Tectonic pressurization of aquifers in the formation of Mangala and Athabasca Valles, Mars

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005je002546, 2006 Tectonic pressurization of aquifers in the formation of Mangala and Athabasca Valles, Mars Jeffrey C. Hanna 1 and Roger J. Phillips 1 Received 1 August 2005; revised 24 October 2005; accepted 28 November 2005; published 8 March [1] Mangala and Athabasca Valles are the type examples of a distinct class of outflow channels that debouch directly from extensional tectonic features. We here demonstrate that the tectonic events responsible for the formation of the graben and fissures at the sources of the channels would have likely resulted in a near-instantaneous pressurization of the surrounding aquifers. Subsequent drainage of the pressurized aquifers though the confining cryosphere to the surface along the tectonically generated faults and fissures would have produced the catastrophic floods responsible for forming the channels. The peak discharges and individual flood volumes would have been dependent upon the magnitude of the individual tectonic events at the source regions. We estimate that individual extensional tectonic events at the source regions of Mangala and Athabasca Valles would have resulted in flood volumes ranging from 3 to 300 km 3 and peak discharges ranging from 10 5 to 10 6 m 3 s 1. Our models further show that the entire extensional tectonic history of Athabasca Valles would have resulted in a total cumulative flood volume of ,000 km 3, whereas that at Mangala Valles would have resulted in a total flood volume of ,000 km 3, both consistent with inferred flood volumes based on the geomorphology. Athabasca Valles in particular is of interest as it is the youngest of the outflow channels, demonstrating that this mechanism has brought substantial volumes of water to the surface in the present epoch. Citation: Hanna, J. C., and R. J. Phillips (2006), Tectonic pressurization of aquifers in the formation of Mangala and Athabasca Valles, Mars, J. Geophys. Res., 111,, doi: /2005je Introduction [2] While the Martian hydrologic cycle in the Noachian epoch (4.5 to 3.7 Ga [Hartmann and Neukum, 2001]) was driven largely by exogenic factors, commonly thought to include precipitation induced aquifer recharge similar to that on Earth [Hynek and Phillips, 2003], the dominant hydrologic processes since the end of the Noachian appear to have been driven by endogenic forces. The primary signature of the Martian hydrologic cycle in the Hesperian (3.7 to 3.0 Ga) and early Amazonian (3.0 to 1.7 Ga) epochs is writ in the form of a number of large outflow channels found across the planet [Baker, 1982]. In these we see the scars left by catastrophic floods that apparently erupted fully formed out of the ground to flow across the surface for a short time, before emptying into the northern plains and either ponding to form an ocean, or freezing and sublimating into the atmosphere [Kreslavsky and Head, 2002]. The outflow channel floods were likely important in redistributing the volatile inventory of Mars, and may have been a significant driver of climate change [Gulick et al., 1997]. 1 McDonnell Center for the Space Sciences and Department of Earth and Planetary Sciences, Washington University, St Louis, Missouri, USA. Copyright 2006 by the American Geophysical Union /06/2005JE [3] While the particular nature of the endogenic forces responsible for the formation of such massive floods has remained elusive, it is clear that the mechanism must have been capable of producing large pore pressures over wide areas. Given their diverse morphology, wide geographic distribution, and broad temporal distribution, it is not likely that a single common mechanism can be called on for the production of all of the outflow channels. Of the circum- Chryse outflow channels, some, such as Ares Valles, formed within regions of chaotic terrain from which water apparently escaped through the confining cryosphere via a distributed network of fractures [Hanna and Phillips, 2003]. Others, including Tiu, Simud, and Kasei Valles, may have formed through the drainage of canyon lakes. [4] We here focus on a particular suite of flood channels that emanate directly from extensional tectonic features. Mangala and Athabasca Valles are the best studied of this class of outflow channel, though a number of other examples are observed across the planet, including Marte Valles [Burr et al., 2002a], Grjótá Valles [Burr et al., 2002a; Plescia, 2003], and Granicus Valles [Mouginis-Mark et al., 1984] in the Elysium Region, and several small unnamed tectonic outflow channels in the Tharsis Region [Mouginis-Mark, 1990; Mouginis-Mark and Christensen, 2005] (Figures 1 and 2). Previous studies [Head et al., 2003; Manga, 2004] have emphasized the role of the tectonic features in providing a conduit for a pressurized aquifer to drain to the surface, thereby assuming that the 1of15

2 Figure 1. Context map of Mars in MOLA topography showing the locations of several representative tectonic outflow channels. White numbers and boxes (where resolved) represent locations of corresponding figures, depicting two unnamed valleys in the Tharsis region (2a and 2b), Granicus Valles (2c), Grjo ta Vallis (2d), Athabasca Valles (3), and Mangala Valles (4). The Cerberus (CF), Memnonia (MF), and nearby Sirenum (SF) fossae are highlighted in black. Figure 2. Tectonic outflow channels in the Tharsis and Elysium regions, including (a) an unnamed valley east of Olympus Mons (portion of THEMIS image V centered on 16.1 N, E) [Mouginis-Mark and Christensen, 2005], (b) an unnamed valley south of Ascraeus Mons (portion of THEMIS image V centered on 6.0 N, E) [Mouginis-Mark and Christensen, 2005], (c) Granicus Valles (portion of Viking MDIM centered on 27.3 N, E) [Mouginis-Mark et al., 1984], and (d) Grjo ta Valles (MOLA shaded relief map centered on 16.1 N, E) [Burr et al., 2002a; Plescia, 2003]. North is toward the top unless noted otherwise. 2 of 15

3 Figure 3. MOLA shaded relief topographic map of the source of Athabasca Valles at one of the Cerberus Fossae fissures (image centered at 9.2 N, E). faulting played a passive role in the generation of the floods. In this study, we demonstrate that the elastic response of the crust to the observed tectonism at the sources of these channels would have resulted in a widespread and nearinstantaneous pressurization of the surrounding aquifers. The pressurized aquifers would then have drained to the surface through the faults generated by the tectonic event, debouching onto the surface and carving the observed flood channels. Thus the tectonism was the direct cause of the floods, providing both the requisite high pore pressures and a conduit for the pressurized aquifer to drain to the surface. [5] We will first review the geology of the channels at Mangala and Athabasca Valles and the inferred properties of the floods responsible for carving these channels. The tectonic pressurization mechanism will then be detailed, before it is applied to understanding the origin of these outflow channel floods through a combined tectonichydrologic model. The significance of this mechanism in the broader scheme of the tectonic and hydrologic history of Mars is then discussed. 