DIKE EMPLACEMENT AND HYDROTHERMAL PROCESSES ON MARS Kathleen Craft, Virginia Tech Advisor: Robert Lowell, Virginia Tech Abstract Many features on the surface of Mars indicate that water contributed to their formation. Hydrothermal salt deposits and mineral hydrates discovered on Mars by the rovers Spirit and Opportunity at the plateau, Home Plate [Squyers et al., 2008], provide evidence that subsurface water from hydrothermal systems may have played a role in surface feature formation. Here we investigate hydrothermal systems on Mars by emplacing a dike below the surface and analyzing the stresses surrounding it as it propagates to the surface. We then relate the stresses to change in permeability and discuss future work. Results from our initial models show that horizontal stresses surrounding the dike are on the order of 10 5 to 10 6 Pa for a range of Young s modulus (E) of 10 9 to 10 11 Pa. These stresses correspond to changes in permeability of 1.0068 for E = 10 11 Pa and crack aspect ratio (ε) = 10-2 to about 27 for E = 10 9 Pa and ε = 10-3. Therefore, dike emplacement increases permeability adjacent to the dike. Further research will determine the resulting flux from the increased permeability and will relate this flux to feature formation. Additionally, an overlying ice layer will be investigated to determine fluid flux contribution to the system. Introduction Evidence of past volcanic activity on Mars is abundant. Mars has the largest volcano in the solar system, Olympus Mons, and many more dot the surface. Surface features indicating subsurface diking near the volcanoes also exist. The heat from the dikes combined with subsurface water (ice or liquid) constitutes a hydrothermal system that may have enabled water to reach the surface on Mars and form morphologic features observed there. Contrary to the fact that there is currently little water vapor in the Martian atmosphere and pure water is not stable at the surface, many Martian landscape features contain characteristics that suggest water was involved in their formation. Examples include hydrothermal salt deposits and mineral hydrates discovered by the rovers Spirit and Opportunity at the plateau, Home Plate, on Mars [Squyers et al., 2008]. These observations indicate there may have been liquid water on Mars at some point in the past. In a similar fashion to hydrothermal systems at Earth s Mid Ocean Ridges (MORs), a hydrothermal system on Mars can provide a means for transporting water, chemicals, and energy to the surface. Then, once the fluid reaches the surface, the flowing water may generate observed fluvial morphological features. In addition to interest in hydrothermal systems for their possible contribution to surface morphology formation, the presence of liquid water and heat together may indicate the possibility for life [Baross and Hoffman, 1985]. Therefore, determining locations of hydrothermal activity on Mars provides a possible strategy for the search for evidence of past life. Although there are many differences between the Earth and Mars, the basic physical processes on both planets are similar. A dike propagating below the surface on the Earth may differ from a Martian dike in breadth, depth of origin, and propagation speed, however, dikes on both planets are governed by gravity, density of the regolith, thermal and structural stresses, etc. A prior study performed by Hanna and Phillips (2006) investigated a system of an emplaced dike and the ensuing pore pressure distribution in an attempt to determine if a sufficient amount of fluid could be rapidly forced to the surface to form flood features observed in the Mangala and Athabasca Valles. Hanna and Phillips (2006) assume an instantaneous dike emplacement that results in an extremely large initial stress level. This high stress exists for about the period of time a dike would take to propagate from its origin to the surface. However, the actual stress in the subsurface would gradually increase rather than be continuously high for the duration of the propagation. My research considers the gradual stress increase by first propagating a dike from its source magma chamber and then calculating adjacent stresses. Results are compared to those calculated by Hanna and Phillips (2006) and differences are discussed. Contrary to previous Martian hydrothermal studies that did not consider important parameters of fracturing and of fluid properties, including tectonic stresses from dike propagation and the effects of pore pressure change on fluid properties, our models include these parameters. The calculated stresses adjacent to the dike are then related to changes in permeability. Previously, I analyzed a hydrothermal system consisting of a hot dike adjacent to a water-filled porous medium (Craft, 2008). In this study, I only took into account the convection that resulted from heat transferred from the dike and used this to calculate a fluid flux to the Martian surface. Craft 1
Considering that the dike emplacement stresses investigated here increase the permeability of the adjacent regolith, the resulting fluid flux to the surface will increase over those values calculated in the heat transfer only model. The calculated flux values will then be compared to estimated fluid flux requirements for the formation of various morphologic features to determine if hydrothermal systems around dikes could be sources of surface feature formation. The stress and permeability results provide a greater understanding of pore-pressure induced fluid flow and of the dikehydrothermal system overall. a. y x 70 km x 70 km grid 20 km deep Fixed in x direction Fixed in x & y directions Methodology In order to investigate dike emplacement, I employed the finite element program FRANC2D (www.cfg.cornell.edu/software/franc2d_casca.htm). This program was used by Germanovich et