Studying the Thermal and Structural Evolution of Planetary Bodies

Transcription

1 Studying the Thermal and Structural Evolution of Planetary Bodies By MOHAMMADALI KARIMI B.S., Iran University of Science and Technology, 2006 M.S., University of Tehran, 2009 THESIS Submitted as partial fulfillment of the requirements for the degree of Doctor of Philosophy in Earth and Environmental Sciences in the Graduate College of the University of Illinois at Chicago, 2015 Chicago, Illinois Defense Committee: Andrew Dombard, Chair and Advisor Peter Doran Eduard Karpov, Department of Civil and Material Engineering Stefany Sit Carol Stein

2 To my family, especially my dad Asghar and my mom Zohre, who believed in me from the time I was a little boy. ii

3 ACKNOWLEDGMENTS First and foremost, I would like to thank my advisor Andrew Dombard for his endless patience and timeless guidance during the long journey toward my Ph.D. I could not have wished for a better mentor. I would like to extend my thanks to the committee members Peter Doran, Eduard Karpov, Stefany Sit, and Carol Stein for their support and valuable advice. Thanks to Minnie and Edna, who helped me with everything in the EAES Department. Thank you NASA for funding my research during my Ph.D. studies. Thanks to my colleagues in the lab and the department, without whom this work would not have been possible. Thanks to my sisters, Sepideh, Saideh and Saba. And thanks to Eli. iii

4 CONTRIBUTION OF AUTHORS Chapters II, III, and IV represent manuscripts for which I am the primary author. These manuscripts will be published in Icarus journal. My advisor, Dr. Andrew J. Dombard, guided me through the entire time of the research and contributed to all three manuscripts. Also, Stuart J. Robbins contributed to the section C.3 (Age of the Impacts, page 21) of Chapter II. iv

5 PREFACE The motivation behind these studies is to better understand the thermal and structural evolution of planetary bodies in the Solar System. The formatting of this dissertation is as such that Chapter II, Chapter III and Chapter IV are in the form of a publication. Each chapter, in terms of the topic, is an independent research. However, in both Chapter III and Chapter IV, the Methodology is referred to Chapter II. Chapter I is an introduction to the three following chapters. Chapter II is a detailed work on the thermal evolution of Mars by examining the viscoelastic deformation of large impact craters. Chapter III focuses on the thermal state of Venus and its rheological parameters by studying the viscoelastic evolution of Mead basin. Chapter IV is regarding the possible deformation of the south polar craters of Vesta and the potential true polar wander on this asteroid. v

6 TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION... 1 A. Background... 1 B. Studying the Thermal Evolution of Mars, Using the Viscoelastic Deformation of Large Craters... 2 C. Studying Lower Crustal Flow Beneath Mead Basin: Implications for the Thermal History and Rheology of Venus... 3 D. On the Possibility of Viscoelastic Deformation of the Large South Polar Craters and True Polar Wander on the Asteroid Vesta... 4 E. References... 6 II. USING THE VISCOELASTIC RELAXATION OF LARGE IMPACT CRATERS TO STUDY THE THERMAL HISTORY OF MARS... 9 A. Abstract B. Introduction C. Martian Impact Craters Identification of the Craters Analysis and Interpretation of Martian Impact Craters Ages of the Craters D. Methodology Thermal Solution Mechanical Solution E. Results F. Discussion G. Conclusions H. Acknowledgments I. References III. STUDYING LOWER CRUSTAL FLOW BENEATH MEAD BASIN: IMPLICATIONS FOR THE THERMAL HISTORY AND RHEOLOGY OF VENUS A. Abstract B. Introduction C. Mead Basin D. Methodology Initial Shape of the Basin Thermal and Mechanical Simulations Viscous Rheology E. Results F. Discussion G. Conclusion H. References vi

7 CHAPTER TABLE OF CONTENTS (continued) PAGE IV. ON THE POSSIBILITY OF VISCOELASTIC DEFORMATION OF THE LARGE SOUTH POLAR CRATERS AND TRUE POLAR WANDER ON THE ASTEROID VESTA 77 A. Abstract B. Introduction C. Methods Evolution of the South Polar Craters Relaxation of the Rotational Bulge Thermal and Mechanical Simulations Material Properties D. Results Evolution of South Polar Craters Possibility of True Polar Wander E. Discussion F. Conclusions G. Acknowledgment H. Reference V. APPENDICES A. Appendix A B. Appendix B. MARC Crater Relaxation.dat File C. Appendix C. MARS Crater Relaxation.f File VI. VITA vii

8 LIST OF TABLES TABLE PAGE CHAPTER II 1. A list of the candidate craters used in this study A list of the candidate QCDs used in this study Martian geologic epoch age estimates. Taken from Werner and Tanaka (2011) List of the candidate craters and QCDs and appropriate background heat flux for them, for both the deep and shallow initial geometries CHAPTER III 1. Parameters for our finite element simulations Inferred background heat flux for both deep and shallow geometry and various crustal thickness values CHAPTER IV 1. Parameters of our finite element simulations viii

9 LIST OF FIGURES FIGURES PAGE CHAPTER II 1. Estimates of Martian heat flux versus time. Boxes are representative of the Martian heat flux derived from lithosphere modeling of specific features. Curves display the results for models of the thermal evolution of Mars. From Solomon et al. (2005) A topographic map of Mars with the locations of the candidate craters and QCDs. The white digits mark the locations of candidate QCDs, and black digits mark the candidate craters. The digits of impacts are the same that assigned in Table 1 and 2 and increase based on the size of the impacts Plot of the depth versus diameter for the candidate craters. The dashed line is an extrapolation of the depth-diameter curve of small fresh craters of Boyce and Garbeil (2007) (solid line). The dotted line shows an alternate curve constrained by the deepest large crater Degree of center-point compensation versus crater diameter. A degree of compensation equal with 1 means isostatically compensated, while values larger and smaller than 1 are overcompensated and undercompensated. The majority of our candidates are undercompensated, despite generally possessing evidence for surface modification, which suggests lower crustal flow Plot of the initial crustal profile of a crater ~200 km in diameter. The solid line shows the topography of the depression of the impact crater, the dashed line shows the rim and ejecta blanket, and the dotted line shows the mantle topography Simulated topography at the surface and subsurface, versus initial topography. Solid and dotted lines are showing the initial and simulated topography at the surface and crust-mantle boundary Simulated subsurface topography for a crater 340 km in diameter (Basin 17). A simulation with a background heat flux of 50 mw m -2 (thin black line) produces similar mantle topography beneath the basin center as suggested by the crustal thickness model (red line). For comparison, the simulated topographies with background heat fluxes of 45 (dotted line) and 55 (dashed line) mw m -2 are plotted. The bold black line is the initial mantle topography The inferred background heat fluxes for the candidate craters and QCDs. White and black circles mark QCDs and craters, respectively. Large and small circles stand for background heat fluxes of > 75 and < 60 mw m -2, respectively. Medium size circles represent a background heat flux of 60 to 75 mw m Contour map of surface heat flux (in mw m -2 ) of Mars during the Noachian, overlain on the Martian topography ix

10 LIST OF FIGURES (continued) FIGURES PAGE 10. a, b. Heat flux vs. distance from the dichotomy boundary. Positive values of distance stand for impacts in the Southern Highlands, and negative values stand for impacts in the Northern Lowlands. a) results using the deep structure; b) results using the shallow structure. R 2 values for the line fit are both ~ a, b. Ratio of current to initial mantle topography underneath impacts vs. their distance from dichotomy boundary, for deep (a) and shallow (b) structure A demonstration of the deformation at the crust-mantle boundary through time for a crater ~200 km in diameter, with background heat flux of 60 mw m -2. Bold black, dashed, green, red, orange and blue lines show the crust-mantle boundary topography after 0, 10, 30, 70, 100, and 200 Myr, respectively Relaxation of the crust-mantle boundary topography for two cases with transient (thin line) and steady state (dotted line) thermal simulations at 100 Myr. The background heat flux for both of the simulations is 50 mw m Effect of surface temperature on lower crustal flow. The bold-solid lines show the initial topography of the Huygens crater at the surface and at the crust-mantle boundary. The dashed, dotted, and thin lines show the simulated crust-mantle boundary for surface temperatures of 180, 240, and 210 K, respectively. The background heat flux is 50 mw m Differences between the final topography at the crust-mantle boundary for a QCD and crater ~300 km in diameter and with a background heat flow of 55 mw m -2. The solid line represents the initial topography, while the dashed and dotted lines show the simulated topography of the crater and QCD, respectively Ratio of relaxed to initial mantle topography vs. crustal thickness. Background heat flux for all of the simulations is 50 mw m CHAPTER III 1. A schematic that shows the crustal profile of Mead basin. Azimuthally average surface topography is plotted according to Herrick and Sharpton (1996). The mantle topography is notional and not based on crustal thickness models The azimuthally averaged free-air (thin solid), topographic (dotted), and Bouguer (thick solid) gravity anomalies over Mead basin, from a degree-and-order spherical harmonic expansion A display of initial topography at the surface and subsurface for both deep and shallow geometries x

11 FIGURES LIST OF FIGURES (continued) PAGE 4. Examples of our simulated results at the crust-mantle boundary of Mead basin (shallow geometry). Red, red dashed, blue, and blue dashed lines show the results of our simulations with background heat fluxes of 60, 65, 70, and 75 mw m -2, and application of a dry rheology. The black line shows the initial topography at the crust-mantle boundary A demonstration of the simulated results with the background heat flux of 20 mw m -2 after applying a wet rheology. Solid lines represent the initial topography (deep geometry) and dotted lines show the simulated results A comparison between the results of our simulations using dry Maryland and dry Columbia diabase. The solid line shows the initial topography of the crust-mantle boundary, while the dotted and dashed lines show the simulated results with the dry Maryland and dry Columbia diabase. The background heat flux for both of the simulations is 65 mw m CHAPTER IV 1. An image taken during the Dawn mission. The rotational bulge at the equator and flattening at poles are evident. Courtesy of NASA/JPL-Caltech/UCLA/MPS/DLR/IDA The topographic map of the southern hemisphere of the asteroid Vesta. The two large craters, Rheasilvia and Veneneia, are shown on the map with their centers marked with white and red signs, respectively. Courtesy of NASA/JPL-Caltech/UCLA/MPS/DLR/IDA A schematic that demonstrates various stages of our hypothesis related to the potential true polar wander for asteroid Vesta Two examples of a planar and a spherical finite element mesh. The planar mesh has 3 crater radii depth and width. Both spherical and planar meshes have surface and subsurface topography. Both meshes are finer underneath the crater depression and coarser farther from impact. These meshes are notional; the actual meshes use far more elements Crustal profile of the south polar craters considered for the simulation. Crustal thickness is 80 km while depth and rim height are 15 and 7 km, respectively An example of a spherical mesh used for testing the potential relaxation of a rotational bulge. The equatorial radius of 285 km is 60 km larger than the polar radius. The core has the constant radius of 110 km Topography profile of Rheasilvia and simulated results. Bold line demonstrates the initial surface topography of Rheasilvia. Thin line shows the simulated topography for background heat flux of 25 mw m 2 and thermal conductivity of 2.5 W m -1 K -1, while dotted line shows the simulated topography for the background heat flux of 30 mw m 2 and thermal conductivity of 1 W m -1 K -1. In this simulation, mesh is planar, crustal thickness is 45 km and basin is undercompensated A demonstration of rotational bulge relaxation (percent) versus applied heat flux xi