2. Geomorphology of Athabasca and Mangala Valles 2.1. Athabasca Valles [6] Athabasca Valles, the youngest of the Martian outflow channels [Tanaka and Scott, 1986], originates within one of the Cerberus Fossae fissures to the southeast of Elysium Mons (Figure 1). These fissures are approximately radial to Tharsis, and likely formed as a result of the combined stress fields produced by volcanic loading on the Tharsis and Elysium rises [Hall et al., 1986]. The channel, shown in MOLA topography in Figure 3, stretches approximately 300 km southwest of the fissure across the young Cerberus volcanic plains, with an average width of approximately 30 km and an average depth of approximately 65 m. The channel interior is marked by streamlined islands and longitudinal grooves, both taken as evidence of high-discharge catastrophic flooding [Burr et al., 2002a, 2002b]. [7] Estimates of the channel discharge based on the fluvial geomorphology are on the order of 1 to m 3 s 1 [Burr et al., 2002a, 2002b], though these estimates assume bankfull flow and are thus are an upper limit to the actual discharge, which may have been considerably lower. Recent estimates of the discharge considering a wider range of parameter space find three orders of magnitude uncertainty in the peak discharge, with values ranging from about 10 4 to 10 7 m 3 s 1 [Mitchell et al., 2005]. Discharge estimates reconstructed from depositional features within the channel yielded a range of peak discharges from to m 3 s 1 [Burr et al., 2004]. [8] We estimate an approximate lower bound on the total volume of the floods to be 420 km 3 of water, based on the MOLA-calculated channel volume and assuming a maximum volumetric sediment load of 0.4 [Komar, 1980]. However, we caution the reader that this estimate is a lower limit only. Taking into consideration the likelihood of lower sediment loads, a more conservative estimate of the flood volume would range from 400 to 1600 km 3, corresponding to volumetric sediment loads of 0.4 to 0.1. We stress, however, that lower sediment loads are possible and even likely, particularly in the waning stages of the flood, and it is therefore possible that total flood volumes may have significantly exceeded even this range. These discharge and flood volume estimates will provide an important test of our model results in section 4.2. [9] Crater statistics indicate that the channel surface of Athabasca Valles ranks as the youngest of the outflow channels, with estimated ages for the latest flood ranging from 2 8 Ma [Burr et al., 2002a] to Ma [Berman and Hartmann, 2002; Werner et al., 2003], though more recent work suggests that these ages are suspect as a result of the superposition of secondary craters from a nearby impact [McEwen et al., 2005]. Werner et al. [2003] argued for a complicated history of flooding, faulting, and volcanism, with fluvial activity dating back as far as 2.6 Ga, although this early onset of fluvial activity has also been called into question [McEwen et al., 2005]. Despite large uncertainties in the age and number of floods, the evidence points toward recent and likely repeated flooding at Athabasca Valles, suggesting that the process responsible for causing the floods must be repeatable, and must operate effectively even under the present climatic conditions. [10] Previous studies [Burr et al., 2002a; Head et al., 2003; Manga, 2004] recognized the role that the fissure likely played in transporting water from a pressurized aquifer at depth, through the cryosphere, and out onto the surface. Burr et al. [2002a] and Head et al. [2003] assumed a uniform hydraulic gradient between the fissure and the top of Elysium Mons, implicitly assuming steady state flow through the aquifer, and found that the estimated discharges could only be reproduced by assuming implausibly high aquifer permeabilities. Manga [2004] avoided this problem by assuming an initially uniformly pressurized aquifer prior to the onset of the flood, and was able to achieve model discharges of approximately 10 6 m 3 s 1 for reasonable aquifer properties. However, that study did not address the origin of the elevated pore pressures, which are the ultimate cause of the flooding Mangala Valles [11] Mangala Valles is the largest of the tectonic outflow channels. The channel originates within a 200 km long 3of15

4 faults. Favored mechanisms included melting of ground ice, compaction of sediments, hydrothermal circulation, and isostatic uplift of nearby aquifers to increase the hydraulic head. They ruled out tectonic forces as a pressurization mechanism due to the fact that the region is clearly dominated by extensional tectonism, whereas compressional tectonism was thought to be required for aquifer pressurization. However, as we demonstrate below, it is extensional, rather than compressional, tectonism that results in aquifer pressurization and ensuing outflow activity. Figure 4. MOLA shaded relief topographic map of the source of Mangala Valles at one of the Memnonia Fossae grabens (image centered at 16.9 N, E). segment of one of the Memnonia Fossae graben to the southwest of Tharsis (Figure 1). The Memnonia Fossae are part of an extensive system of graben and fissures that radiate from the Tharsis rise. These radial extensional tectonic features formed as a result of Tharsis loading and the resultant membrane/flexural stresses within the lithosphere [Banerdt and Golombek, 2000]. The main channel, shown in MOLA topography in Figure 4, flows for roughly 900 km over Noachian and Hesperian aged plateau and plains surfaces, with a typical width of 10 km and a typical depth of 100 m. [12] Tanaka and Chapman [1990] estimated the minimum flood volume based on the channel volume to be approximately 5000 km 3 of water. Using MOLA topography, we revise this estimate to approximately 8600 km 3, but we again caution the reader that this is only a lower bound, and the likely range would be between 10,000 and 40,000 km 3 of water, with greater volumes possible. The peak discharges are poorly constrained, since the negligible slope in the upper reaches of the channel precludes the use of the Manning equation, but, by comparison with other outflow channels, estimates in the range of 10 6 to 10 7 m 3 s 1 seem plausible. Crater statistics and stratigraphy suggest at least two episodes of flooding in the late Hesperian and early Amazonian epochs, correlating with the Pavonis I and Pavonis II episodes of Tharsis-centered tectonism [Tanaka and Chapman, 1990]. The temporal correlation of the channel ages with distinct tectonic episodes seems to suggest a causative relationship between the two as well. [13] McKenzie and Nimmo [1999] demonstrated that large volumes of water could be generated by melting the cryosphere above dikes, potentially explaining the floods at Mangala Valles. However, this mechanism acts over much longer timescales (on the order of 10 6 years) than are necessary to produce a catastrophic flood. Tanaka and Chapman [1990] discussed a variety of possible causative mechanisms for the floods at Mangala Valles, all involving elevated pore pressures and channeling of fluids along the 3. Tectonic Pressurization of Aquifers 