al. (2010) previously to model a dike below a Mid-ocean ridge on Earth. The Germanovich et al. (2010) analysis found agreement between where the finite element model predicted the Axial Summit Trough (AST) would reach the seafloor and the actual location. Therefore, FRANC2D provides a reasonable means to predict dike propagation behavior. Figure 1 shows the model set-up. First I placed a 10 km wide x 1 km thick lens-shaped magmatic intrusion 20 km below the surface within a 70 km x 70 km grid. The shape of the lens resembles that of a chamber below a mid-ocean ridge on Earth and is a reasonable shape to assume exists below the surface on Mars. Boundary conditions include fixing the left and right boundaries of the grid in the x (horizontal) direction and fixing the bottom boundary in the y (vertical) direction, while the top boundary remained free. Martian gravity was applied in the negative y direction and the density of basalt was applied to the grid. Lithostatic load, therefore, increases downwards within the grid. To begin the dike emplacement, the magma lens was first pressurized to 1% over the lithostatic load at that depth. I then used Franc2d to assess where the points of greatest tensile stress were along the boundary of the magma lens. One location of maximum stress was found to be near the end of the lens. A crack was initiated there and then FRANC2D was used to propagate the crack to the surface by means of locating the direction of greatest tensile stress. A dike was propagated for a range of Young s modulus values from 10 9 to 10 11 Pa. Also, different gravity values were used to investigate how dike emplacement might change for different planetary bodies. Figure 2 shows an emplaced dike with Martian gravity and a Young s modulus of b. g 10 km 1.01 lithostatic load 1 km Figure 1: Model set-up a. Overall view of model showing location of magma lens and boundary conditions b. Zoomed in view of magma lens showing dimensions and applied loads 10 10 Pa. Once the dike completed its propagation to the surface, I calculated the stresses adjacent to the dike. These stresses are calculated within about 200 m of the dike in order to observe the stress changes within the area where the boundary layer will occur. The boundary layer thickness is known from previous calculations in Craft (2008). The stress differences between initial lithostatic stresses and the resulting stresses after dike emplacement correlate to changes in permeability as described by equations (1) through (4) (Germanovich, personal comm., 2010): K eff = K 0 [1 C * D p /ε] (1) Craft 2
and vertical stresses, s = (1/2)*(sigma_xx+sigma_yy). For both cases, the permeability-stress relationships make the assumption that cracks in the regolith do not interact. Results Figure 2. Completed dike emplacement for Martian gravity and Young s modulus of 10 10 Pa. where K eff = effective permeability, K 0 = permeability before fracturing, C = coefficient dependent on crack geometry (~1), D p = change of the effective stress component perpendicular to the fracture plane, and ε = initial crack aspect ratio. D p is defined as: D p = (s - p) - (s 0 - p 0 )= (s-s 0 ) - (p-p 0 ) (2) where s is the stress component perpendicular to the fracture and p is the fluid pressure in the fracture (s 0 and p 0 being their values before dike injection). If p- p 0 <<s-s 0, then the above formula simplifies to: D p = s-s 0 (3) The stresses calculated adjacent to the dike ranged from about 2 x 10 5 to 2 x 10 6 Pa in the x- direction and 10 8 Pa in the y-direction. Comparing these results to Hanna and Phillips (2006) who obtained average stresses on the order of 4 x 10 7 Pa, the horizontal stresses in my model are about 20 to 200 times smaller. One possible reason for the large discrepancy is that Hanna and Phillips (2006) emplace the dike instantaneously and as a result obtain infinitely large stresses at the beginning. Therefore, their model does not consider the time it takes the dike to propagate to the surface. On the other hand, my model needs to incorporate pore pressures and thermal stresses, which were considered in the Hanna and Phillips (2006) models. These parameters will be considered in future research. Next, the permeability change with the change in stress was calculated using equation (1) for a range of Young s modulus values from 10 9 to 10 11 Pa and for two different crack ratios of ε= 10-2 and 10-3. Table 1 lists the results for the Case 1 fractures. Case 1 fractures are assumed vertical, parallel, and correspond to the existing joint system or dike margins. Case 2 permeability changes, those with random fractures, will be calculated in future work. Table 1: Mars Permeability Change (K eff /K 0 ), Case 1 Compressive stresses are positive, so that for decreasing stresses s < s 0 and D p < 0. Then K > K 0 in (1) and permeability increases as a result of dike injection. Similarly, if p-p 0 >> s-s 0 in (2), then (2) reduces to: D p = -(p-p 0 ) (4) and permeability increases when pressure in the fracture rises (i.e., p > p 0 and D p < 0). Two different cases are considered for the fractures surrounding the emplaced dike: (Case 1) All fractures are parallel, vertical, and correspond to the existing joint system or dike margins (similar to a midocean ridge sheeted dike zone on Earth) and (Case 2) Fractures are random. For Case 1, I calculate the horizontal stress component, sigma_xx (perpendicular to fracture), with FRANC2D and set the stress equal to s, s = sigma_xx. For Case 2 where the fractures are random, I set s equal to the average of the horizontal The change in permeability for all changes in stress is an increase in permeability. For E = 10 11 Pa and ε = 10-2, the permeability only increases slightly, while for E = 10 9 Pa and ε = 10-3 the permeability increases significantly by more than an order of magnitude. Additional calculations were performed to get an idea of how the dike width relates to changes in Young s modulus and also the gravity load. Other planetary bodies besides Mars may have diking occurring and it would be advantageous to know how they differ. Gravity levels of Enceladus (.111 m/s 2 ), Europa (1.314 m/s 2 ), Mars (3.71 m/s 2 ), & Earth (9.8 m/s 2 ) were applied to investigate dike width sensitivity. Table 2 lists the dike widths for the various gravities Craft 3