12 SUMMARY In the three main chapters (II, III and IV) of this thesis, the focus is on better understanding of the thermal and structural evolution of two neighboring planets, Mars and Venus, and the second most massive asteroid in the Solar System, Vesta. Chapter II: We have investigated the thermal history of Mars by modeling the viscoelastic deformation of large craters and Quasi Circular Depressions (QCDs) in the Southern Highlands and Northern Lowlands, respectively. The benefit of this study is the global distribution of the modeled features (craters and QCDs) that cover a large portion of Mars, yielding a thermal map that is less regionally biased relative to other studies that model specific features (e.g., rift flanks, volcanoes, etc.) that are geographically clustered, sparse, or both. The results of this study demonstrate a higher background heat flux for the Northern Lowlands relative to the Southern Highlands at least through the Noachian epoch. This observation suggests a thermal fingerprint to whatever process formed the hemispherical Highlands/Lowlands dichotomy that lasted for at least several hundred million years. Chapter III: Unlike Mars, Venus has few large craters. Thus, we have modeled the viscoelastic deformation of Mead Crater, Venus, in order to put constraints on the background heat flux, and to determine an appropriate crustal and mantle rheology of our sister planet. Mead appears to have undergone significant lower crustal flow, and this study suggests a higher background heat flux than predicted by global thermal models; though with the limited spatial sampling, it is unknown if this higher heat flow is simply regional variation. In addition, this study shows that the Venus s crust and mantle seem to be dry relative to those of the Earth. Chapter IV: The second most massive asteroid in the solar system has a highly oblate shape, whose formation likely requires a warm asteroid with a compliant lithosphere, at least early in the asteroid s history. In addition, there are two large (diameters comparable to Vesta s radius) craters at the asteroid s south pole that are slightly shallow and with tall central peaks, similar to relaxed craters on some icy satellites. Further, the large craters locations near the south pole suggest they have served as loads that produced True Polar Wander, driving the craters towards the pole. Here, we model the possible viscoelastic deformation of south polar craters and test the feasibility of True Polar Wander. The results suggest that the somewhat unusual shapes of the basins are a product of a planetary scale impact and not of relaxation, and that true polar wander is not a likely outcome for these craters. xii

13 CHAPTER I I. INTRODUCTION A. Background A planetary body s transfer of internal heat is the engine that powers tectonic processes, formation of volcanoes, and many other geologic activities, and as such is of utmost importance. Investigating the thermal state of our planet Earth, as opposed to other planetary bodies, is simpler due to the abundance of data and the possibility of direct measurement (e.g., boreholes, surface heat flow measurements, etc. [Hagermann, 2007]). As of today, there are only two non- Earth in situ heat flow measurements, conducted during the Apollo 15 and 17 missions on the lunar surface. Additionally, the InSight mission is scheduled to perform measurement on the surface of Mars in 2016 (Banerdt et al., 2012). The obtained measurements, however, are extremely limited geographically and could be subject to error. Moreover, the process of performing in situ surface heat flow measurements on other planets is both expensive and technologically challenging (Wieczorek, 2007). Therefore, an indirect approach is generally employed to study the thermal evolution of planetary bodies. A common approach is geodynamic modeling of the lithosphere -- the rigid outermost layer of a planetary body. Since the thickness of the lithosphere, and hence how it deforms, is highly sensitive to the thermal state of a planet, lithospheric modeling allows us to probe into the thermal evolution of a planet. Multiple studies over decades have employed geodynamic modeling to unravel the processes behind planetary evolution by focusing on various geologic features such as volcano induced flexure, wrinkle ridges, etc. (e.g., Comer et al., 1985; Anderson and Grimm, 1998; McGovern et al., 2001, 2004; Montesi and Zuber, 2003; Dombard and Phillips, 2010). 1

14 2 For my dissertation, I focus on impact craters -- geologic features that are ubiquitous throughout the Solar System and geographically widespread. I explore the lithospheric deformation associated with large impact craters, and, thus, learn about the corresponding thermal state of a planetary body. Multiple past studies showed significant mantle uplift underneath large craters on terrestrial worlds that partially compensates the surface basin, likely formed by collapse of a transient crater during the impact event (e.g., Melosh, 1989; Wieczorek and Phillips, 1999; Neumann et al., 2004, Namiki et al., 2009). The lateral pressure gradient induced by this crustal thickness variation could, when coupled with a sufficiently high background heat flux and a sufficiently thick crust, induce lower crustal flow underneath that basin (e.g., Nimmo and Stevenson, 2001). This lower crustal flow reduces the topography on the crust-mantle boundary. Due to the loss of buoyancy, lithosphere (by default thinner than the crust if lower crustal flow is operating) must not fully support the surface topography and flexes upward in response. As a result, the basin becomes shallower. Development of lower crustal flow and the subsequent lithospheric deformation are very sensitive to the background heat flux of a planet. By exploring this viscoelastic deformation, I am able to further our understanding of the thermal evolution of planetary bodies where this phenomenon may have occurred: Mars, Venus, and asteroid Vesta. B. Studying the Thermal Evolution of Mars, Using the Viscoelastic Deformation of Large Craters Chapter II focuses on Mars. Here, I constrain the thermal state in the Southern Highlands and the Northern Lowlands by examining the viscoelastic deformation of large craters and Quasi- Circular Depressions (QCDs), presumably buried impact craters. Much research has been done

15 3 on the thermal history of Mars, yet most studies have investigated specific geologic features at specific locations such as volcanoes on Tharsis, rift systems, the crustal dichotomy boundary, and the polar caps. In addition, since most previous studies are limited to the Southern Highlands of Mars, they do not allow for a global analysis of Martian thermal evolution. In this study, however, I take advantage of large impacts craters and QCDs in the range of ~ km in diameter, whose locations provide a more equal sampling distribution over the surface of Mars. The ages of the impact craters are constrained by crater counts performed by a co-author. I then use the finite element method to simulation lower crustal flow to determine values for the background heat flux that allows for the relaxation of crust-mantle boundary topography to the current state estimated from existing models of crustal thickness derived from analysis of the gravity and topography of Mars. By combining the heat flux results, I construct a thermal map of Mars that has a better spatial coverage than previously available and find a previously undiscovered regional variation in surface heat flow associated with the hemispherical crustal dichotomy of Mars. C. Studying Lower Crustal Flow Beneath Mead Basin: Implications for the Thermal History and Rheology of Venus Chapter III is dedicated to the thermal history of Venus and the rheological behavior of its crust and mantle. Unlike the surfaces of the Moon and Mars, the surface of our sister planet lacks numerous large craters. I explore the largest crater on Venus, Mead, with a diameter of 270 km (Herrick and Sharpton, 1996), because Mead is the only crater on Venus that is resolved in existing gravity models. Using the latest gravity model of Venus, I determine the peak gravity anomaly over Mead basin. Analysis of the gravity model shows that most of the anomaly is

16 4 dominated by the surface topography, indicating that the mantle uplift beneath Mead basin is small. This finding is consistent with previous studies regarding the crustal thickness of Venus (e.g., Banerdt et al., 1994). I hypothesize that the lower crustal flow likely played a significant role in the relaxation of mantle uplift underneath Mead. Therefore, I simulate the viscoelastic deformation of Mead basin to investigate the role of the lower crustal flow in deformation of the surface and subsurface topography, and constrain the background heat flux in the vicinity of Mead. While this study focuses only on one crater and its results are not global, it can, nevertheless, place constraints on previous estimations of the thermal state. Furthermore, I test various viscous creep rheology parameters of hydrous and anhydrous materials, and my results indicate a relatively low water content of the crust and mantle of Venus. D. On the Possibility of Viscoelastic Deformation of the Large South Polar Craters and True Polar Wander on the Asteroid Vesta The focus of Chapter IV is on the dwarf planet Vesta, the second largest asteroid in the Solar System and a world with a prominent rotational bulge. NASA s Dawn mission revealed the presence of two large craters in the south polar region of Vesta (Russell et al., 2012), with the larger crater Rheasilvia (diameter of ~500 km) superimposed on the smaller crater, Veneneia (diameter of ~ 400 km) (Schenk et al., 2012). These craters appear to be anomalously shallow, while the high standing central peak of Rheasilvia reaches the elevation of the surrounding terrain. Such morphology has been observed on strongly relaxed craters of some icy satellites of Saturn (e.g., Dombard et al., 2007; White et al., 2013). In the first section, I examine the evolution of the south polar craters of Vesta and investigate the possibility of viscoelastic deformation of the surface topography to the current state. This task allows me to determine

17 5 whether the shallowness and the large central peak are an outcome of the post-impact viscoelastic deformation of the south polar craters or the result of a planetary scale impact, with my results suggesting the latter. The diameters of these large south polar craters are comparable to that of the asteroid, and both craters are located in the vicinity of the south pole. The probability of two large impacts occurring at near the south pole is less than 10%. In the second part of this study, I explore the possibility of the occurrence of these impacts nearer to the equator followed by true polar wander. Two large impacts could place a large negative load on the lithosphere, inducing a torque and reorienting the body to the current position (Melosh, 1980; Matsuyama et al., 2006). In this case, any old rotational bulge would need to relax and a new one would need to form. I test the possibility of whether the lithosphere is weak enough to permit this relaxation. Like in the first part, I find that Vesta s lithosphere is too strong to allow this predicted deformation under any reasonable thermal state. As unlikely as it seems, these large basins appear to have formed near the south pole.