3.1. Overview [14] The stress change within the crust during a tectonic event is capable of pressurizing any aquifer contained therein. Extensional tectonic features such as fissures and graben can form as a result of the catastrophic release of gradually accumulated extensional stress within the crust, or as a consequence of the forceful injection of a dike at depth, or from some combination of the above processes [Rubin, 1992; Rubin and Pollard, 1988]. For the first case, the extensional stresses are applied gradually over geologic timescales, such that there is ample time for the water to flow into and fill the enlarged pore space. The tectonic event results in a rapid release of this extensional stress at the fault, resulting in an effective compression of the surrounding crust and the pore space within. For the case of dikeinduced extensional tectonism, a similar compression of the surrounding crust ensues in order to accommodate the opening of the dike. In each of these cases, the sense of the overall change in stress and strain in the surrounding crust is compressional. The tectonic event occurs on a much more rapid timescale than the hydraulic diffusion timescale of typical aquifers, and thus the elastic response occurs under undrained conditions, in which the water cannot flow in response to changes in pore pressure and the amount of water in the pore space must be conserved. As a result, a significant fraction of the stress change within the crust during the tectonic event is borne by the water trapped in the pore spaces, resulting in a near-instantaneous pressurization of the aquifer. For the cold climate conditions thought to have prevailed on Mars during the period of outflow channel formation, the tectonically pressurized aquifers would be trapped beneath a thick cryosphere, preventing direct flow to the surface. However, the faults and fissures produced during the tectonic event would have provided a conduit through the cryosphere, allowing the aquifer to drain to the surface, resulting in the floods that carved the observed channels. [15] We first model the elastic stress change within the crust during the tectonic event, using a boundary element technique. This stress change translates directly into the aquifer pressurization, which then provides the initial condition for a finite difference model of flow through the aquifer and the ensuing discharge to the surface. The modeled discharges and flood volumes can be compared with the values inferred from the geomorphology. The details of the model implementation and execution are described below. Section 3.2 develops the basic theory and equations used in the models. The assumed tectonic geometries chosen to represent the graben and fissure at the 4of15

5 sources of Mangala and Athabasca Valles within the boundary element model are discussed in section 3.3. The choices of parameter values used in the tectonic and hydrologic models are discussed in section Tectonic Pressurization Theory and Hydrologic Modeling [16] The stress change resulting from a tectonic event is calculated using a modified version of the displacement discontinuity boundary element code to solve the equations of mechanical equilibrium with the generalized Hooke s Law for linear elasticity [Crouch and Starfield, 1983]. This technique simultaneously solves for discontinuities in the displacement vectors (shear and normal offsets) across the elements along all boundaries subject to specified conditions of stress and/or displacement, using a single matrix inversion involving only the boundary points themselves (see Crouch and Starfield [1983] for more details). In short, the solution for the displacement discontinuities on the boundaries is that in which the applied stresses on the boundaries (the sum of the locally applied stress and the projected remote stress) are in equilibrium with the stresses induced by the deformation. We model the features of interest here by representing the surface as a stress-free boundary, faults as boundaries with zero normal offset and zero shear stress, dikes as boundaries with zero shear stress and an applied normal stress representing the magma pressure, and open fissures as boundaries with zero shear and normal stress. The assumed geometry of faults, dikes and fissures used in the models are detailed in section 3.3. The resulting stress field generated by the tectonism is then calculated from the displacement discontinuities at the boundary elements. Further discussion of the application of the displacement discontinuity method to tectonic modeling is given by Rubin and Pollard [1988], Rubin [1992], and Schultz et al. [2004]. [17] As stated earlier, the tectonic event occurs on a more rapid timescale than the hydraulic diffusion timescale of typical aquifers, and the stress change within the aquifer must be borne in part by the water within the pore space. This aquifer pressurization can be represented as Ds pore ¼ B Ds xx þ Ds yy þ Ds zz 3 where Ds pore is the change in pore fluid pressure, Ds ii are the normal stress changes in the crust in the three principle directions, and B is the aquifer pressurization coefficient. For an aquifer with a known compressibility and Poisson s ratio under drained conditions, the aquifer pressurization coefficient is calculated following the work of Rice and Cleary [1976]: b B ¼ d b r b d b r þ n ðb w b r Þ where b d is the drained compressibility of the aquifer, b r is the compressibility of the pore-free rock mass, b w is the compressibility of the water, and n is the porosity. [18] As the elastic medium represented in the tectonic models is the same as the medium represented in the hydrologic models, it is necessary to select consistent ð1þ ð2þ parameter values throughout, accounting for the fact that the presence of the water within the pore space changes the undrained elastic properties of the rock. The tectonic modeling utilizes the undrained values of Young s modulus and Poisson s ratio, which can be calculated from the drained values as [Rice and Cleary, 1976] n u ¼ 3 n d þ B ð1 2n d Þ ð1 b r =b d Þ 3 B ð1 2n d Þ ð1 b r =b d Þ 1 þ n u E u ¼ E d 1 þ n d ¼ 3 ð1 2 n d Þb 1 d 1 þ n u 1 þ n d where n d and E d are the drained values of Poisson s ratio and Young s modulus, and n u and E u are the undrained values. The hydrologic modeling, on the other hand, occurs over a much longer timescale under drained conditions in which the water can freely move through the pores in response to pressure gradients, and thus the drained value of the aquifer compressibility is used within the aquifer model. [19] The hydrologic modeling utilizes a fully explicit finite difference model [Hanna and Phillips, 2005a] to simulate flow through the aquifer in response to the tectonically induced pore pressures and the drainage through the faults or fissures to the surface. Flow within the aquifer is governed by the consolidation equation [Domenico and ¼ 1 rðkrhþ ð4þ S s where h is the hydraulic head (m), K is the hydraulic conductivity (m s 1 ), and S s is the specific storage (m 1 ). The hydraulic head is a potential term, which includes both the elevation z of a fluid parcel above a datum, as well as the aquifer pore pressure s pore : h ¼ s pore r w g þ z The hydraulic conductivity describes the resistance to flow within the aquifer, and is determined by the intrinsic permeability of the aquifer k (m 2 ; 1 darcy = m 2 ), the fluid viscosity m (Pa s), the acceleration of gravity g, and the density of water r w : K ¼ k r wg m The specific storage describes the elastic response of the aquifer to pressure changes: S s ¼ r w gnb w þ b pore where b w (Pa 1 ) is the compressibility of water, and b pore is the compressibility of the aquifer matrix under drained conditions. [20] Flow through the aquifer ultimately escapes to the surface through the observed faults and fissures. In addition to the high along-strike permeability of the faults, both ð3þ ð5þ ð6þ ð7þ 5of15

