using these parameters, the temperature at the base of a 30 km thick seismogenic layer is 630–700 K, comparable to the isotherm controlling intraplate seismicity in Earth’s crust (Chen and Molnar, 1983). Once the depth and the temperature at the BDT are known, the heat flow may be calculated using Fourier’s Law: dT , dz
3.2. Thermal modeling
F = −k
On Earth’s continents the maximum depth of intraplate earthquakes is bounded by the transition from the frictionally unstable to the conditionally stable regime, a transition which coincides with the onset of plasticity of the corresponding rock (Scholz, 1998). This transition occurs when the stresses necessary to initiate sliding along preexisting cracks (seismic slip) become larger than those needed for ductile deformation (aseismic slip). Given the rheology of the rocks and the depth of the transition Z, the isotherm corresponding to Z may be calculated by equating the relevant stresses. Brittle failure initiates
where k is the thermal conductivity. Large uncertainties are connected to the value of k, which strongly depends on material properties like porosity and water content. (McGovern et al., 2004) assume k = 2.5 W m−1 K−1 , while (Schultz and Watters, 2001) assume a conductivity of 3.2 W m−1 K−1 . Taking the presence of a top layer of poorly conducting megaregolith into account we adopt a rather low column averaged thermal conductivity of k = 2 W m−1 K−1 (Squyres et al., 1992; Clifford, 1993). Due to the uncertainties connected to k, we prefer to use thermal gradients for the comparison with previous studies.
(4)
Thaumasia thrust faults
4. Results 4.1. Mechanical and thermal modeling Fig. 6 shows the sensitivity of the calculated surface deformation with respect to changes of the faulting angle (a) and depth of faulting (b), while keeping all other parameters constant. As a reference, the topographic data for the western lobate scarp and the spread of one standard deviation are also given. Starting with a faulting angle of 30◦ and a depth D = 30 km, an
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increase of θ by 10◦ removes the syncline. A decrease of θ by 10◦ moves the syncline 20 km away from the scarp. A similar sensitivity can be observed for changes of the depth of faulting D, while θ is kept constant at 30◦ . Decreasing D to 20 km moves the syncline 17 km closer to the scarp, while the syncline is removed for D = 40 km. This sensitivity forms the basis of our modeling approach. Fig. 7a shows contour plots of the misfit (in meters) between the positions of the synclines of simulated and measured mean topography for the western (1) and eastern (2) scarps
Fig. 6. Variation of simulated profiles with respect to the measured data when varying depth (a) and angle of faulting (b) for the western scarp while keeping all other parameters constant.
Fig. 7. (a) Contour plot of the misfit between simulated and measured mean topography for the western (1) and eastern (2) scarps as a function of faulting angle and depth. The lines represent the misfit between the measured and simulated position of the trailing syncline in meters. Acceptable fits are obtained for a misfit of less than 2 km. (b) The mean topographic profile (broken line) and best fit simulated profile obtained for a faulting angel of 30◦ for the western (1) and eastern (2) scarps. The mean spread of the measured profiles is indicated by the dotted lines.