18 6 E. References Anderson, S., and Grimm, R. E. (1998). Rift processes at the Valles Marineris, Mars: Constraints from gravity on necking and rate dependent strength evolution. Journal of Geophysical Research: Planets ( ), 103(E5), doi: /98je Banerdt, W., Konopliv, A., Rappaport, N., Sjogren, W., Grimm, R., and Ford, P. (1994). The isostatic state of Mead crater. Icarus, 112(1), doi: /icar Banerdt, W., Smrekar, S., Alkalai, L., Hoffman, T., Warwick, R., Hurst, K., et al. (2012). INSIGHT: An integrated exploration of the interior of Mars. Paper presented at the Lunar and Planetary Institute Science Conference Abstracts, 43. pp Comer, R. P., Solomon, S. C., and Head, J. W. (1985). Mars: Thickness of the lithosphere from the tectonic response to volcanic loads. Reviews of Geophysics, 23(1), doi: /rg023i001p Dombard, A., and Phillips, R. (2010). Viscoelastic finite-element simulations of the flexure under the north polar cap of mars. Paper presented at the Lunar and Planetary Science Conference, 41. pp Dombard, A. J., Bray, V., Collins, G., Schenk, P., and Turtle, E. (2007). Relaxation and the formation of prominent central peaks in large craters on the icy satellites of Saturn. Paper presented at the Bulletin of the American Astronomical Society, 39. pp Hagermann, A. (2005). Planetary heat flow measurements. Philosophical Transactions.Series A, Mathematical, Physical, and Engineering Sciences, 363(1837), doi: /rsta Herrick, R. R., and Sharpton, V. L. (1996). Geologic history of the Mead impact basin, Venus. Geology, 24(1), doi: / (1996)024<0011:ghotmi>2.3.co;2. Matsuyama, I., Mitrovica, J., Manga, M., Perron, J., and Richards, M. (2006). Rotational stability of dynamic planets with elastic lithospheres. Journal of Geophysical Research: Planets ( ), 111(E2). McGovern, P. J., Solomon, S. C., Head, J. W., Smith, D. E., Zuber, M. T., and Neumann, G. A. (2001). Extension and uplift at Alba Patera, Mars: Insights from MOLA observations and loading models. Journal of Geophysical Research: Planets ( ), 106(E10), doi: /2000je

19 7 McGovern, P. J., Solomon, S. C., Smith, D. E., Zuber, M. T., Simons, M., Wieczorek, M. A., et al. (2002). Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution. Journal of Geophysical Research: Planets ( ), 107(E12)(5136) doi: /2002je McGovern, P. J., Solomon, S. C., Smith, D. E., Zuber, M. T., Simons, M., Wieczorek, M. A., et al. (2004). E07007-correction to" localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution"(doi /2004JE002286). Journal of Geophysical Research-Part E-Planets, 109(7) doi: /2004je Melosh, H. J. (1989). Impact cratering: A geologic process. Research Supported by NASA. New York, Oxford University Press (Oxford Monographs on Geology and Geophysics, no.11), 1989, 253 p., 1. Melosh, H. (1980). Tectonic patterns on a reoriented planet: Mars. Icarus, 44(3), doi: / (80) Montési, L. G., and Zuber, M. T. (2003). Clues to the lithospheric structure of mars from wrinkle ridge sets and localization instability. Journal of Geophysical Research: Planets ( ), 108, 5048(E6) doi: /2002je Namiki, N., Iwata, T., Matsumoto, K., Hanada, H., Noda, H., Goossens, S., et al. (2009). Farside gravity field of the Moon from four-way doppler measurements of SELENE (kaguya). Science, 323(5916), doi: /science Neumann, G., Zuber, M., Wieczorek, M., McGovern, P., Lemoine, F., and Smith, D. (2004). Crustal structure of Mars from gravity and topography. Journal of Geophysical Research: Planets ( ), 109(E08002) doi: /2004je Nimmo, F., and Stevenson, D. (2001). Estimates of Martian crustal thickness from viscous relaxation of topography. Journal of Geophysical Research: Planets ( ), 106(E3), Russell, C. T., Raymond, C. A., Coradini, A., McSween, H. Y., Zuber, M. T., Nathues, A., et al. (2012). Dawn at Vesta: Testing the protoplanetary paradigm. Science (New York, N.Y.), 336(6082), doi: /science Schenk, P., O'Brien, D. P., Marchi, S., Gaskell, R., Preusker, F., Roatsch, T., et al. (2012). The geologically recent giant impact basins at Vesta's south pole. Science (New York, N.Y.), 336(6082), doi: /science

20 8 White, O. L., Schenk, P. M., and Dombard, A. J. (2013). Impact basin relaxation on Rhea and Iapetus and relation to past heat flow. Icarus, 223(2), Wieczorek, M. A. (2007). The gravity and topography of the terrestrial planets. Treatise on Geophysics ,, doi: /j.icarus Wieczorek, M. A., and Phillips, R. J. (1999). Lunar multiring basins and the cratering process. Icarus, 139(2), doi: /icar

21 CHAPTER II II. USING THE VISCOELASTIC RELAXATION OF LARGE IMPACT CRATERS TO STUDY THE THERMAL HISTORY OF MARS Chapter II will be published in Icarus as: Mohammadali Karimi 1, Andrew J. Dombard 1, Debra L. Buczkowski 2, Stuart J. Robbins 3, Rebecca M. Williams The Department of Earth and Environmental Sciences (MC-186), University of Illinois at Chicago, 845 W. Taylor St., Chicago, IL 60607, USA. 2 - Planetary Exploration Group, Space Department, Johns Hopkins University Applied Physics Laboratory, MS 200-W230, Johns Hopkins Road, Laurel, MD 20723, USA. 3 - Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80309, USA. 4 - Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, AZ 85719, USA. 9

22 10 A. Abstract We simulate the long-term deformation of Martian craters and investigate the role of lower crustal flow in the evolution of surface and subsurface topography. Using the finite element method and a viscoelastic rheological model, we model the deformation of more than 30 large craters and Quasi-Circular Depressions (QCDs), in the diameter range of ~ km, in both the Northern Lowlands and Southern Highlands. We determine the most appropriate background heat fluxes that produce the current topography beneath the impacts at the crust-mantle boundary. Our study shows that a higher background heat flux leads to more relaxation at the surface and subsurface. By applying various viscous creep parameters for hydrous and anhydrous rheologies, we demonstrate that Mars s interior is wet to a certain degree, which is consistent with other estimates. Since craters and QCDs are distributed fairly equal on the surface of the Red Planet, this study provides a less regionally biased picture of the thermal history of early Mars. Based on our results, the ancient average background heat flux in the Northern Lowlands was higher than that of the Southern Highlands, which could indicate that whatever process formed the crustal dichotomy had a thermal signature at least through the middle Noachian.

23 11 B. Introduction Many previous studies of Mars have looked at the thermal history of the planet (e.g., Comer et al., 1985; Anderson and Grimm, 1998; McGovern et al., 2001, 2002; Montesi and Zuber, 2003; Watters and McGovern, 2006; Mohit and Phillips, 2006; Dombard and Phillips, 2010) because heat is the engine that drives a planet s geological evolution. There are, however, issues associated with these previous studies that may limit their applicability. These studies are limited to a few specific geographical locations (e.g., the Tharsis Montes, Vallis Marinaris, etc.); therefore, there is limited information about any regional variations of the Martian heat flux. For instance, it is hard to determine systematic differences between various locations of Mars such as the Northern Lowlands, the Southern Highlands, under the polar caps, and Tharsis. Thus, any conclusions of thermal history derived from these studies may be regionally biased and may not capture the background thermal state of the planet. Figure 1 shows a compilation of the previous studies and displays model estimates of Martian heat flux versus time. There exists the potential that past geodynamically determined estimates of heat flux (boxes in the figure) might not be regionally representative, and these estimates (and their associated errors) cannot reliably distinguish between thermal models of Mars. There has never been an in situ measurement of Martian heat flux on its surface (though the InSight mission will change that for at least one place on Mars [Banerdt, 2012]); therefore, indirect measurement/modeling is key to revealing the thermal history of Mars. Here, we model the lithospheric deformation associated with large ancient Martian impact features, which thus may provide a geographically less biased tracer of the thermal history of Mars. The work of Neumann et al. (2004) on Martian crustal thickness revealed that the mantle is uplifted beneath many large craters, likely as a result of the collapse of the transient crater

24 12 immediately after the impact (e.g., Melosh, 1989; Wieczorek and Phillips, 1999). Sufficiently thick crust and high temperatures in the lower crust plus the pressure gradient generated by the crustal thickness variations may induce lower crustal flow (e.g., Nimmo and Stevenson, 2001; Mohit and Phillips, 2006, 2007; Karimi and Dombard, 2011). The lower crustal flow then moves the material from outside to inside underneath the crater depression and serves to reduce the topography at the crust-mantle boundary. Due to the loss of the isostatic support, the buoyant support of the surface topography transfers to the lithosphere, which results in an upwards flexural response and shallowing of the crater. Indeed, previous studies have shown the major role of the viscoelastic relaxation on the evolution of lunar basins (e.g., Neumann et al., 1996; Mohit and Phillips, 2006), as well as on Mars (Mohit and Phillips, 2007). There are shortcomings with these initial analyses, however. For instance, Dombard et al. (2007) demonstrated the important role of the remnant impact heat in the deformation of large craters. Furthermore, the ages of the studied basins were not well constrained. In this study, we constrain the heat flux of the Southern Highlands and Northern Lowlands by simulating the lower crustal flow beneath large craters and Quasi-Circular-Depressions (QCDs) (presumably buried craters [e.g., Watters et al., 2006; Frey, 2006]). We employ finite element analysis with a non-linear viscoelastic rheology to simulate the deformation of impact craters at the surface and within the subsurface, and include the effect of remnant impact heat on the local viscosity. Consequently, we are able to place constraints on the thermal evolution of Mars. Since Martian impact craters have a better spatial distribution over the surface of the planet than other isolated geological features, this probe provides a more complete sampling of the thermal history of Mars than previous studies.

25 13 Figure 1. Estimates of Martian heat flux versus time. Boxes are representative of the Martian heat flux derived from lithosphere modeling of specific features. Curves display the results for models of the thermal evolution of Mars. From Solomon et al. (2005).

26 14 C. Martian Impact Craters 1. Identification of the Craters We consider craters and QCDs in the range of ~200 to 500 km in diameter. The lower limit is dictated by the resolution of the crustal thickness model of Neumann et al. (2004) and (2008), which uses spherical harmonic representations of the gravity and topography of Mars. The MGS95J gravity model of Mars contains spherical harmonic coefficients up to degree and order 95 (newer versions of gravity models contain coefficients up to degree and order 110); however, the model is only robust to spherical harmonics degree and order 75. Therefore, we limit the smaller end of the craters size to ~200 km, which is intermediate between the full wavelength and half wavelength resolutions of a degree 75 spherical harmonics expansion on Mars. (The gravity and topography models of Mars used in this study are currently available and archived at NASA s Planetary Data System [ Several considerations limit the large end of the crater size range. First, we limit the candidates to those with relatively simple histories. For example, the very large Martian basins (e.g., Hellas and Argyre) have gone through many processes (e.g., volcanic infilling, sedimentation, or both) and consequently have complex histories (e.g., Dohm et al., 2015). In addition, the lower crustal flow that we simulate here is a function of the flow channel thickness relative to the horizontal length scales (e.g., Nimmo and Stevenson, 2001). Since the thickness of the channel is relatively small for very large craters, the role of the lower crustal flow is less significant for craters larger than ~500 km. Furthermore, the planar approximation used in our simulations would begin to break down for diameters larger than ~500 km, necessitating a more complex simulation that includes planetary curvature. Consequently, we constrain the size of our candidate craters to ~ km.