6 Figure 5. (left) Assumed tectonic geometry (not to scale) and (right) modeled average stress change in the crust for the fissure at the source of Athabasca Valles for (a) the maximum width fissure model and (b) the minimum width fissure model. Negative stress changes are defined as compressional, indicating areas of aquifer pressurization. In the schematic diagrams, gray shaded regions represent the dike, while black lines represent the open fissure. faults and dikes are commonly surrounded by a damage zone of highly elevated permeability as a result of an interconnected network of large-aperture fractures [Gudmundsson, 2001; Gudmundsson et al., 2001]. These open fractures will provide a pathway for flow to drain through the otherwise impermeable cryosphere. Discharge to the surface is modeled by assuming that the faults, dikes, and fissures present essentially no resistance to flow along them. This is done by applying a constant head condition along these boundaries, simulating the instantaneous hydraulic communication with the surface. This assumption will result in an overestimation of the discharge in the earliest stages of the flood, as will be discussed further in section 4.2, but will not affect the later discharges or the total flood volume. The aquifer discharge into the faults and fissures is calculated from Darcy s Law as q ¼ K rh where q (m s 1 ) is the volumetric flux per unit area. The total discharge out of the aquifer and into the channel, Q (m 3 s 1 ), is the integral of the aquifer discharge over the area of the faults and dikes draining the aquifer. The flood volume is simply the time integral of the total discharge. [21] It is important to emphasize that the fissure and graben at the sources of Athabasca and Mangala Valles did not likely form in single events. Rather, the observed tectonic features are the end result of a long tectonic history, ð8þ with the accumulated displacements of a large number of faulting events. Similarly, the observed flood channels appear to be the end result of a long hydrologic history involving multiple floods. Thus the single-event flood volume must be scaled by the width or depth of the observed fissure or graben relative to the modeled singleevent value in order to calculate the cumulative flood volume over the entire tectonic and hydrologic history of the tectonic outflows. [22] In summary, the undrained elastic parameters are used in a boundary element model to calculate the stress change in the crust, which translates via equations (1) and (2) into the aquifer pressurization. These aquifer pore pressures are used as the initial condition in the finite difference model of the hydrologic response via equations (4) and (5), and the discharge to the surface via equation (8). The flood volume from a single tectonic event is then scaled by the ratio of the observed graben depth or fissure width to the modeled value to get the cumulative flood volume over the entire tectonic history. The peak discharges and cumulative flood volumes can then be compared with the values inferred from the channel geomorphology Model Fault Geometry Athabasca Valles [23] The fissure at the source of Athabasca Valles likely formed as a result of repeated dike intrusion during the emplacement of a giant dike swarm [Ernst et al., 2001], driven in part by the membrane/flexural stresses generated by loading on the Tharsis and Elysium rises [Hall et al., 1986]. The presence of young lava flows surrounding the fissure suggests that the dike may have erupted to the surface at some time during its formation, though the fresh appearance of the fissure walls suggests that the most recent activation of the fissure occurred without subsequent discharge of lava or water [Berman and Hartmann, 2002; Burr et al., 2002a]. [24] We consider two end-member models for the origin of the Cerberus Fossae fissure, which should bracket the range of possible scenarios. The first is the maximum width fissure, in which the magma pressure is sufficient to maintain a column of magma all the way to the surface. The dike in this scenario would extend from some specified depth to the surface, with the maximum width occurring at or near the surface, depending on the crustal stress field. The second end-member model is the minimum width fissure, in which the magma pressure within the dike is at the critical level where the stress intensity factor [Broek, 1986] at the upper dike tip is just sufficient to propagate a fissure all the way to the surface. The magma level in this scenario is well below the surface, and the maximum extension occurs at depth within the magma filled dike. The geometry of the fissures and dikes used in the models is depicted in Figure 5 (left). [25] The total amount of extension across the Cerberus Fossae fissure at the source of Athabasca Valles is uncertain. The fissure width is approximately 1000 m at the channel source, though this has likely been enlarged somewhat through erosion and mass wasting. We consider values of the total extension across the fissure of between 200 and 500 m. The fissure has an along-strike length of approxi- 6of15

7 mately 200 km, and we assume that the floods drained the pressurized aquifer along this entire length Mangala Valles [26] The Memnonia Fossae graben at the source of Mangala Valles exhibits the morphology of a classic flatfloored graben, suggesting that the near-surface tectonism can be represented by two inward dipping normal faults. On the basis of a combination of the surface morphology of the graben swarm as a whole and the radiating pattern relative to the Tharsis rise, it has been suggested that the Memnonia Fossae graben are the surface manifestation of a giant dike swarm [Ernst et al., 2001; Mège et al., 2003; Wilson and Head, 2002]. In a study of a nearby graben associated with the Memnonia swarm, Schultz et al. [2004] found that the surface topography within and around the graben is indicative of a combination of dike and graben induced uplift. On the basis of these different lines of evidence, we concur that the graben at the source of Mangala Valles was likely formed through a combination of dike emplacement at depth and normal faulting at the surface. [27] The study of Schultz et al. [2004] found a best fit model with two nonintersecting normal faults dipping inward at an angle of 70, with one fault penetrating to a depth of 5.3 km and the other continuing to a depth of 8 km. The modeled faulting event was followed by the formation of a dike