We investigated the Ceraunius Fossae area, Northern Tharsis, in order to obtain quantitative information on the tectonic extension affecting this area. Tectonic structures of the Ceraunius Fossae area have been previously described using Viking images and interpreted as extensional structures. Laser altimetry data (MOLA) can be used to quantitatively investigate these structures with a better resolution. We developed a method to obtain E-W oriented profiles (perpendicular to the main tectonic structures) with a sufficiently high resolution to analyze tectonic structures in spite of the low data density in this direction. We interpreted all the recognizable extensional structures along the profiles, and using a simplified structural model, we estimated tectonic extension along these transects. The extension calculated over the entire profiles is 36 km (e24 = (l1 − l0)/l0 = (910 km − 874 km)/874 km = 0.041) and 42 km (e26 = (730 km − 688 km)/688 km = 0.061) along profile 24 and profile 26, respectively. In the most deformed area, extension reaches the value of 22 km (emax = (l1 − l0)/l0 = (186 km − 164 km)/164 km = 0.134). Since the extension accounted by the topographic doming is negligible, a significant horizontal crustal motion is required to explain the observed extension.
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 The Ceraunius Fossae lies on the northern part of Tharsis (Figure 1), a very large volcanic region that includes the largest shield volcanoes of the solar system. Tharsis is the site of magmatic-driven activity that includes deformation of crustal materials, dike emplacement, and emplacement of lavas due to mantle processes such as plumes [Mège and Masson, 1996; Baker et al., 2002]. The latter seems to be one of the main causes of the evolution of the whole province [Mège and Masson, 1996; Baker et al., 2002; Dohm et al., 2002]. The whole Tharsis area is affected by tectonic structures such as radial and concentric grabens, and wrinkle ridges that testify its complex evolutionary history [Banerdt et al., 1992; Anderson et al., 2001].
 Five main evolutionary stages of the Tharsis region were recognized by Anderson et al. [2001, 2004]. The first stage is recorded by extensional features in Noachian highly cratered terrains that outcrop in Sirenum, Claritas Fossae, Ceraunius Fossae (Figure 2), Tempe Terra, Acheron Fossae, in the northern part of Noctis Labyrinthus and in the whole peripheral areas of Tharsis. The presence of extensional structures also characterizes the second and the third stages, respectively, in Late Noachian-Early Hesperian units (Thaumasia and Valles Marineris) and in Early Hesperian units (Thaumasia, Tempe Terra, Ulysses, Noctis Labyrinthus and Valles Marineris). In addition, wrinkle ridges are located on Early Hesperian units and associated to stage 3 of Anderson et al. . Their concentration reaches the acme in the ridged plains (Lunae, Solis and Thaumasia Plana). Extensional structures affect the Late Hesperian–Early Amazonian units in Tempe Terra, Alba Patera and in peripheral areas of Olympus Mons and Tharsis Montes. The fifth stage of the tectonic activity on Tharsis started in Early Amazonian age, and its evidences are observable around the largest shield volcanoes.
 In the Ceraunius Fossae area, the relatively large outcrop of “Fractured Rocks” (HNf and Hf units) of Late Noachian–Early Hesperian age [Scott and Tanaka, 1986; Tanaka, 1986, 1990] offers the opportunity to study the deformation of these old terrains. The HNf and Hf units are buried below the Early Amazonian–Middle Amazonian Ceraunius Fossae Formation (Acf) on the eastern side, and below the Tharsis Montes Formation (At4 and At5 members) on the western and southern sides [Scott and Tanaka, 1986; Tanaka, 1986, 1990]. The large deformation of HNf and Hf terrains could be related to the peak of tectonic activity in the Alba Patera region during the Noachian (stage 1 of Anderson et al. ). The upper Ceraunius Fossae and Tharsis Montes Formations are slightly deformed by minor faulting and low angle tilting.
 Both the studied area and the subject of this study are similar to those of Plescia ; however, we have restrained our attention to the oldest HNf and Hf terrains and used MOLA data to obtain a more precise estimate of tectonic extension. We have applied proven structural geology methods, as explained in the next section, to infer the tectonic extension in the area; we also discuss the relationship with crustal bulging and its geodynamic implications.
2.1. Topographic Profiles
 We used MOLA altimetry data [Smith et al., 1999, 2001] to construct two parallel topographic profiles, hereafter called profile 24 and profile 26 (Figure 3), along the E-W direction at 24.5° and 26° latitude, respectively. The profiles were drawn perpendicular to the N-S striking tectonic structures of the studied area.
 Unfortunately, as a consequence of the nearly polar orbits of the Mars Global Surveyor satellite, MOLA data are not dense enough to obtain the details needed in this study, along a latitudinal (E-W) profile. On the other hand, altimetry data are dense along the orbital paths that intersect the profile traces at irregular intervals (Figure 4).