27 15 Impact craters of this scale, with an obvious surface expression in imagery, are virtually absent in the Northern Lowlands so we are restricted to QCDs. By using Mars Orbiter Laser Altimeter (MOLA) data, it is feasible to characterize surface topography and distinguish even subtle topographic features on the surface. Using MOLA data, many QCDs, which cannot be observed in images, have been discovered in the Northern Lowlands and these are generally interpreted to likely be buried impact craters (Frey et al., 1999; Frey et al., 2002; Frey, 2003; Buczkowski et al., 2005a,b). Thus, we extract craters and QCDs within the size range of ~ km from an existing crater database (Barlow, 1988) and a QCD database, although not every impact will be a candidate for our study. Among the impacts in the desired size, we select those craters and QCDs that show definitive mantle uplift centered beneath the surface depression, by taking azimuthally averaged profiles of topography on the crust-mantle boundary from the marscrust3 model of Neumann et al. (2004, 2008). Consequently, we find 23 craters and 8 QCDs that meet our requirements. Figure 2 shows the locations of the candidate craters and QCDs. More detailed information on the candidate craters and QCDs is listed in Tables 1 and 2.

28 16 Figure 2. A topographic map of Mars with the locations of the candidate craters and QCDs. The white digits mark the locations of candidate QCDs, and black digits mark the candidate craters. The digits of impacts are the same that assigned in Table 1 and 2 and increase based on the size of the impacts.

29 17 Table 1. A list of the candidate craters used in this study. Latitude Longitude Impact # Diameter (Km) Current Depth* (m) Impact Age (Hartmann) Ga Impact Age (Neukum) Ga Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable Not Datable * Top of the rim to the bottom of the floor Table 2. A list of the candidate QCDs used in this study. Latitude Longitude Impact # Diameter (Km)

30 18 2. Analysis and Interpretation of Martian Impact Craters Our simulations require knowledge of the initial shape of the craters. Studies of the geometric properties of smaller fresh craters (e.g., Boyce and Garbeil, 2007; Garvin et al., 2003) have provided information regarding the initial shape of craters at the time of formation (e.g., initial depth and rim height as a function of diameter). All large craters of the size used in this study have been modified to some degree, so fresh craters to constrain initial shape are lacking. Constraints based on smaller craters can be extrapolated, however these extrapolations could be different from the real initial shape of the basins. Having slightly different initial shapes for large craters can modify the final results of our modeling. To mitigate this uncertainty, we considered a range of initial shapes. Figure 3 shows the depths of the candidate craters versus their diameter. We extrapolate (dashed line) the depth-diameter curve of smaller fresh craters of Boyce and Garbeil (2007) (solid line). All of our craters are shallower than predicted by this extrapolation. This depth-diameter curve (Boyce and Garbeil, 2007), however, was based on craters smaller than 50 km in diameter. It is thus conceivable that large craters are inherently shallower than this prediction. At a minimum, the initial depths of our craters will be constrained by the depth of the deepest candidate crater, Newton (dotted line in Fig. 3). As is clear from either curve, the candidate craters all appear much shallower than expected. This apparent alteration could result from either post-impact surficial processes (e.g., surface infilling), the effects of the lower crustal flow, or both. Indeed, Mars has undergone significant surface modification such as fluvial/aeolian erosion and deposition of sediments/volcanic materials since the Noachian era (e.g., Irwin et al., 2013; Head et al., 2001), and most of our craters are fairly degraded. A significant role for lower crustal flow, however, is indicated by consideration of the degree of isostatic compensation of the craters. Figure 4 presents the degree

31 19 of compensation at the crater center versus diameter, based on the current depth versus the current crust-mantle boundary topography of the candidate craters in our study and assuming a crustal density of 2900 kg m -3 and a mantle density of 3500 kg m -3 (Zuber, 2001). Various studies (e.g., Namiki et al., 2009; Konopliv et al., 2001) suggested that the formation of a large crater on a terrestrial planet should yield a final crater largely compensated in its central regions (i.e., sufficient excess mass from an uplifted dense mantle to compensate the missing mass in the surface topography). If surface infilling was the primary cause for the shallowness of these craters (Fig. 3), without any significant change of the topography on the crust-mantle boundary, then the craters should appear as overcompensated. Our observation, however, indicates that our candidate craters are mostly undercompensated (Fig. 4), which strongly implicates lower crustal flow as having a major role in the evolution of the craters. Figure 4 does show three overcompensated craters, but further investigation shows that their surfaces are heavily eroded. This overcompensation is likely due to the surface infilling/erosion with modest amounts of lower crustal flow.

32 20 10 Depth (km) Diameter (km) Figure 3. Plot of the depth versus diameter for the candidate craters. The dashed line is an extrapolation of the depth-diameter curve of small fresh craters of Boyce and Garbeil (2007) (solid line). The dotted line shows an alternate curve constrained by the deepest large crater Degree of compensation Diameter (km) Figure 4. Degree of center-point compensation versus crater diameter. A degree of compensation equal with 1 means isostatically compensated, while values larger and smaller than 1 are overcompensated and

33 21 undercompensated. The majority of our candidates are undercompensated, despite generally possessing evidence for surface modification, which suggests lower crustal flow. 3. Ages of the Craters We employ superposed crater mapping techniques to determine the ages of our candidate craters. The most original-appearing and high-standing regions of these crater rims were mapped in THEMIS Daytime IR (Christensen, 2004; Edwards et al., 2011) and MOLA gridded elevation data (Smith et al. 2001). Superimposed craters down to 1 km in diameter are then extracted from a global Mars crater database (Robbins and Hynek, 2012). Standard crater size-frequency distributions are then created. Regions of each size-frequency distribution that best parallel the two main published isochron systems are then fit, and the ages are calculated (Neukum et al., 2001; Hartmann, 2005; based on the chronology of Ivanov 2001). (For more details on this method, see Robbins et al ) Note that using the new chronology of Robbins (2014) would not significantly change the conclusion of this work because most of these large craters formed where Robbins (2014) agrees to within ~200 Ma of Ivanov (2001). Application of this method allows constraints on the impact age of the candidate craters. According to the Neukum isochron, the age of the impacts are in the range of Early through Mid Noachian. The Hartmann isochron yields an impact age of Early Noachian through Early Hesperian. Both impact-age ranges cover the early eras of Martian history (Table 3). The resultant ages span a fairly limited range of ~0.5 Gyr, with no large candidate craters having formed in the last 3.5 Gyr of Martian history.

34 22 Table 3. Martian geologic epoch age estimates. Taken from Werner and Tanaka (2011), Robbins et al (2013). Epoch Time (Ga), a Time (Ga), b Early Noachian >3.97 > 3.96 Middle Noachian Late Noachian Early Hesperian a Ivanov (2001) choronology used in Neukum system. b Hartmann (2005) chronology. The absolute model ages of QCDs cannot be determined via the crater mapping techniques in Robbins et al. (2013). Because of heavy surficial processes and long term burial, the rims of buried craters are not clear; therefore, absolute age of original impacts cannot be modeled. Frey (2008) has employed N(50) and larger-crater model ages to date large QCDs, but those QCDs are not used here because they greatly exceed our size range. Since QCDs have similar size and spatial distribution as the craters, their originating impacts can be considered to have comparable ages as craters (Frey, 2006). Studies show that the Northern Lowlands of Mars were buried during the early Noachian or even in an earlier epoch before ~4 Ga (e.g., Frey, 2006). Consequently, a minimum impact age of Early Noachian for the QCDs seems reasonable.

35 23 D. Methodology In this study, we use the commercially available MSC Marc-Mentat finite element package ( to model the viscoelastic relaxation of large Martian craters. Our goal is to determine the range of heat fluxes necessary to permit sufficient lower crustal flow to form the current shape of the crust-mantle boundary beneath candidate craters and QCDs. We employ a two-layer axisymmetric mesh of one radial plane to simulate the surface and subsurface deformation. The basic structure of our mesh is formed of 4-noded quadrilateral elements. To minimize the effects of the far edge boundaries on the crater evolution, the side and bottom boundaries are placed 3 crater radii away (e.g., Dombard and McKinnon, 2006); we have tested to insure that our results are not sensitive to edge effects at these far boundaries. Following Dombard and McKinnon (2006), we use a simplified shape for the surface topography, with a 4 th order polynomial depression and an ejecta blanket exterior to the rim following an inverse 3 rd power law. To determine the shape of the initial uplifted crust-mantle boundary, we implement a Gaussian-like exponential function ( exp[-r 5 ], where r is radius). This function produces a smooth geometric transition between mantle uplift (underneath crater depression) and surrounding flat mantle. We assume the central part of the craters at the surface and subsurface to be in the isostatic equilibrium. The uplifted crust-mantle boundary, however, is narrower than the width of the crater at the surface (e.g., Dombard et al., 2013) and lacks the rim and ejecta topography (Fig. 5). We consider the width of the mantle uplift at its half maximum to be about ~50% of the crater radius. The gravitational signature of non-mare mascons on the Moon shows that the width of the large positive central free-air gravity anomaly surrounded by a negative free-air gravity anomaly is smaller than the size of the crater (Category C mascons in Dombard et al., 2013). Mantle uplift (beneath a large crater) is primarily caused by the isostatic response of

36 24 the crust-mantle boundary to the collapsing transient crater, which is narrower than the final crater structure. Post-impact processes affecting the transient crater (e.g., inward and upward collapse) lead to a larger and wider (than the width of mantle uplift) surface basin (Dombard et al., 2013).

37 Depth (km) Distance (km) Figure 5. Plot of the initial crustal profile of a crater ~200 km in diameter. The solid line shows the topography of the depression of the impact crater, the dashed line shows the rim and ejecta blanket, and the dotted line shows the mantle topography.