with a maximum width of 30.5 m extending from a depth of 0.5 km to 18 km and crosscutting the longer of the two faults, with the magma pressure varying hydrostatically within the dike from zero at the upper dike tip. Faulting and dike emplacement was driven by an extensional stress regime in which the ratio of the least horizontal to the vertical compressive stress was 0.4. The observed graben topography was fit by three such episodes of faulting and dike injection. The graben in that study was particularly shallow, with a depth of about 20 m, and was located in a smooth plains unit to the east of Mangala Valles, which was likely the locus of recent resurfacing. The same graben, traced into adjacent older terrain had a depth of over 100 m. We interpret the study of Schultz et al. [2004] to reveal only the most recent episodes of dike injection and faulting, recorded since the last resurfacing event filled the earlier graben and smoothed the surface topography. Thus their results are representative of the few most recent tectonic events, but do not encompass the entire tectonic history of the Memnonia Foassae. [28] The graben at the source of Mangala Valles crosses both Hesperian-aged plains as well as higher Noachian-aged plateau units. The depth of the graben ranges from 700 to 1700 m, with the variation in depth due primarily to the variation in the adjacent topography. The graben floor has a relatively constant elevation despite the variation in rim topography, suggesting that the graben may have originally been deeper and then experienced some degree of infilling with sedimentary or volcanic materials. In the calculation of the total flood volume over the entire tectonic history, we assume a final graben depth of 1 km. The pronounced graben at the source of the channel has a length of approximately 200 km, and it is clear that the flooding would have drained the pressurized aquifer along at least this segment of the graben. However, the graben does continue along strike in both directions for distances of hundreds of kilometers. These distal portions of the graben are more subdued, possibly as a result of volcanic or sedimentary infilling. Thus we also consider the possibility that the floods at Mangala drained an additional 100 km of graben in either direction beyond the main graben, effectively doubling the potential flood volumes and discharges. [29] We consider two possible scenarios for the formation of the graben/dike. First, we simply assume the same geometry as the Schultz et al. [2004] model. In that study, the graben and dike were formed independently, and the resulting elastic surface displacements were simply added to find the best fit to the observed topography. We also consider a variation of that model that more nearly matches the theory of dike-induced graben formation. It is thought that the near-tip stress field of the growing dike is needed to drive slip on the graben faults, but that as the dike later continues to grow, it can propagate through the graben faults, changing the sign of the stress on them and locking them [Rubin, 1992; Rubin and Pollard, 1988; Schultz et al., 2004]. In extensional stress regimes the deviatoric stress increases with depth, as discussed in section 3.4, and so dikes will tend to grow from the bottom up as the magma pressure increases during lateral propagation. The upper dike tip propagates toward the surface, driving slip on the faults until the dike tip reaches the depth of the lower fault tips, at which point the dike continues to grow without subsequent fault slip. [30] In order to represent this in our two dimensional model, we form the graben simultaneously with a partially formed dike, extending upward to just below the intersection of the normal faults. We then lock the slip on the faults within the model, and allow the dike to complete its formation in the resulting stress field. Thus the slip on the normal faults is driven by both the regional extensional stress field and the stress field produced by the growing dike beneath, while the final dike dimensions are similarly affected by the stress field induced by the faulting. In this model, hereafter referred to as the two-stage graben model, two symmetric normal faults extend to a depth of 5 km with a dip of 70. The final dike extends from a depth of 0.5 to 20 km. We also consider the effect of a greater depth to the bottom dike tip of 30 km. The magma pressure at the upper dike tip is set equal to the horizontal compressive stress, and varies hydrostatically within the dike. These two basic model setups are depicted schematically in Figure 6 (left). [31] The above tectonic models for the sources of Athabasca and Mangala Valles are set up within the boundary element model in order to calculate the resulting stress fields. The results are used to model the pore pressures and the ensuing hydrologic response, as previously described Model Parameters [32] The results of both the tectonic and hydrologic modeling are dependent upon the choice of parameters. Hanna and Phillips [2005a] demonstrated the importance of the spatial and temporal variation of the hydrologic parameters in modeling large and transient pore pressures. However, the necessity of choosing the elastic parameters consistently between the tectonic and hydrologic models supercedes the advantages of a detailed aquifer model in this case. Failure to choose self-consistent elastic parameters results in violation of the conservation of water volume, 7of15

8 Figure 6. (left) Assumed tectonic geometry (not to scale) and (right) modeled average stress change in the crust for the graben at the source of Mangala Valles for (a) the Schultz-style graben and (b) the two-stage graben model of this study. In the schematic diagrams, gray shaded regions represent the dikes, while black lines represent the faults. For the two-stage graben diagram, the darker gray represents the dike forming simultaneously with the faults, while the lighter shade of gray represents the completion of the dike formation after the faults become locked. and the generation of unrealistically large or small floods. This constraint places limitations on the hydrologic modeling, as the boundary element model used in the tectonic modeling is limited to the case of spatially uniform elastic parameters, and the hydraulic and elastic parameters are inherently related. It is thus necessary in this case to select values of the elastic parameters that will be representative of both the cryosphere and aquifer as a whole, and values of the porosity and permeability that will be representative of the average for the aquifer. The elastic parameters of the cryosphere will be affected by the presence of ice within the pores. However, Young s modulus and Poisson s ratio for an ice-cemented porous crust will not differ significantly from the water-saturated crust under undrained conditions due to the low porosity and the similar compressibility of ice and water. [33] The aquifer is assumed to extend from the base of the cryosphere, which is impermeable to flow, to some maximum depth below which there is negligible porosity and permeability. While the depth to the base of Martian aquifers is unknown, Hanna and