 We developed a method to obtain E-W profiles with a sufficiently high resolution to analyze the tectonic structures, taking into account that (1) the tectonic structures are very long and have a linear shape in map view at the scale considered in this work and (2) there is an angle, although not large, between the structures' axis and the Mars Global Surveyor orbital paths. The procedure that we used resembles the data stacking generally used in seismic data processing, and in the study of the magnetic anomaly of the (terrestrial) oceanic crust. Due to the sparse altimetry data in the E-W direction, the resulting E-W profiles would be rough; however, it is possible to construct many parallel profiles within a narrow latitudinal band. Altimetry data taken from these parallel profiles are not equivalent owing to the angle of about 8° between tectonic structures and orbital paths (Figure 4). Taking advantage of the linear features (in map view) of the tectonic structures, these profiles can be easily stacked combining data taken within a given latitudinal band.
 The algorithm used to build the altimetry profiles was coded in a slightly different way than classical stacking. This was intended to take advantage of the variable density of intersections between orbits and profile traces, and thus to reduce the associated errors. We have proceeded as follows: we have divided the profile in small intervals of L° Longitude. Then we searched all altimetry data in the area delimited by the interval and a lateral band of B° Latitude perpendicular to the profile. Among these data points, we choose the N data points with the smallest distance δ from the profile. If we do not find at least N data points, we increase the longitude interval length by another L° and repeat the searching.
 The profile quotes are then calculated from the weighted average of those N data points, with weight w = 1/δ. The coordinates of the N data points are projected perpendicular to the profile trace and the weighted-mean distance calculated along the profile is taken as the location of the mean altitude. The absolute deviation S = 1/N ∣zi − ∣, where zi are the altitude values and is the mean of zi, is used as a simple estimate of altitude errors.
 This procedure seems to be quite robust with respect to the N, L and B parameters. We carried out experiments to build profiles using different interval length, lateral width and number of averaged points (chosen within reasonable values), and we did not observe any major differences in the profiles. Then, we proceeded in calculating the profiles used in this work with parameters N = 10, L = 1/1000° and B = 0.4°. To test the reliability of the results we compared the calculated profiles with MOC images. Figure 4 shows a selected section of the reconstructed topographic profile 24 overlapped to a MOC image and confirms the good correspondence between the features recognizable on the profile and on images. We are confident that the result is representative of the real topography; however it should be emphasized that the profiles have to be considered as averaged profiles in which minor features, that do not have a consistent linear shape among the width B of the lateral band, are averaged out. In the regional contest of this work, we consider this as an advantage of the method, rather than a limitation.
 As further test to validate our method we have compared the scarp width obtained from the topographic profiles with that resulting from MOC images. Wide-angle MOC images were used to estimate the scarps width along part of profile 24 and the results are compared with that measured on the profile in Figure 5. However, the 252 m/pixel resolution of the wide-angle images is less than ideal to estimate the dimension of features that are often of the same order of magnitude, therefore we have also attempted to use the high-resolution MOC images. We searched high-resolution images of slope scarps with a N-S orientation and with a sufficiently extended length (about 50 km). No suitable images were found along the measured profiles and only a few images were found near the study area. The available images represent small structures near the studied profiles that satisfy only in part the needs of orientation and length, however we proceeded constructing topographic profiles crossing these structures and estimating the slope width from images and profiles. Results are also shown in Figure 5 with gray markers. Data from both wide-angle and high-resolution data sets show linear correlation coefficients which are significant at the 95% confidence level (according to Student's t test). The slopes of the best-fit lines are of about 0.85 for wide-angle images and 0.89 for high-resolution images, which we regard as more reliable. The slope values different from 1 suggest that the actual scarp width (as seen on the MOC images) is about 89% of that estimated from the topographic profiles; therefore the slope inclination measured from the topographic profile is probably slightly shallower than the actual one.
2.2. Errors Due to the Orientation of the Tectonic Structures
 If the axes of the tectonic structures are not perpendicular to the profile trace, the length of slope projections on the profile will be biased, resulting in an error in the measurements of the slope inclination.
 In an idealized situation such as that of Figure 6a, and neglecting the errors due to the nonplanar geometry, it is possible to calculate the difference between the real and the measured slope inclination, as a function of the angles θ and γ, using simple geometric considerations.