38 26 The results of Garvin et al. (2003) constrained the initial height of the rim. To determine the initial depth (top of the rim to the floor) of these craters, we use a shallow and deep extrapolation of the depth-diameter curve of Boyce and Garbeil (2007) (see Fig. 3). Because of the uncertainty in the initial depths of large craters on Mars, using 2 initial depths enables us to constrain upper and lower limits of the heat flux for each crater. For the shape of the candidate QCDs, we apply a flat surface, with no topography, while the subsurface topography is identical to that of a same sized crater, using both the shallow and deep values. (Initial crustal profiles of all candidate craters and QCDs, for both deep and shallow geometries, are provided in the Appendix A.) In these simulations, the average crustal thickness for craters in the Southern Highlands is 50 km (Zuber, 2001). Average crustal thickness is thinner in the Northern Lowlands (~35-40 km; Zuber, 2001; Zuber et al., 2000). In our simulations however, we consider a background crustal thickness of 45 km for QCDs, slightly thicker than the average, because of the proximity of the candidate QCDs to the crustal dichotomy boundary. Furthermore, we ran a few test-simulations to investigate the sensitivity of the crater deformation to the background crustal thickness. We assume a crustal density of 2900 kg m -3 and a mantle density of 3500 kg m -3 (Zuber, 2001). These crustal and mantle domains are subdivided into finite element meshes that typically have of order of 10 4 elements. In our mesh design, a higher resolution (fine mesh) is applied to the near basin, while farther from the basin the resolution decreases (coarse mesh). We have confirmed that the results are not sensitive to the exact mesh geometry. With these meshes in hand, we first perform a thermal simulation and input its results as the initial state into a mechanical simulation.

39 27 1. Thermal Solution Since temperature ultimately controls the viscosity structure within the subsurface, we need to know the thermal state of the system. Here we assume that the thermal system is timeindependent; therefore in our study, we do not consider the change of heat flux due to secular cooling of the planet or other temporal effects on the temperature structure. We perform a steady state thermal finite element simulation, finding the conductive equilibrium between a specified basal heat flux and an average surface temperature (heat fluxes on the sides are locked at zero). We assume that the surface temperature is constant and equal with the current average surface temperatures of 210 K, though we test a range of values to examine the effect of this assumed value. The thermal conductivity of the crust and mantle are 2.5 and 4 W m -1 K -1, respectively. In this simulation, we also approximate the thermal effect of remnant impact heat. During a crater s formation, impact heat raises the temperature of the subsurface under the impact site and can result in substantial melting of the near surface material. Consequently, our simulations begin immediately after solidification of any melt (up to ~10 kyr after the impact; Spray and Thompson, 2008), but before substantial dissipation of the thermal anomaly. To approximate the impact heat in our simulations, we constrain the temperature of the uplifted nodes at the crustmantle boundary beneath the craters to that of the undeflected crust-mantle boundary far from impact, yielding uplifted isotherms underneath the crater that serve as a proxy for impact heat. While we run steady state simulations, the thermal system is not steady state. In reality, the thermal state changes through dissipation of the impact heat and through secular cooling of the planet. The background heat flux of Mars will change over a characteristic time scale of order 100 Myr (cf. Fig. 1). Additionally, diffusion of an impact thermal anomaly buried tens of kilometers deep also occurs over comparable time scales, assuming a diffusivity of 10-6 m 2 s -1.

40 28 As will be demonstrated below, the majority of the deformation occurs relatively early (time scale of up to a few tens of Myr) when driving stresses are highest, so this steady-state assumption suffices. 2. Mechanical Solution For the two sides of the mesh free-slip boundary conditions are applied, whereas the nodes at the bottom of the mesh are fixed. A vertical gravitational body force with an acceleration of 3.7 m s -2 (Mars surface gravity) is applied to the entire mesh. The application of gravity ultimately provides the driving force for the lower crustal flow, as the uplifted crust-mantle boundary (and the surface) seeks to achieve gravitational equilibrium (i.e., a flat interface). In our simulations, we employ a viscoelastic rheology with no plasticity (a continuum approximation for brittle failure). The elastic parameters are selected to be typical values for crustal and mantle materials (e.g., Turcotte and Schubert, 2014). The nominal elastic Young s moduli for the crust and mantle are 65 and 140 GPa, respectively. The Poisson s ratios for both are At this value of the Poisson s ratio, the material is compressible, and the application of a gravitational load will result in self-compaction, with large deviatoric stresses that grow with depth. In order to avoid this gravitational self-compaction, we set the Poisson s ratio to , very close to incompressibility limit of 0.5, and we drop the Young s moduli by a factor of 0.8 in order to maintain the flexural rigidity of a lithosphere. Simulations utilizing this incompressibility trick were previously shown to be nearly identical to simulations with a compressible viscoelastic material (cf. Dombard et al., 2007). The viscous creep rheology of the crust follows the experimentally determined flow parameters for dislocation creep in a wet Maryland diabase (Caristan, 1982). We use a wet rheology, as opposed to a dry one, because of significant and building evidence for water-related activity on early Mars (e.g., Head et al., 2001;

41 29 Dohm et al., 2009). For the creep rheology of the mantle, we use parameters for dislocation and diffusion creep of a wet natural peridotite (Karato and Wu, 1993). We will test our model with dry crustal and mantle rheologies (Mackwell et al., 1998; Karato and Wu, 1993). Simulations are run for a total model time of 100 Myr, a time sufficient to capture any appreciably lower crustal flow and a time after which any (unmodeled) cooling of the system would retard any further flow. To examine the validity of this time frame, we run our simulations for longer times and investigate the final outcomes (see below). The time steps in the simulation are controlled by the minimum Maxwell time, which is dependent upon the elastic moduli and viscosity (Turcotte and Schubert, 2014). High temperature promotes low viscosities (consequently smaller Maxwell time), hence, small time steps. As the time step decreases, the required time to finish the simulations becomes longer. In order to keep the running time for simulations of the order of days to weeks, we limit the minimum viscosity to Pa s. We have tested our models with smaller minimum viscosity (e.g., Pa s), which led to the order of magnitude smaller time steps but similar end-model results. Although strains are typically small, we implement a full large strain formulation, which includes the second-order term of the strain displacement relationship (e.g., Ranalli, 1995) and a geometric update. During the simulation, the mesh geometry changes continuously, and since the topography is the source of stress, updating the geometry is required. Additionally, we apply a constant dilatation scheme across the elements that eliminates numerical error while simulating nearly incompressible behavior (e.g., viscous creep).

42 30 E. Results Our study demonstrates the role of the lower crustal flow in the evolution of a large impact crater at the surface and within the subsurface for a sufficiently high background heat flux and thick crust. The pressure gradients generated by crustal thickness variations transfer lower crustal material from the periphery to underneath the crater, thereby reducing the topography at the crust-mantle boundary. In our simulations, we include remnant impact heat, and our results indicate a significant role of that in the deformation, specifically when the basal heat flux is relatively smaller (40-55 mw m -2 ) rather than larger (more than 55 mw m -2 ). Unsurprisingly, the amount of deformation in the subsurface is larger for a higher background heat flux, due to the lower viscosity of the material. Correspondingly, a thicker crust leads to high temperatures in the lower crust and similar results. Additionally, the development of lower crustal flow leads to substantial mechanical decoupling of the surface from the subsurface. As the mantle topography relaxes, the negative surface topography of the basin largely loses the buoyant support from the topography on the crust-mantle boundary. Support of the surface topography then must come almost exclusively from a lithosphere thinner than the crust, which results in upward flexure and a reduction in surface topography (Fig. 6). A simulation with no density contrast across the crust-mantle boundary (and hence no buoyant support) further illuminates this concept. While both cases see over a kilometer of shallowing of the surface basin, they are within a few hundred meters of each other. As the size of the crater increases, the amount of deformation at the crust-mantle boundary is less compared with that of a smaller crater, for the same background heat flux. That is, a larger crater requires a higher heat flux to go through the same amount of relaxation. This result is a

43 31 common finding of lower crustal flow studies (e.g., Nimmo and Stevenson, 2001), and arises because of the larger lateral distances over which the material must flow for a larger crater. The basis of our results originates from comparing the current crust-mantle boundary topography beneath the craters with that of our predicted/simulated results. For example, Figure 7 shows the simulated deformation at the crust-mantle boundary for various heat fluxes versus the current mantle topography and constrains the appropriate background heat flux for the shallowed structure of Basin 17. Since the surface of Mars is subject to alteration via surficial processes, matching the surface topography has secondary value. Using our simulated results, we find the most appropriate heat fluxes that reproduce the current topography at the crust-mantle boundary, determined from the crustal thickness model of Neumann et al. (2008). Table 4 lists the inferred background heat flux for the candidate craters and QCDs.

44 Surface Elevation (km) Depth (km) Distance (km) -50 Figure 6. Simulated topography at the surface and subsurface, versus initial topography. Solid and dotted lines are showing the initial and simulated topography at the surface and crust-mantle boundary, respectively Depth (km) Distance (km) Figure 7. Simulated subsurface topography for a crater 340 km in diameter (Basin 17). A simulation with a background heat flux of 50 mw m -2 (thin black line) produces similar mantle topography beneath the

45 33 basin center as suggested by the crustal thickness model (red line). For comparison, the simulated topographies with background heat fluxes of 45 (dotted line) and 55 (dashed line) mw m -2 are plotted. The bold black line is the initial mantle topography. Table 4. List of the candidate craters and QCDs and appropriate background heat flux for them, for both the deep and shallow initial geometries. Impact #* Background heat flux (mw m -2 ) (Deep / Shallow) Impact #* 1 70 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 40 * cf. Tables 1 and 2 Background heat flux (mw m -2 ) (Deep / Shallow)

46 34 F. Discussion The craters in our study are all, except for one, in the Southern Highlands. QCDs, however, are located in both the Southern Highlands and Northern Lowlands. The combination of these impact craters and QCDs has a fairly even geographic distribution and covers large areas on the surface of Mars (Figs. 3 and 8). The geographical distribution of candidate craters and QCDs, combined with their impact ages, enables us to explore the variation of Martian surface heat flux through space (and time, though to a lesser degree). Figure 8 shows the location of impacts (QCDs and craters), and the size of the symbols is related to the inferred surface heat flow. Analysis of our candidate craters in the Southern Highlands indicates that the craters closer to the crustal dichotomy boundary formed under a relatively higher background heat flux, with decreasing values farther from the boundary. To view further this apparent spatial relationship, we show a thermal contour map (interpolated using the Gaussian method) in Fig. 9. Again, this map shows that the average background heat flux of Mars in the Northern Lowlands was higher than that of the Southern Highlands (during the Noachian), although the relative sparseness of the data points suggest that much of the structure in these contours are artifacts. Consequently, we can illustrate this spatial relationship even more quantitatively by plotting (Fig. 10) the inferred heat flux as a function of distance from the dichotomy boundary (as mapped by Andrews-Hanna et al., [2008]). Although there is significant scatter in the heat flow values, there is a clear trend with lower values in the far south and higher values in the Lowlands.