Table 2: Dike width as a function of Young s modulus and gravity and also for the range of Young s modulus values (10 9 10 11 Pa) under Martian gravity. As shown, dike width increases with increasing Young s modulus and decreases with increasing gravity. The decrease in width for the increasing gravity is likely due to the increase in lithostatic load at a given depth. Also, all the dike widths are smaller than would be expected when comparing to how dikes form on Earth. However, the widths will reach a larger and more reasonable size with consideration of additional parameters during dike propagation. These parameters include the application of an outwards acting load within the dike that represents magma pressure. Further detail is provided in the Future Work section of this paper. Summary Overall, the research performed here provides great insight into diking processes on Mars and how dike emplacement affects the permeability of the surrounding regolith. The physical processes of magma-hydrothermal systems on Mars are similar to those on Earth and can provide mechanisms for transporting water, chemicals, and energy to the surface. Through modeling and use of Mars data, this project provides a more complete picture of dike emplacement coupled with a hydrothermal system and the role of such processes in the formation of observed surface features. The initial results I obtained from evaluating a simplified magma-driven hydrothermal system (Craft, 2008) suggest that these systems could be formation mechanisms for surface morphology on Mars if coupled with additional fluid from diking effects and melting/dissociation of an ice or hydrate layer. With the diking work presented here and future work, greater insight into planetary hydrothermal processes and the possibility of their function as surface morphology formation mechanisms is obtained. Additionally, understanding hydrothermal systems on Mars may help to provide clues in the search for biological habitable zones on other planets. Future Work To increase the accuracy of this model I will incorporate a pressure load within the dike that acts outwards as the dike propagates. This load will depend on the dike size and magma transported into the dike. Dike width will expand due to this pressure and the surrounding stresses will change from those previously calculated. The magma transported from the lens to the dike will also change the pressurization of the magma lens and will be considered. I will also incorporate thermal stresses resulting from the hot dike moving through the porous medium into the model. Next, with the improved model stress results, the corresponding permeability changes for both Case 1 and Case 2 fracture types, will be calculated. The permeability values will then be used to determine the heat and fluid fluxes that will occur at the Martian surface. By assuming that convection next to the hot dike occurs vigorously and within a thin layer, I will apply boundary layer theory to calculate the heat and fluid fluxes. Equations (5) and (6) show the calculations for heat output, Q, and fluid flux, Φ m. Each is integrated over the boundary layer thickness, δ. where Q is the heat output, ρ f is the density of the water, u is the vertical velocity of the fluid, T is the temperature, c p,f is the specific heat of the fluid. Further details on this analysis are described in Craft (2008). Comparing the resulting flux values to estimated flux values for forming surface features on Mars (Kraal, (5) (6) Craft 4
2007), I will determine which features might have been formed by dike driven flow. The boundary layer calculations are steady state, yet the thin dikes obtained will cool relatively rapidly. Therefore, I will also perform numerical simulations using the code FISHES (Lewis and Lowell, 2009) to obtain time dependent simulations of hydrothermal flow in the presence of a cooling dike and will gain a more accurate understanding of the flow over time. In addition to the stress and time-dependency analyses, I plan to also consider a layer of ice or permafrost that may exist just below the surface of Mars in some locations. The convection occurring next to the dike will transfer heat to the overlying ice and will cause melting. Over time this melt layer will thicken and once the Rayleigh number surpasses the critical Rayleigh number, convection will occur in this layer as well. I will also calculate the time required to begin convection and the amount of fluid flux that results. This flux can then also contribute to the surface flow and feature formation. Acknowledgements I would like to thank the Virginia Space Grant Consortium, the Multicultural Opportunities and Academic Program of Virginia Tech, and the Geosciences Department at Virginia Tech for their support of this research. References Baross and Hoffman (1985), Origins of Life, v. 15, 327-345. Craft, K.L. and R.P. Lowell (2010), (in preparation). Craft, K. L. (2008), M.S. thesis, Georgia Institute of Technology, Atlanta, GA. Germanovich et al. (2010), J. Geophys. Res., in press. Hanna, J. and R. Phillips (2006), J. Geophys. Res., v.111, E03003. http://www.cfg.cornell.edu/software/franc2d_casca.htm accessed 2/5/2010. Kraal, E. (2007), Personal Communication. Lewis, K.C. and R.P. Lowell (2009), J. Geophys. Res., 114, B05202, doi:10.1029/2008jb006029. Squyres, S. et al. (2008), Science, 320, 1063 1067. Craft 5