Phillips [2005a] estimate an approximate upper limit to be the brittle-plastic transition on early Mars, at a depth of 10 to 20 km, below which open pore space is unstable. This value is in agreement with the observation of substantial crustal permeability at great depths within the Earth s crust [e.g., Huenges et al., 1997]. Our nominal model assumes an aquifer extending from the base of the cryosphere at an assumed depth of 1 km to the base of the aquifer at a depth of 20 km, though an aquifer base of 10 km is also considered. Aquifer compressibilities under drained conditions are generally in the range of to 10 9 Pa 1 [Domenico and Schwartz, 1990; Hanna and Phillips, 2005a]. Since we are interested in a value that can be taken to be representative of the aquifer as a whole, we choose the lower value of Pa 1 as our nominal aquifer compressibility. Compressibilities of the pore-free rock mass are typically less than Pa 1 [Domenico and Schwartz, 1990], and we choose Pa 1 as our nominal value. In the megaregolith model of Hanna and Phillips [2005a], the Martian crust was modeled with a porosity of approximately 0.16 at the surface, decreasing to values of approximately 0.05 below the base of the megaregolith. We adopt a value of 0.05 as most representative of the aquifer as a whole. We assume a value of the drained Poisson s ratio of 0.15, consistent with values for porous aquifers [Rice and Cleary, 1976]. [34] The nominal model described above results in a value for the undrained Young s modulus of 21.0 GPa, and an undrained Poisson s ratio of The aquifer compressibility coefficient, B, in this scenario has a value of We also consider more conservative models with a lower aquifer compressibility ( Pa 1 ), and with a higher value of the undrained Poisson s ratio (0.25). The values for the drained and undrained elastic parameters and the aquifer pressurization coefficient for all cases are summarized in Table 1. [35] For the hydrological modeling, it is also necessary to represent the permeability of the aquifer. In geologically stable environments, the permeability decreases with depth due to the closure of the pore space and fracture network as a result of elastic compression and pressure solution [Hanna and Phillips, 2005a]. However, we are interested in the permeability in the crust surrounding fissures and graben immediately after a large tectonic event. Recently activated faults are surrounded by a damage zone in which the permeability is increased by several orders of magnitude compared to the surrounding host rocks [Gudmundsson, 2001; Gudmundsson et al., 2001]. Furthermore, the reactivation of cross faults running perpendicular to the main extensional faults [Wilkins and Schultz, 2003] will increase the effective permeability of the surrounding aquifer further. It is unknown how the transient postfaulting permeability will vary with depth and pore pressure, making typical models of the variation of permeability applied to stable environments inapplicable. As a first-order model, we assume a relatively high permeability of m 2, comparable to that typical in the upper 1 km of the crust in stable environments. Uncertainties in the permeability will introduce uncertainty in the magnitude of the discharge and the duration of the floods, but will not affect the total flood volumes from the models. Table 1. Elastic Parameters and Associated Derived Constants Model b aq,pa 1 n d E u, GPa n u B Nominal High-n d Low-b aq of15

9 or beneath the aquifer. We adopt 0.57 as the ratio between s 3 and s 1 in our nominal model, but also consider the effects of a more strongly extensional stress regime with a ratio of This range brackets the value of 0.4 found by Schultz et al. [2004] for the stress driving faulting at the Memnonia Fossae. The lithostatic and hydrostatic magma pressures within the dikes are calculated assuming rock and magma densities of 2700 and 2400 kg m 3, respectively. [37] Once the elastic properties and the stress state of the crust are specified, the assumed geometry of faults and dikes can be used to calculate the resultant displacements and stress field from any tectonic event within the boundary element model. The hydrologic response is then modulated by the choices for the aquifer properties. Figure 7. Normal displacement along the dike and fissure walls for the minimum and maximum width fissure models for the fissure at the source of Athabasca Valles. [36] The prefaulting stress within the crust is a key boundary condition, as it is the combination of the regional extensional stress and the magma pressure in the dikes that drives the tectonism. The regional extensional stress field from loading induced membrane/flexural deformation at the Tharsis and Elysium Rises likely played an important role in the formation of the Memnonia and Cerberus Fossae [Banerdt and Golombek, 2000; Hall et al., 1986]. Measurements of the deviatoric stress in a variety of terrestrial tectonic environments suggests a crustal stress state in equilibrium with the frictional strength of the most suitably oriented faults with a coefficient of friction in the range of 0.6 to 0.7 [Brudy et al., 1997; Scholz, 2002]. In terms of the principle stresses, this can be represented as [Scholz, 2002] h i s 0 s 0 3 ¼ 1 ð m2 þ 1Þ 1=2 m 2 t 0 ðm 2 þ 1Þ 1=2 þ m where s 1 0 and s 3 0 are the effective principle stresses (stress minus pore pressure), m is the coefficient of friction, and t 0 is the fault cohesion. At depths greater than 1 km, the fault cohesion is small relative to the shear stresses that can be maintained on the fault and can thus be neglected. For extensional stress regimes with vertically oriented s 1 equal to the lithostatic pressure and assuming a friction coefficient of 0.6, the ratio between the critical least horizontal compressive stress and the vertical lithostatic stress can be calculated from (9) for dry conditions or for saturated conditions with hydrostatic pore pressure as s 3 s 1 s 3 s 1 ð9þ ð m2 þ 1Þ 1=2 m dry ðm 2 þ 1Þ 1=2 þ m ¼ 0:32 ð10þ 1 r w ð m 2 þ 1Þ 1=2 m wet r r ðm 2 þ 1Þ 1=2 þ m þ r w ¼ 0:57 r r Thus greater extensional stresses could be supported by the faults in the absence of pore pressure within the cryosphere 4. Results and Discussion 4.1. Tectonic Modeling [38] The stress fields resulting from the minimum and maximum width fissure models for the tectonism at the source of Athabasca Valles are shown in Figure 5. In both models, the compressional stress change peaks toward the bottom of the dike, as a result of the increase in both deviatoric stress and magma pressure with depth. For the maximum width fissure there is significant compressional stress change in the crust along the dike all the way to the surface, while for the minimum width fissure the stress change only becomes compressional below a depth of about 8 km. This difference is significant, as for more realistic aquifer models the compressibility and permeability of the aquifer at greater depths would be markedly decreased, thereby potentially diminishing the efficacy of the aquifer pressurization for the deeper dike in the minimum width fissure model. The single-event surface fissure widths are 0.9 and 82.9 m for the minimum and maximum width