47 35 Figure 8. The inferred background heat fluxes for the candidate craters and QCDs. White and black circles mark QCDs and craters, respectively. Large and small circles stand for background heat fluxes of > 75 and < 60 mw m-2, respectively. Medium size circles represent a background heat flux of 60 to 75 mw m-2. Figure 9. Contour map of surface heat flux (in mw m-2) of Mars during the Noachian, overlain on the Martian topography.

48 Heat Flux (mw m -2 ) a Distance (km) Heat Flux (mw m -2 ) b Distance (km) Figure 10. a, b. Heat flux vs. distance from the dichotomy boundary. Positive values of distance stand for impacts in the Southern Highlands, and negative values stand for impacts in the Northern Lowlands. a) results using the deep structure; b) results using the shallow structure. R 2 values for the line fit are both ~0.5.

49 37 These observations suggest that a thermal signature from whatever process that formed the crustal dichotomy, which predates the candidate QCDs and craters (Frey et al., 2002), persisted throughout the Noachian. Additionally, the increase in surface heat flux from the Lowlands to the Highlands would seem to preclude formation mechanisms for the crustal dichotomy that put the locus of activity in the southern hemisphere, including degree 1 mantle convection, and mantle overturn (e.g., Roberts and Zhong, 2006; Zhong and Zuber, 2001). This thermal signature would instead seem more consistent with mechanisms that place the locus of activity in the north, including one or several gigantic impacts, removal of the basal lowlands crust by mantle convection, and crustal thinning due to plate tectonics (Andrews-Hanna et al., 2008; Sleep, 1994; McGill and Dimitriou, 1990; Frey and Schultz, 1988; Wilhelms and Squyres, 1984; Wise et al., 1979; Lingenfelter and Schubert, 1973), although we cannot distinguish these remaining mechanisms from our heat flow trends. This heat flow trend does carry an element of model dependency related to the choices we use in our simulations. We discuss our various tests on the sensitivity of our results to these choices next, but first, we point out here that this trend is also revealed in the observations that guide our simulations. Figure 11 shows the ratio of the current mantle topography to its predicted initial state for our candidate craters and QCDs as a function of distance from the dichotomy boundary, which again reveals a systematic trend of lower values as one heads from Highlands to Lowlands. This observation is consistent with lower crustal flow, and we have interpreted the heat flows associated with this process. But even if our values are off (or if some other process altogether governs this observation, such as differences in the collapse of the transient craters in the different crustal regimes), this observation shows that some aspect of the crustal dichotomy has affected the morphometry of large Noachian craters.

50 38 Current Mantle Topography / Initial Mantle Topography a Distance (km) Current Mantle Topography / Initial Mantle Topography b Distance (km) Figure 11. a, b. Ratio of current to initial mantle topography underneath impacts vs. their distance from dichotomy boundary, for deep (a) and shallow (b) structure.

51 39 The most obvious aspect of our simulations that could affect our results is the choice to use a steady-state thermal structure when the actual thermal structure was time-dependent (i.e., diffusion of the impact thermal anomaly). To begin to understand the impact of this, we plot the evolution of topography on the crust-mantle boundary from one of our simulations that we ran for a period of 200 Myr, longer than our standard time of 100 Myr (Fig. 12). Most of the deformation occurs early (within ~30 Myr), with very small differences for longer times. This behavior is universal among our simulations and arises because the lateral pressure gradient that drives lower crustal flow decreases significantly with reduction of the topography on this interface. Over this tens of millions of years time scale, the thermal state is relatively static, suggesting that our implementation of steady state thermal conditions suffices. To test further the validity of our steady state thermal simulation and demonstrate the role of the lateral pressure gradient in the evolution of a crater, we run a transient simulation in which the impact heat diffuses over time. Figure 13 presents the simulated mantle topography underneath a crater, ~185 km in diameter, for two cases: (a) impact heat diffuses over time (which is computationally more expensive and time consuming) and (b) a steady state thermal simulation. For the simulation in which the impact heat diffuses over time, the relaxation of mantle topography is only slightly less than that of the steady state thermal simulation, which was expected (cf. Fig. 12). This observation justifies the application of a steady state thermal simulation in our study, as well as the evident role of the lateral pressure gradient in the relaxation of these craters.

52 Depth (km) Distance (km) Figure 12. A demonstration of the deformation at the crust-mantle boundary through time for a crater ~200 km in diameter, with background heat flux of 60 mw m -2. Bold black, dashed, green, red, orange and blue lines show the crust-mantle boundary topography after 0, 10, 30, 70, 100, and 200 Myr, respectively.

53 Depth (km) Distance (km) Figure 13. Relaxation of the crust-mantle boundary topography for two cases with transient (thin line) and steady state (dotted line) thermal simulations at 100 Myr. The background heat flux for both of the simulations is 50 mw m -2.

54 42 Another factor controlling the thermal structure is the surface temperature, but the average surface temperature of Mars of 210 K used in this study is likely not universal because of the differing latitudes of the craters and the differing climatic conditions in the distant past. In order to test the sensitivity of our model to changes in surface temperature, we perform a number of simulations with different values, ranging from 180 to 240 K. Results of our simulations (final simulated topography at the crust-mantle boundary) for various surface temperatures are plotted in Fig. 14. Apparent from this figure, the temperature difference of ± 30 K does not have a significant effect on the final results of our simulations. Furthermore, our simulations show that as the background heat flux increases, the effects of the surface temperature on the final topography of the crust-mantle boundary become even smaller. Geometric effects may also influence our results. For instance in order to explore the thermal evolution of the Northern Lowlands, we have simulated the deformation of large QCDs by modeling no surface topography. It is not certain, however, whether the infilling occurred immediately after the crater formation or at some time after the initial period of several tens of millions of years when lower crustal flow would have been the most prevalent. Thus, we test the effect on the lower crust by simulating a flat surface vs. a surface with crater topography. Figure 15 shows the final topography at the crust-mantle boundary for a QCD and crater of the same size; the difference between the simulated topographies of a QCD and crater at the crust-mantle boundary is relatively small. The QCD, with a flat surface, went through slightly more deformation within the subsurface, likely because of the slightly wider flow channel. Additional simulations show that as the applied background heat flux increases, the difference between the final topography under a QCD and a crater decreases. Consequently, infilling does not have a significant effect on the process of deformation at the crust-mantle boundary, and this

55 43 observation stands as further evidence for the mechanical decoupling discussed in the previous section Depth (km) Distance (km) Figure 14. Effect of surface temperature on lower crustal flow. The bold-solid lines show the initial topography of the Huygens crater at the surface and at the crust-mantle boundary. The dashed, dotted, and thin lines show the simulated crust-mantle boundary for surface temperatures of 180, 240, and 210 K, respectively. The background heat flux is 50 mw m -2.

56 Depth (km) Distance (km) Figure 15. Differences between the final topography at the crust-mantle boundary for a QCD and crater ~300 km in diameter and with a background heat flow of 55 mw m -2. The solid line represents the initial topography, while the dashed and dotted lines show the simulated topography of the crater and QCD, respectively.

57 45 We also generally apply a single value for the nominal crustal thickness of 45 km for the Lowlands and 50 km for the Highlands. Since the crustal thickness could be different from place to place, we run simulations to examine the sensitivity with respect to the crustal thickness. Our simulations show that the process of crater deformation is sensitive to the crustal thickness value. Figure 16 shows the ratio of relaxed to initial topography on the mantle boundary vs. crustal thickness for a crater ~200 km in diameter. As the crustal thickness increases, the amount of relaxation at crust-mantle boundary increases, due to the temperature increase in the lower crust and the larger flow channel thickness. Conversely for a thinner crust, relaxation is less, thus requiring a higher background heat flux. It is significant to note, however, that the hemispherical differences in crustal thickness likely cannot explain the trends seen in the observations (Fig. 11) or our modeled interpretations (Fig. 10) because we would expect to see more relaxation in the Southern Highlands with its thicker crust, which is not the case. The observation of larger mantle topography underneath craters in the Southern Highlands rather than Northern Lowlands (Fig. 11) suggests that regardless of the model sensitivity and modeling choices, the background heat flux should be noticeably higher in the Northern Lowlands.

58 46 Relaxed Mantle Topography / Initial Mantle Topography Crustal Thickness (km) Figure 16. Ratio of relaxed to initial mantle topography vs. crustal thickness. Background heat flux for all of the simulations is 50 mw m -2.

59 47 Our choices for the rheologies can also impact our results. For example, we have assumed that the viscous creep rheology follows the flow rules of a wet material. To test this assumption, we run simulations with the viscous creep parameters determined for anhydrous Maryland diabase and anhydrous Columbia diabase for the crust and anhydrous olivine for the mantle (Mackwell et al., 1998; Karato and Wu, 1992). These results demonstrate that for the same background heat flux, the amount of deformation observed for the dry rheology is significantly less than that of the wet rheology. In other words, an implausibly high heat flux would be required in order to reproduce the current topography at the surface and subsurface when dry viscous creep parameters are applied. Thus, this study is consistent with the notion that Mars s interior is wet to a certain degree (e.g., Grott and Breuer, 2008). Additionally, previous analysis of crater relaxation of Ganymede and Callisto showed that plastic deformation (a proxy for brittle faulting) has no major effect on the final relaxed topography of craters at the surface (Dombard and McKinnon, 2006). In our study, we apply a viscoelastic rheology with no plasticity, but we tested a few cases with plasticity (effectively applying Byerlee s rule). While the role of plastic deformation because of bending stresses near the surface could affect the final topography of the surface, our results show that plastic deformation does not have any significant effects on the final topography of the crust-mantle boundary.

60 48 G. Conclusions We use the finite element method with a viscoelastic rheological model to simulate the longterm deformation of Martian craters and QCDs at the surface and subsurface. For a sufficiently high background heat flux, lower crustal flow is efficient and reduces the topography at the crust-mantle boundary, and the loss of internal buoyancy results in lithospheric flexure and uplift of the surface topography. We use this phenomenon to determine the appropriate background heat flux for 31 craters and QCDs on Mars, which enables us to produce a thermal map of the Red Planet during the Noachian. Our study shows that in the Southern Highlands, craters closer to the dichotomy boundary experienced a higher background heat flux relative to craters farther from it. In addition, the average background heat flux of the Northern Lowlands is higher than that of the Southern Highlands. This evidence suggests that whatever process formed the crustal dichotomy, its thermal signatures still existed through the Noachian. H. Acknowledgments This study was supported by NASA grant NNX08AE98G to AJD.