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as a function of faulting angle and depth. For faulting angles between 25◦ and 35◦ , corresponding to f = 0.35–0.85 (Anderson, 1951), acceptable fits with misfit below 2 km are obtained for D = 27–35 km and 21–28 km for the western and eastern scarp, respectively. Clearly, there is a trade-off between faulting angle and depth. Fig. 7b shows the mean topographic profiles (broken lines) and best fit simulated profiles (solid lines) obtained for a faulting angle of 30◦ for the western (1) and eastern (2) scarps. The spread of one standard deviation of the measured profiles is indicated by dotted lines. The method produces good fits to the observed surface deformation. The steeply sloping scarp face, gently dropping back scarp as well as the position of the trailing depression are satisfactorily reproduced. The offset of the base of the syncline with respect to the reference level depends on the faulting angle, with low angles giving smaller offsets. However, since the level of offset is strongly depending on regional slope, it cannot serve as a further constraint to the faulting geometry. The range of seismogenic layer thicknesses determined for the two scarps investigated places bounds on the respective thermal environments at the time these structures formed. Using Eq. (3), the temperatures at the BDT may be calculated. For D = 27–35 km and 21–28 km we obtain TBDT = 620–700 and 630–710 K. Assuming a surface temperature of 220 K, the thermal gradient at the time of scarp emplacement can be constrained to 12–18 and 15–23 K km−1 at the western and eastern scarps, respectively. Using Fourier’s Law (Eq. (4)) and assuming k = 2 W m−1 K−1 , this implies heat fluxes in the range of 24–36 and 30–46 mW m−2 . The determination of heat fluxes from elastic and seismogenic layer thicknesses is sensitive to the adopted crustal rheology. Assuming a dry diabase flow law for the crust (Mackwell et al., 1998) the temperatures at the BDT increase to 850–950 K, implying heat fluxes of 36–54 and 44–68 mW m−2 . However, the strength of martian faults suggests that they are in contact with liquid water below the surface, indicating a wet rheology to be more appropriate (Barnett and Nimmo, 2002; Grott et al., 2005). Furthermore, weaker rheologies lead to considerably lower heat flow values. We have here assumed that the bulk of the martian crust is basaltic, as is indicated by geochemical evidence (e.g., Nimmo and Tanaka, 2005). The values chosen for Young’s Modulus and Poisson ratio differ slightly from those adopted by (Schultz and Watters, 2001) and (Watters et al., 2002), who assume E = 80 GPa and ν = 0.25. However, changing E and ν has only minor effects on the results. Adopting E = 80 GPa and ν = 0.25 the range of acceptable depths of faulting for the western scarp is shifted to 26–32 km, as compared to 27–35 km obtained using 100 GPa and 0.33. Our choice of Poisson ratio is motivated by the fact that higher ν leads to more pronounced trailing synclines. This greatly improves the reliability of the fitting procedure while leading to negligible changes of thermal gradient and heat flux. The detrending performed in the data analysis may slightly affect the position of the trailing syncline, moving it away from the surface break. This implies that the thermal gradients determined here are upper limits, since a shorter distance between
scarp face and syncline implies a lower depth of faulting, which in turn requires higher gradients. 4.2. Displacement and strain For a faulting angle of θ = 30◦ the total amount of slip corresponding to the best fit is 2100 m for the eastern and western scarps. This is slightly larger than the measured kinematic offset d = h sin(θ ) of 1900 m, where h is the height of the scarp with respect to its surroundings. The displacement falls within the slip ranges observed for other martian scarps, being larger than the mean slip observed for the Amenthes–Northern Cimmeria thrust fault population, which is ∼1 km, but smaller than that determined for Amenthes Rupes, which accommodates 3 km of displacement (Watters and Robinson, 1999; Watters, 2003). On Earth’s continents, the maximum displacement D on faults scales with their planimetric length L (Cowie and Scholz, 1992a, 1992b; Kim and Sanderson, 2005) D = γ L,
(5)
where γ is a constant related to material properties and tectonic setting and 100 > γ > 10−3 . This relationship also holds for planetary faults (Schultz, 1997; Watters and Robinson, 1999; Watters et al., 2000), with γMercury = 6.5 ± 3.2 × 10−3 and γMars = 5.9 ± 2.0 × 10−3 (Watters et al., 2000). The planimetric length of the two faults investigated here is ∼250 km for the western and ∼150 km for the eastern scarp, giving displacement–length ratios γ of 8.4 × 10−3 and 1.4 × 10−2 , respectively. These values are typical for martian scarps and fall within the range derived by Watters (2003) for the Amenthes and Arabia Terra thrust fault populations. Given the age determinations derived from crater statistics, the timespan it took the scarps to form may have been as long as 300 Myr. This implies very low displacement rates of ∼10−3 mm yr−1 , much slower than typical displacement rates for terrestrial intraplate thrust faults, which range from 0.01 to 1 mm yr−1 (Wesnousky, 1999). Assuming these higher rates, the scarps considered might have formed within as little as ∼2 Myr. 5. Discussion and conclusions We have modeled the topography above two surface breaking thrust faults in the southern Thaumasia region to constrain the faulting geometry and thus the thickness of the seismogenic layer thickness at the time of scarp emplacement. The faults accommodate 2100 m of displacement and extend to a depth of D = 27–35 and 21–28 km, respectively, implying thermal gradients of 12–18 and 15–23 K km−1 . The ratio between accommodated displacement and planimetric fault length found for the two scarps is typical for martian conditions (Watters, 2003), being 8.4 × 10−3 and 1.4 × 10−2 , respectively. Evaluating the crater size-frequency distribution of key surface units connected to the faulting, the time of scarp formation was constrained to 3.5–4.0 Gyr for the western and >3.7 Gyr for the eastern scarp.