models, respectively. The cross-sectional profiles of the dikes and fissures for both models are shown in Figure 7. [39] The stress fields for the two-stage and Schultz-style models for the Memnonia Fossae graben at the source of Mangala Valles are presented in Figure 6. The sense of the stress change reverses beyond the dike tips, above 0.5 km depth and below 20 km depth. These regions would experience aquifer depressurization, however the upper dike tip is located within the permanently frozen cryosphere, and the lower dike tip is near the bottom of the hydrologically active zone. The upper dike tip stress field is moderated somewhat by the extension that has already occurred in the graben at these shallow depths. The dike profiles and fault slip for the Schultz-style and two-stage graben models are shown in Figure 8. These two models result in similar stress fields and displacements, with graben depths of 4.5 and 9.5 m, respectively Hydrological Modeling [40] The average stress field induced by the tectonic event maps directly into the aquifer pressurization through use of equation (1). These distributions in excess pore pressure were used to model the time evolution of the discharge and flood volume. At the onset of the flood, the hydraulic gradient is essentially infinite along the faults and dikes as the constant head condition is applied, and is limited only by the model grid resolution. As the grid in the vicinity of 9of15

10 Figure 8. Normal and shear displacement along the dike walls and faults for the Schultz-style graben model and the two-stage graben model of this study for the graben at the source of Mangala Valles. Solid lines indicate horizontal displacement on dike walls, and dashed lines indicate shear displacement on faults (left-lateral slip defined as positive). this boundary condition is further refined, this initial onset discharge will approach infinity. This is a numerical artifact of the fact that the diffusion of the flood pulse within the conduits to the surface is ignored, and affects only the early time steps in the model. For the purpose of comparison, we take the discharge after 10 3 s as representative of the peak flood discharges Athabasca Valles [41] Looking first at the modeled floods from the fissure at the source of Athabasca Valles, presented in Figure 9 and Table 2, we see that the discharges after 10 3 s range from m 3 s 1 (minimum width fissure, 10 km aquifer) to m 3 s 1 (maximum width fissure). The discharge decreases exponentially with time, while the flood volume gradually flattens out as the discharge wanes (Figure 9). These discharges are in rough agreement with the crude estimates based on the channel geomorphology of 10 4 to m 3 s 1 [Burr et al., 2004, 2002a; Mitchell et al., 2005], though we again stress the large uncertainties in these estimates. Individual flood volumes range from 3.8 km 3 (minimum width fissure, 10 km aquifer) to 78.5 km 3 (maximum width fissure). [42] The cumulative flood volumes provide the best test of the model results, as they are dependent primarily upon the geometry and total displacements of the faults and dikes, whereas the peak discharges and single event flood volumes are highly sensitive to the assumed aquifer parameters and the magnitude of the individual tectonic events. Looking at the cumulative flood volume over the entire tectonic history, there is a large discrepancy between the maximum and minimum width fissure models, with cumulative flood volumes of 474 and 13,850 km 3, respectively, assuming 500 m total extension. Despite the fact that the single event flood volume is greater for the maximum width fissure model, the cumulative flood volume is dramatically greater for the minimum width fissure model. This can be understood by noting that the flood volume from a single tectonic event scales with the vertically averaged single event horizontal displacement, which is generally proportional to the maximum displacement at depth, while the total number of tectonic events and floods scales with the inverse of the single event horizontal displacement at the surface. Thus the cumulative flood volume over the entire tectonic history scales roughly with the ratio of the maximum horizontal displacement to the surface displacement. This ratio is 1.02 for the maximum width fissure, and 25.1 for the minimum width fissure. Thus, provided that the aquifer at large depths has sufficient permeability and compressibility, there is the potential for much greater flood volumes over the entire tectonic history of the channel for the minimum width fissure model. [43] Increasing the preexisting deviatoric stress results in a modest increase in the single-event flood volume, but also increases the modeled single-event surface extension, resulting in a slightly lower cumulative flood volume. Increasing the value of the drained Poisson s ratio or decreasing the aquifer compressibility results in only a modest decrease in the cumulative flood volume. Decreasing the aquifer thickness to 10 km results in a more dramatic decrease in the flood volume, since there is little aquifer pressurization as a result of the focusing of the tectonic stress change at depths below the base of the aquifer in this model (Figure 5). Figure 9. (left) Evolution of the discharge and (right) flood volume for the flood in Athabasca Valles for the minimum and maximum width fissure models, assuming a 20 km dike height, 20 km aquifer thickness, ratio between s 3 and s 1 of 0.57, and the nominal crustal elastic model. 10 of 15

11 Table 2. Summary of Hydrological Modeling Results for the Athabasca Valles Floods Tectonic Model Elastic Model Dike Height, km Aquifer Thickness, Km Stress Ratio, s h /s v Fissure Width, m Q (10 3 s) m 3 s 1 V ind (10 7 s), a km 3 V total (200 m), b km 3 V total (500 m), c km 3 Minfiss Nom Minfiss Hi-n d Minfiss Lo-b aq Minfiss Nom Minfiss Nom Minfiss Nom Maxfiss Nom a Flood volumes for individual tectonic events are given after 10 7 s have elapsed. b Total flood volumes over the entire tectonic history assuming total surface extension of 200 m. c Total flood volumes over the entire tectonic history assuming total surface extension of 500 m Mangala Valles [44] The modeled hydrologic response to the graben formation at the source of Mangala Valles is presented in Figure 10 and Table 3. The evolution of the discharge and flood volume with time (Figure 10) is similar to the model results for Athabasca Valles, as a result of the similarities in the dike properties assumed to be driving the tectonism. Peak discharges range from m 3 s 1 (two-stage graben model, 10 km aquifer) to m 3 s 1 (Schultzstyle graben), with single event flood volumes ranging from 22.1 km 3 (two-stage graben, low compressibility aquifer) to km 3 (two-stage graben, 30 km dike height). Considering the possibility that the floods drained an additional 100 km of graben in either direction beyond the main source graben would double these maximum discharge and volume estimates to m 3 s 1 and km 3. These peak discharges are in agreement with the rough estimates based on the channel morphology of 10 6 to 10 7 m 3 s 1. [45] The modeled cumulative flood volumes over the entire tectonic history of the graben range between 