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67 CHAPTER III III. STUDYING LOWER CRUSTAL FLOW BENEATH MEAD BASIN: IMPLICATIONS FOR THE THERMAL HISTORY AND RHEOLOGY OF VENUS Chapter III will be published in Icarus as: Mohammadali Karimi, Andrew J. Dombard The Department of Earth and Environmental Sciences (MC-186), University of Illinois at Chicago, 845 W. Taylor St., Chicago, IL , United States. 55

68 56 A. Abstract Mead, the largest crater on Venus, has low topographic relief at the surface and at the crustmantle boundary. Due to high surface temperatures, viscous deformation could play an important role in crustal structure. Using the finite element method, we simulate the long-term viscoelastic deformation of Mead crater and investigate the role of lower crustal flow in the evolution of the surface and subsurface topography. We examine the thermal states that allow this evolution to occur and determine the background heat flux. Our study constrains the background heat flux in the vicinity of Mead basin to mw m -2. This surface heat flow is higher than the average Venusian global value of mw m -2 suggested by thermal models. In addition by applying hydrous and anhydrous creep rheological parameters, we demonstrate that the Venus s interior is rheologically dry and that the crust near Mead is relative high in plagioclase.

69 57 B. Introduction Studying the deformation of crusts and lithospheres leads to a better understanding of the internal structure and thermal history of planetary bodies. Previous studies on the thermal evolution of Mars and the Moon have investigated the viscoelastic relaxation of large craters primarily driven by lower crustal flow, and have constrained the background heat flux of these planetary bodies (e.g., Mohit and Phillips, 2006, 2007; Karimi et al., 2015). Unlike the Moon and Mars, the surface of Venus lacks numerous craters. There are about 1000 craters on the surface of Venus, among which Mead, with the size of 270 km in diameter, is the largest (e.g., Herrick and Sharpton, 1996) and the only one to be resolved in gravity models, a fact likely to not be rectified by future orbiting platforms because of Venus s thick atmosphere. Indeed, the earlier study of Banerdt et al. (1994), using the MGNP60FSAAP gravity model, showed that Mead basin is not compensated isostatically. Banerdt et al. (1994) also demonstrated that unlike large lunar basins with uplifted mantle underneath the crater depression (e.g., Neumann et al., 1996), there is a lack of definitive mantle uplift beneath Mead basin. Due to high surface temperatures and a thick crust, a large amount of lower crustal flow is likely for a large impact crater on Venus (e.g., Grimm and Solomon, 1988; Karimi and Dombard, 2011). In this study, we investigate the possible viscoelastic deformation of Mead basin at the surface and within the subsurface, and determine the role of lower crustal flow in the relaxation of mantle topography. Using the Finite Element Method (FEM), we simulate the crustal deformation and use it as a probe of the heat flux of Venus. Furthermore, by testing various viscous creep parameters, we aim to determine the appropriate viscous rheology for the crust and mantle of Venus.

70 58 C. Mead Basin Mead, the largest exposed crater on the surface of Venus at 12.5 N 57.2 E, was first revealed by the Magellan mission (Herrick and Sharpton, 1996). The age of Mead (less than 0.5 Gyr) falls within the estimated average surface age of Venus, ranging from 300 to 750 Myr (McKinnon et al., 1997). This crater is a shallow basin with an apparent depth of about 1100 m; in contrast, a fresh crater of this diameter should have the minimum depth of 1350 m (McKinnon et al., 1997; Herrick and Sharpton, 1996). The central part of the basin (Fig. 1) has topographic variations and is not flat (Herrick and Sharpton, 1996). We plot the azimuthally averaged free-air gravity signal from Mead in Fig. 2, created from an expansion of the MGNP180U 180-degree spherical harmonic potential model of Venus (archived in NASA s Planetary Data System [ We omit degrees below 15 from the expansion, which detrends regional signals of a scale of ~2500 km. We also truncate the expansion at degree 150, in order to avoid possible errors occurring at higher degrees (Wieczorek, 2007). An expansion to degree 150 has a spatial resolution of ~ km. Consequently, Mead, with a diameter of 270 km, is the only crater on the surface of Venus that can be resolved (though just barely) in existing gravity models. Previous studies have determined the current topographic structure of Mead basin (e.g., Herrick and Sharpton, 1996), finding a depth of ~1100 m. Assuming a crustal density of 2900 kg m -3, the predicted free air gravity anomaly arising from a basin this deep is ~130 mgal (Fig. 2). Thus similar to Banerdt et al. (1994), we find that the gravity anomaly is dominated heavily by the surface topography, and the contribution of the subsurface topography to the gravity signal is small. Assuming a density contrast across the crust-mantle boundary of 400 kg m -3 (Dombard et al., 2007; James et al., 2013), we predict the maximum mantle uplift to be ~3 km.

71 59 Crustal Profile of Mead Basin 2500 Elevation (m) surface 0 crust ~ -30,000 crust-mantle boundary mantle Distance (km) Figure 1 A schematic that shows the crustal profile of Mead basin. Azimuthally average surface topography is plotted according to Herrick and Sharpton (1996). The mantle topography is notional and not based on crustal thickness models Gravity Anomaly (mgal) Distance (km) Figure 2. The azimuthally averaged free-air (thin solid), topographic (dotted), and Bouguer (thick solid) gravity anomalies over Mead basin, from a degree-and-order spherical harmonic expansion.

72 60 The mantle uplift beneath Mead was undoubtedly much higher initially. Studies of lunar and Martian crustal thickness show that the mantle is uplifted beneath large impact craters (e.g., Neumann et al., 1996; Neumann et al., 2004; Neumann et al., 2008). This phenomenon is likely due to the collapse of the transient crater (e.g., Melosh, 1989; Wieczorek and Phillips, 1999). Namiki et al. (2009) suggested a nearly isostatically compensated structure for large craters at the central point. Applying the same concept to Mead with an expected initial depth of 1350 m, the initial mantle uplift should have been more than 10 km. Clearly, the shape of Mead has evolved, and the very high surface temperatures of Venus (740 K) implicates viscous processes, specifically lower crustal flow. Like for many large craters on Mars (Karimi et al., 2015), high temperatures in the lower crust result in a relaxation of the mantle topography. This viscous response also serves to decouple mechanically the surface topography from the compensating mantle topography. The surface basin, in turn, flexes upwards, the remaining topography having virtually lost any isostatic support and now having to be supported by the strength of a lithosphere thinner than the crust. The mechanics just described are more complex than has been previously modeled (e.g., Grimm and Solomon, 1988); consequently, we re-examine the case of Mead here. In particular, we explore the thermal states and rheological conditions that allow the relaxation of the surface and subsurface topography to the current state.

73 61 D. Methodology 1. Initial Shape of the Basin We use the same methodology as described in Karimi et al. (2015), simulating 1 radial plane beneath an axisymmetric crater with the bottom and side boundaries sufficiently far to not affect the solutions. To model the viscoelastic deformation of Mead basin, the shape of the fresh crater is required. Since we are not certain about the initial depth of Mead crater at the time of formation, we consider two cases of (1) shallow and (2) deep structures that bracket the likely initial depth. This approach permits constraint of the upper and lower limits of the background heat flux. For the shallow structure, we use the depth-diameter curve of McKinnon et al. (1997), which indicates that the initial depth of Mead basin at the time of formation was ~1350 m. For the deep structure, we double the value of the shallow structure, because other Venusian craters, albeit smaller than Mead, are twice as deep (e.g., Cleopatra, Basilevsky and Ivanov, 1990). Furthermore, Sharpton (1994) investigated Venusian crater morphology (using Magellan data) and suggested that any previous geometric properties regarding the depth of craters should be considered as a lower bound. The shape of the crater depression and the topography of the ejecta blanket are determined by a 4 th order polynomial and an inverse 3 rd law, respectively (Dombard and McKinnon, 2006), where we assume that the rim height above the background terrain represents ~25% of the total depth of the crater. In order to determine the initial crust-mantle boundary topography beneath the surface depression, we apply a Gaussian-like exponential function scaled to compensate the surface topography at the center point of the crater. We expect the mantle uplift to be narrower than the diameter of Mead basin, as shown in Fig. 3 (see Karimi et al., 2015 for details). The background crustal thickness is considered to be 30 km (Anderson and Smrekar, 2006; James et

74 62 al., 2013). We also consider other thickness values of 35 and 40 km in order to test the sensitivity of our modeling to the crustal thickness. Figure 3 shows both initial geometries (shallow and deep) for Mead basin Elevation (km) Depth (km) Distance (km) Figure 3. A display of initial topography at the surface and subsurface for both deep (solid line) and shallow (dotted line) geometries.

75 63 2. Thermal and Mechanical Simulations Following Karimi et al. (2015), we simulate the thermal state beneath the basin, then pipe the results into a mechanical simulation. In the thermal simulation, we find the steady state equilibrium between an average surface temperature of 740 K for Venus (Florensky et al., 1977; Seiff, 1983) and an applied basal heat flux. We also consider a proxy for the remnant impact heat by fixing the temperature of the uplifted crust-mantle boundary to that of this boundary far from the crater. Strictly speaking, the thermal state should evolve as the remnant impact decays with time; we have shown previously, however, that results assuming steady state thermal conditions are nearly identical to a transient thermal state, because most lower crustal flow occurs early before the remnant heat has decayed appreciably (Karimi et al., 2015). The results of the thermal simulation, which modulates the temperature structure, are input into the mechanical simulation, which uses mechanical parameters appropriate for Venus. The gravitational force with an acceleration of 8.87 m s -2 is applied that, coupled with the density values of 2900 kg m -3 and 3300 kg m -3 for the crust and mantle (Nunes et al., 2006; Dombard et al., 2007), supplies the driving force for lower crustal flow. The elastic moduli for the crust and mantle of Venus are consistent with those of a terrestrial planet (Table 1). We run our simulations for the time frame of 100 Myr, which is a long enough time to record any lower crustal flow. To keep the computer time tractable (a few weeks or less), we apply a minimum viscosity of Pa s to the mesh, and confirm that our results are not sensitive to this cut-off (see Karimi et al for details of the simulations).