 The Mars Global Surveyor orbital paths in the study area has an angle γ of about 8.3° with positive (clockwise) or negative sign with respect to the geographic North. The ratio between real and apparent slope width (b′/b) is defined as = , and it is plotted in Figure 6b as a function of the angle and γ = 8.3°. The relationship between the real slope α and the measured slope inclination α′ (inclination error) is tan α = tan α′; its value is plotted as a function of θ in Figure 6b, for α ranging from 55° to 65° and γ = 8.3°. Both positive and negative θ, and thus inclination errors, are possible; however, negative inclination errors are larger. MOLA paths have both positive and negative γ; for negative γ (γ = −8.3°) the resulting graph is symmetric to Figure 6b with respect to the vertical axis. Since orbits with positive and negative γ occur in approximately equal number, it is likely that the negative and positive errors are mostly averaged out. If, at a given point, the number of orbits with opposite γ is different, the error due to the orientation of the structure is more likely to result in an underestimation of the dip angle. This is because negative inclination errors are larger than positive errors. The comparison of scarps width from MOC images and measurements on topographic profiles (Figure 5), suggests that this probably occurred to a small extent (about 10%). The errors in inclination estimated from the comparison with MOC images are <3° for slope scarps between 45° and 75° in inclination.
2.3. Interpretation of Profiles
 In the study area, the HNf and Hf units are affected by a pervasive extensional tectonics with dominantly N-S striking graben structures. Grabens are several hundreds of kilometers long and have small spacing along the width direction (kilometers to few tens of kilometers).
 Some details of the profiles, taken in different sections, are shown in Figure 7 together with the related tectonic interpretation and error bars.
 According to our interpretation, the largest and deepest structures often include smaller-scale grabens and are bounded by stair-step arranged scarps (Figure 7a). On the contrary, most of the small grabens are simple structures with only two bounding faults that show similar throw (Figure 7b), quasi-horizontal floor and equally elevated sides (e.g., Figures 7a and 7c). The floor of fault block appear subhorizontal (Figure 7) in spite of the large vertical exaggeration showing the absence of large scale block rotations.
 In this study, we recognized and measured depth, width and scarp inclination of 274 graben structures along the 910 km long “profile 24” and of 400 graben structures along the 730 km long “profile 26”. According to the comparison of scarp width with MOC images (Figure 5), values of scarps inclination are probably underestimated of about 2° on average. Moreover, since topographic profiles corroborated by MOC images locally show evidences of mass wasting and scarp retreating processes, the present slopes may not coincide with the fault planes.
 Therefore we inferred position and inclination of graben bounding faults from the morphology of graben scarps (Figure 7). According to our interpretation, inclination of faults planes range from 45° to 60° with an average value of 55°. For the above mentioned reasons, we decided to assume a fault inclination angle of 60° to calculate the tectonic extension. This value, which is rather close to the measured average value, was largely used in the literature being justified by a variety of mechanical [e.g., Anderson, 1951] and direct observations on graben fault dips on the Moon and Mars [e.g., Golombek et al., 1996; Davis and Golombek, 1990; Golombek, 1979; Banerdt et al., 1992, and references therein].
2.4. Tectonic Extension
 Fault displacement is calculated as a function of the topographic relief (Figure 8). Graben extension was calculated on the basis of the conservative assumption of purely dip-slip fault displacement (i.e., a null displacement component along the fault strike direction). This assumption is reasonable in the Ceraunius Fossae context because there are no large evidences of significant strike-slip tectonics (e.g., en echelon pattern of fault system). Total extension across each graben was calculated as a function of graben depth and of dip angle of bounding faults: D = (d/tan α1) + (d/tan α2); where D is the total extension across the graben, d is the graben depth, α1 and α2 are the dip angles of the eastern and western bounding faults, respectively (which we assumed = 60°). Since we considered block rotation negligible and planar faults, the above-described method provides the values of tectonic extension.
 The regional longitudinal strain (ereg) along the profile was calculated as: ereg = Σ (D)/l0; where Σ D is the summation of the extension along the individual graben and l0 is the original length of the profile.
3. Results and Discussion
3.1. Graben Morphometry
 The two studied topographic transects show many similarities and their main structures can be correlated from one profile to the other (Figure 3). Each profile shows two parallel crustal bulges separated by a narrow topographic depression. The western bulge is higher (more than 4000 m above the reference level) and wider (about 300 km) than the western one, and it is affected by more pervasive normal faulting.
 Most of the extension calculated along the profiles occurs between −106° and −110° longitude, where HNf terrains crop out. Although most of the deformation is located in the oldest (HNf and Hf) terrains, the younger Acf Formation is also affected by less extension, suggesting that tectonic activity lasted until the Middle Amazonian.
 Graben dimension ranges from 250 m to more than 15 km in width, and from 10 m to 1 km in depth. The largest and deepest graben structures are located in the more elevated parts of the studied profiles (from −106° to −110° longitude) close to the hinge zone of the western bulge. Only few large grabens (up to 1500 m in width) are located in the western part of the profiles, in the Early Amazonian–Middle Amazonian terrains of the Ceraunius Fossae Formation (Acf). Following our interpretation of a tectonic activity that continued through the Middle Amazonian, we explain these wide and shallow structures as the inheritance of Noachian grabens that, although mostly buried by Early Amazonian to Middle Amazonian lava flows, continued to be active, accumulating younger, small vertical displacements.