2866 km 3 (for the two-stage graben model in a 10 km thick aquifer) and 22,460 km 3 (for the Schultz-style graben assuming a 400 km graben length). These volumes agree well with the estimate of 8000 to 40,000 km 3 of water based on the channel volume. The greater cumulative flood volume from the Schultz-style graben again arises from the differing ratios of the surface horizontal displacement to the maximum horizontal displacement at depth. In the Schultz-style graben, slip on the faults is driven only by the preexisting extensional stress state of the crust, while in the two-stage graben model developed here, slip on the faults is driven by both the near-tip stress field of the dike and the preexisting regional extensional stress. In both models, the final dike width is determined primarily by the combination of the magma pressure and the regional stress field. Thus similar final dike widths are observed in both models, while the two-stage graben model experiences greater initial fault slip and thus more surface extension. The resulting higher ratio of the total extension to the surface extension in the Schultz-style graben leads to greater cumulative flood volumes. [46] Increasing the preexisting deviatoric stress results in a substantial increase in the single-event flood volume and a slight increase in the cumulative flood volume. Increasing the value of the drained Poisson s ratio results in a modest decrease in the cumulative flood volume. Decreasing the aquifer thickness to 10 km or decreasing the aquifer compressibility results in a more dramatic decrease in the flood volume; however, the very existence of the channels suggests the presence of a high-compressibility and highpermeability aquifer at depth to supply the floodwaters Geological Evidence [47] Given that the model results support the efficacy of tectonic aquifer pressurization in the generation of large floods, we now turn our attention to possible geological evidence for this mechanism. The unique feature of this model is that it predicts localized pressurization of the aquifers immediately adjacent to the tectonic features, rather Figure 10. (left) Evolution of the discharge and (right) flood volume for the flood in Mangala Valles for the Schultz-style and two-stage graben models, assuming a 20 km dike height, 20 km aquifer thickness, ratio between s 3 and s 1 of 0.57, and the nominal crustal elastic model. 11 of 15

12 Table 3. Summary of Hydrological Modeling Results for the Mangala Valles Floods Tectonic Model Elastic Model Dike Height, km Aquifer Thickness, km Stress Ratio s h /s v Graben Depth, m Q (10 3 s) (200 km), m 3 s 1 V ind (200 km), a km 3 V total (200 km), b km 3 V total (400 km), c km 3 Two-stage Nom ,548 Two-stage Hi-n d ,935 Two-stage Lo-b aq Two-stage Nom Two-stage Nom Two-stage Nom ,191 Schultz Nom ,230 22,460 a Flood volumes for individual tectonic events are given after 10 7 s have elapsed, assuming a 200 km along-strike graben length. b Total flood volumes over the entire tectonic history assuming a final graben depth of 1 km and a 200 km along-strike graben length. c Total flood volumes over the entire tectonic history assuming a final graben depth of 1 km and a 400 km along-strike graben length. than a more distributed regional pressurization as would be predicted by pressurization through the compaction of sediments [Tanaka and Chapman, 1990] or by a distant perched aquifer [Burr et al., 2002a; Head et al., 2003]. The melting of ground ice by dikes [McKenzie and Nimmo, 1999; Burr et al., 2002a] would not result in any excess pressurization of the aquifer unless there were large bodies of segregated ground ice deep within the crust, for which there is no evidence. Figures 5 and 6 show that pore pressures in excess of 20 MPa can be generated along the dike margins in the top portions of the aquifers, exceeding the lithostatic pressure for cryosphere thicknesses less than about 2 km. Thus we posit that evidence for localized pressurization in the vicinity of the tectonic feature would support the tectonic pressurization mechanism. [48] The presence of disrupted crust in the form of chaos regions is commonly interpreted to indicate the presence of superlithostatic pore pressures, as in the circum-chryse outflow channels [Carr, 1979]. Chaotic terrain, then, acts as a barometer of sorts, providing us with a crude measure of the paleopore pressure within the confined aquifers at the time of formation. Figure 11 shows the presence of chaotic terrain within a large crater that lies along the Mangala source graben to the west of the channel (also seen in the SW corner of Figure 4). Such chaotic terrain is not found elsewhere in the region, suggesting that the elevated pore pressures were focused along the graben. The preferential occurrence of chaotic terrain within the crater is likely attributable to the mechanical weakness of the crater floor relative to the surrounding bedrock, a pattern also seen in Aram Chaos in the circum-chryse region. We suggest that this chaotic terrain provides circumstantial evidence for localized pressurization around the source graben of Mangala Valles, which supports, but does not prove, this tectonic mechanism of aquifer pressurization. The absence of any chaotic terrain in the vicinity of the source of Athabasca Valles may simply reflect the presence of a thicker cryosphere at the time of the formation of that younger outflow channel. [49] We leave for future work the search for additional evidence of tectonic aquifer pressurization at these study sites and elsewhere. This model makes a number of predictions that may be observable in the geologic record. It is predicted that faulting and flooding events should be contemporaneous, which, to first order, is supported by the temporal correlation between the faulting and flooding events at Mangala Valles [Tanaka and Chapman, 1990]. The spatial extent of aquifer pressurization can be predicted based on the inferred fault geometry and displacement. Furthermore, there should be a first-order relationship between the extent and magnitude of faulting events and the resulting flood volume, with larger tectonic features producing greater flood volumes. Such a relationship does seem to exist for the observed range of tectonic outflow channels (Figure 2). However, further geological evidence for the importance of tectonic aquifer pressurization in generating the observed channels is needed Terrestrial Analog [50] The hydrologic effects of tectonic aquifer pressurization have been documented in several normal faulting terrestrial earthquakes [Muir-Wood and King, 1993]. It was found that the tectonic events were followed by a period of several months to a year of increased spring and river discharges in the region of the fault, with total excess flow volumes of approximately 0.5 km 3 of water. Using a similar, though simpler, approach to that above, Muir-Wood and King [1993] found a reasonable agreement between the modeled and observed hydrologic response. However, there Figure 11. Chaos region within a crater along the Mangala Valles source graben. (portion of MOC Geodesy Campaign Mosaic centered on 19.3 N, E; image is from NASA JPL Malin Space Science Systems). 12 of 15