Thaumasia thrust faults
As a consistency check for the thermal gradients determined here we consider the strength envelope formalism of McNutt (1984), an approach that connects the lithospheric flexure to its thermal environment. For the investigated scarps, the lithospheric curvature is 2.5–4 × 10−7 m−1 . On Earth’s continents the seismogenic layer thickness Ts is similar to the effective elastic thickness Te (McKenzie and Fairhead, 1997; Maggi et al., 2000), with Ts usually being slightly larger than Te . Assuming Te = Ts , the minimum thermal gradient at the time of faulting can be constrained to 11–17 K km−1 , a value consistent with the results presented here. The thermal gradients at the time of scarp emplacement determined here are comparable to the values obtained by Schultz and Watters (2001) and McGovern et al. (2004) for other Noachian structures in the southern highlands, their values being dT /dz = 14–20 at Amenthes Rupes and >20 K km−1 in Noachis Terra, respectively. The seismogenic layer thickness of 21–35 km is also roughly consistent with elastic thickness estimates by Williams et al. (2006), who analyzed line-of-sight gravity data from the Mars Global Surveyor mission and obtained Te < 20 km in the Thaumasia Highlands at the time of load emplacement. However, the thermal gradient determined by the analysis of rift flank uplift at the nearby Coracis Fossae for a similar time period is higher by almost a factor of two, being 27–33 K km−1 (Grott et al., 2005). This implies a change of the magmatectonic and thermal environment after the formation of the thrust margin, which is consistent with the observation that rifting on Mars is connected to magmatic activity (Hauber and Kronberg, 2001; Grott et al., 2005; Kronberg et al., 2005). Heat flow values obtained near active rifts may therefore be viewed as elevated with respect to the background values in magmatically inactive areas. In this context, we interpret the heat flow values determined here to be close to the global background. The thermal gradients and heat flow values presented here have been derived on the assumption of a linear temperature profile within the seismogenic layer (Eq. (4)), an assumption only strictly valid if there is no crustal heat production. A concentration of radioactive elements within the crust would lead to a deviation from the linear temperature profile assumed here and result in a more parabolic shape. Thus, the temperature gradient within the seismogenic layer would no longer be constant. Rather, steeper gradients and higher heat flows near the surface and lower values at the BDT would be expected. However, crustal heat production is probably low (Nimmo and Tanaka, 2005) and we do not expect its influence to be significant. To serve as meaningful constraints on thermal evolution models, the true global mean thermal gradient needs to be known. This is difficult to estimate and the best guess so far is that it was contained within a 17–32 K km−1 interval during the late Noachian–early Hesperian period. This problem should be addressed in more detail in the future, possibly by weighting the mean value by the appropriate surface shares of active and inactive areas. Since we would presume that inactive areas dominate, the global mean is probably closer to the lower bound.
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