 Graben width (Figures 9a and 9c) and depth (Figures 9e and 9g) vary largely and show distributions closely resembling exponential distributions (Figures 9b, 9d, 9f, and 9h). The relationship between the logarithm of graben depth and the logarithm of graben width is shown on Figures 9i and 9l; the Early Amazonian–Middle Amazonian terrains and Late Noachian–Early Hesperian terrains have been plotted separately (Figures 9i and 9l, respectively) because of their different degree of deformation and structural style.
 Grabens affecting Fractured Rocks (HNf and Hf Formations) are nearly (r = 0.68) self similar (Figure 9l), while data measured on the Ceraunius Fossae (Acf) Formation cannot be used to show any relationship (r = 0.306) between graben width and depth (Figure 9i).
 The general low value of correlation coefficients suggests that both graben width and depth values could not depend from the same parameters. Whereas the graben width is mostly controlled by rheology parameters (number, thickness and spacing of the existing rheological layers) and by mechanical interactions between the graben border faults [Melosh and Williams, 1989], the graben depth is mostly controlled by fault mechanics parameters.
 On the western part of the study area (Figure 9i), the lower value of the correlation coefficient (r = 0.306) could be ascribed to additional causes: (1) the presence of Noachian graben buried below Early Amazonian–Middle Amazonian lava flows during their last activity phases, as explained above, and/or (2) the effect of the mechanical discontinuity between the base of Acf Formation and the top of HNf Formation during the development of new small grabens. In the first case, wide grabens could show a small vertical displacement (and consequently graben depth) because the earliest displacement was obliterated by Early Amazonian–Middle Amazonian lava flows, and only the last phases of graben evolution are recorded by surface evidence.
3.2. Extension and Strain
 Extension measured across each graben and cumulative extension along the studied profiles are shown in Figure 10. Most of the extension is accommodated in the central part of the profiles (between −106° and −110° longitude) where the local strain is as large as 13% (emax = (l1 − l0)/l0 = (186 km − 164 km)/164 km = 0.134), and tectonic structures have larger dimensions. In this section of the profile, where HNf terrains are exposed, the largest structure accommodates an extension of up to 1.5 km. On the basis of our measurements, the regional tectonic extension in the study area is about 36 km (e24 = (l1 − l0)/l0 = (910 km − 874 km)/874 km = 0.041) along profile 24 and 42 km (e26 = (730 km − 688 km)/688 km = 0.061) along profile 26. This is significantly larger than previous results based on the interpretation of Viking images [e.g., Plescia, 1991].
 The calculated cumulative extension of the western part of profile 24, where Early Amazonian–Middle Amazonian terrains (Acf Formation) crop out, is about 4.8 km, that corresponds with a strain of 1.1%. This extension, that occurred after the Early Hesperian, represents a small fraction of the total extension affecting the studied area, suggesting that most of the tectonic evolution of the Ceraunius Fossae occurred in Noachian-Early Hesperian age, during the early stages of the Tharsis evolution.
 The concurrence of the largest extension and the most pronounced bulging of the topographic surface apparently suggests a causal relationship between the two. This possibility was verified by measuring the extension due to the bending of the topographic surface. The results show that the finite longitudinal strain due to bulging is negligible (e = 5.55 × 10−5), and therefore the whole extension along the profiles must be ascribed to crustal horizontal movements.
 Our interpretation agrees with the hypothesis of Tanaka , which interpreted the same set of grabens to be the expression of a regional extensional stress system.
 This work attempted a quantitative evaluation of the extension that occurred in the Ceraunius Fossae area based on laser altimetry data (MOLA).
 Our results show that the studied area is affected by a relatively large extension. In the oldest and most deformed terrains (along 26° latitude and between −106° and −110° longitude) extension reaches 22 km (emax = 0.134), a much larger value than previously estimated. The discrepancy between our and previous results can be ascribed to the higher resolution that could be obtained from MOLA data compared to Viking images.
 According to our interpretation, also the younger Acf units are tilted and slightly fractured. This suggests that the bulge activity continued at least until Early Amazonian times. The amount of the measured extension cannot be explained by the bulging of the topographic surface. Our calculations show that the fraction of extension caused by bulging is extremely small; for this reason we interpret the whole extension along the profiles as the result of crustal horizontal motion.
 This work was supported by the Italian MIUR (Cofin projects 2002). We thank Gian Gabriele Ori and Angelo Pio Rossi for invaluable help with data. Discussions with Stefano Mazzoli were the source of many insights. We are also grateful to Mauro De Donatis for providing some of the software used in this work. The reviews by Daniel Mège, Jeff Plescia, and an anonymous reviewer greatly helped to improve this paper.