76 64 3. Viscous Rheology As a phenomenon controlled by the ductile flow properties of the materials, an understanding of the viscous rheology is required. Water, through its effect on viscosity, plays an important role in the nature of the rheology of the crust and mantle. Hence, our knowledge of how this process operates on Venus could enhance our understanding of the water content of the crust and mantle. Laboratory experiments of high-temperature creep in rocks have shown a non-linear relationship between strain rate and stress, which can be described by the following flow rule (e.g., Ranalli, 1995): ε = A( σ! d! )exp( Q RT ) in which ε is equivalent strain rate, σ is equivalent deviatoric stress, R is the gas constant, d is grain size, and T is absolute temperature. A, n, m and Q are the experimentally obtained values. There is also a pressure dependent term that affects the activation energy in the numerator of the exponential, but it is small for the relatively low pressure lithospheric processes and hence ignored here. Previous geodynamic modeling studies of Venusian features (e.g., Grimm and Solomon, 1988; Nunes et al., 2006; Dombard et al., 2007) have used various parameters for dry (anhydrous) and wet (hydrous) viscous creep rheologies such as Caristan (1982), Karato and Wu (1993) and Mackwell et al. (1998). The major difference between various viscous creep rheologies is the relative proportion of pyroxenes to feldspars that can affect the stiffness of materials under stress. In addition, thin layers of water in silicate crystals can play an important role in the creep behavior of the rocks. High temperatures at the surface and the assumption of a linear temperature increase in the crust and upper mantle suggest a relative depletion of water,

77 65 and consequently, a dry interior for Venus. While we nominally use parameters for anhydrous materials, we also carry out simulations using hydrous rheologies in order to test the sensitivity to variations in rheological parameters (Table 1). Table 1. Parameters for finite element simulations used in this study. Parameters Values Geometry Crater radius 135 km Initial depth m Initial topographic relief of the crust-mantle boundary ~10-20 km Crustal thickness km Mesh width 405 km Mesh depth 405 km Thermal Analysis Surface temperature 740 K Thermal conductivity, crust 2.5 W m -1 K -1 Thermal conductivity, mantle 4 W m -1 K -1 Mechanical Analysis Gravitational acceleration 8.87 m s -2 Density, crust 2900 kg m -3 Density, mantle 3300 kg m -3 Poisson s ratio 0.5 Young s modulus, crust 52 GPa Young s modulus, mantle 112 GPa Crustal creep rheology Hydrous/Anhydrous diabase a,b Mantle creep rheology Hydrous/Anhydrous olivine c Minimum viscosity Pa s a Caristan 1982; b Mackwell et al. 1998; c Karato and Wu 1993

78 66 E. Results Our study shows that for a sufficiently thick crust and a high enough background heat flux, lower crustal flow is effective in relaxing the subsurface topography, which in turn results in shallowing of the surface crater. Variations in crustal thickness induce a pressure gradient that drives the lower crustal flow. This lower crustal flow moves material from surrounding the basin to underneath, thus reducing the mantle topographic relief. During relaxation of the crust-mantle boundary, the surface depression loses buoyant support. It is the lithosphere then that supports the topography, which flexes upward causing the surface shallowing (cf. Karimi et al., 2015). As Fig. 4 shows, our study demonstrates a larger amount of relaxation within the subsurface for a higher background heat flux. This result is expected because a warmer thermal state drops the viscosity, which facilitates more lower crustal flow. Similarly, higher temperatures at the base of a thick crust (vs. a thin crust) lead to a lower viscosity and larger deformation. In order to determine a suitable thermal state for Mead basin, we search for background heat fluxes that relax the crust-mantle boundary to a high degree. Surface topography, in contrast to the crust-mantle boundary topography, is of secondary value due to its exposure to surficial processes (e.g., volcanic infilling). Table 2 shows the background heat fluxes most consistent with the observation of minimal topography (~3 km) on the crust-mantle boundary beneath Mead. These inferred heat fluxes can be considered lower limits. For instance, heat flows need to be ~15-20% higher than listed in Table 2 to result in mantle uplift of 1 km.

79 67-20 Depth (km) Distance (km) Figure 4. Examples of simulated results at the crust-mantle boundary of Mead basin (shallow geometry). Red, red dashed, blue, and blue dashed lines show the results of our simulations with background heat fluxes of 60, 65, 70, and 75 mw m -2, respectively, and application of a dry rheology. The black line shows the initial topography at the crust-mantle boundary. Table 2. Inferred background heat flux for both deep and shallow geometry and various crustal thickness values. Crustal Thickness Background Heat Flux (mw m -2 ) Background Heat Flux (mw m -2 ) (km) Deep Geometry Shallow Geometry

80 68 F. Discussion Our study constrains the background heat flux of Venus in the vicinity of Mead basin to within the range of 55 to 90 mw m -2. Previous studies of thermal modeling of Venus have constrained the global average surface heat flux of Venus to the range of mw m -2 (e.g., Phillips and Hansen, 1998). Our study, therefore, might suggest that the global heat flux of Venus is noticeably higher than that of Phillips and Hansen (1998); however, it is equally plausible that this discrepancy might be due to regional variations that are smoothed over in global thermal models. Our study also suggests that a wet rheology does not seem to be appropriate for Venus, and instead, a dry rheology seems more suitable. As compared to a dry rheology (cf. Fig. 4), application of a hydrous rheology (wet Maryland diabase and wet peridotite) reduces the entire topographic relief at the surface and subsurface in a very short time. Figure 5 shows the results of this simulation: despite using a deep geometry and relatively low background heat flux (20 mw m -2 ), the topography at the surface and the crust-mantle boundary is quickly and completely relaxed. Such strong relaxation associated with a wet rheology is inconsistent with the current surface topography of Mead basin. Recent laboratory work by Filiberto (2014) suggested that the igneous rocks of Venus might be compositionally diverse as those of our planet and to some degree wet, seemingly in conflict with our results. The study of Filiberto (2014), focusing on volatile content of Venus, suggests ~ 0.2 wt% water in Venus basalts, which equates to ~200 ppm water in the mantle. The dry olivine of Karato and Wu (1993) used in our study is nominally a water free sample. The experimental study on olivine rheology places the threshold water content for dry-to-wet olivine on 300 ppm

81 69 (Korenaga and Karato, 2008). Therefore, the possible hydration state suggested by Filiberto (2014) does not negate our results - suggesting a dry peridotite as an appropriate mantle material. Additionally, the mineralogical composition of the rocks also affects the rheology. Mackwell et al. (1998) tested the viscous behavior of 2 types of anhydrous diabases: Maryland and Columbia. Here, the Maryland diabase has almost identical percentages of plagioclase and pyroxene, while Columbia is richer in plagioclase (> 70%). The significance is that a higher percentage of plagioclase tends to weaken the material viscously, as dislocation creep in the crystal lattice of plagioclase occurs more readily (Chen et al., 2006). In order to produce the desired deformation at the surface and subsurface, simulations with dry Maryland diabase and dry peridotite (due to high stiffness and lack of water) require an uncomfortably high background heat flux (> 100 mw m -2 ), which is more difficult to ascribe to regional variations from a global average. Figure 6 shows the simulated topography at the crust-mantle boundary with a dry Maryland diabase and a dry Columbia diabase for the crust. These results barely show any deformation at the crust-mantle boundary beneath Mead basin after using the dry Maryland diabase, with much more prevalent lower crustal flow for the case with the dry Columbia diabase. We interpret this result as an indication that the Venusian crust in the vicinity of Mead has a fairly high proportion of plagioclase, in addition to being anhydrous.

82 Surface Elevation (km) Depth (km) Distance (km) Figure 5. A demonstration of the simulated results with the background heat flux of 20 mw m -2 after applying a wet rheology. Solid lines represent the initial topography (deep geometry) and dotted lines show the simulated results Depth (km) Distance (km) Figure 6. A comparison between the results of our simulations using dry Maryland and dry Columbia diabase. The solid line shows the initial topography of the crust-mantle boundary, while the dotted and

83 71 dashed lines show the simulated results with the dry Maryland and dry Columbia diabase. The background heat flux for both of the simulations is 65 mw m -2. Various factors can affect our results. One aspect is the surface temperature. In our modeling, we apply an average surface temperature of 740 K, and so we also test our simulations with surface temperature changes of ±30 K. Our models do not show significant differences in the final topographies of the surface and the crust-mantle boundary, similar to what we have found for Mars (Karimi et al., 2015). We also test the effects of crustal thickness on the deformation of the surface and subsurface. For a thicker crust, we see a higher amount of relaxation, because of a wider flow channel due to the thicker crust and higher temperatures at the base of this crust. Similarly, a higher background heat flux is needed to relax the mantle topography using the deep geometry, because this higher initial mantle uplift limits the thickness of the flow channel, as well as necessitates the inward flow of more material. Consequently, simulations using the thinnest crust and deep geometry require the highest background heat flux (Table 2).

84 72 G. Conclusion The small topographic relief at the crust-mantle boundary underneath Mead basin can be explained by lower crustal flow. Our finite element simulations indicate that the viscoelastic deformation of the lithosphere is an efficient process that can relax the mantle uplift. We constrain the background heat flux of Venus in the vicinity of Mead basin to a range of 55 to 90 mw m -2, which is higher than the estimated global average surface heat flux, though possibly reflecting regional variations. Our study also shows that the viscous creep rheology of dry Columbia diabase and dry peridotite best match the rheological behavior of the Venusian crust and mantle, respectively. These results suggest that Venus s interior is dry to a certain degree (drier than that of our planet), and that the crust near Mead is relative high in plagioclase.

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89 CHAPTER IV IV. ON THE POSSIBILITY OF VISCOELASTIC DEFORMATION OF THE LARGE SOUTH POLAR CRATERS AND TRUE POLAR WANDER ON THE ASTEROID VESTA Chapter IV will be published in Icarus as: Mohammadali Karimi, Andrew J. Dombard The Department of Earth and Environmental Sciences (MC-186), University of Illinois at Chicago, 845 W. Taylor St., Chicago, IL , United States. 77

90 78 A. Abstract The asteroid Vesta, located within the inner asteroid belt, is a differentiated body with a prominent rotational bulge. NASA s Dawn mission revealed the presence of two large impact craters in the south polar region, one with a high standing central peak. The prominent central peak is reminiscent of large craters on some icy satellites that may have experienced strong topographic relaxation. Thus, we use the finite element method and a viscoelastic rheology to examine the feasibility of relaxation processes operating on these craters. The location of these basins near the south pole is also unusually and suggests true polar wander, and so we investigate the likelihood of relaxation of the rotational bulge, a requirement preceded by true polar wander. Given the plausible thermal state of Vesta (by calculating the heat generated through the decay of long-lived radioactive elements), we find that the lithosphere is not compliant enough to allow the strong relaxation of the large south polar craters, and thus the peculiar morphology is likely a product of the formation of these large, planetary scale basins on Vesta. Additionally, the asteroid has not been warm enough to permit the relaxation of the rotational bulge. Consequently, these craters both happened to form near the south pole, as unlikely as that is.

91 79 B. Introduction 4 Vesta is the second most massive asteroid in the Solar System and has an average diameter of ~525 km (Russell et al., 2012). Previous geochemical analyses of howardite-eucrite-diogenite (HED) meteorites have demonstrated that the asteroid is a differentiated body with an iron core and silicate crust and mantle (Coradini et al., 2011; Russell et al., 2012). The shape of the asteroid is well fit by an ellipsoid with the major axes of 286x278x223 km; the shortest dimension is aligned with Vesta s spinning axis (Russell et al., 2012). Observations clearly demonstrate a large rotational bulge for Vesta, which is consistent with a short rotational period of 5.3 hr for the asteroid (Fig. 1). Images by the Hubble Space Telescope revealed a large morphological feature in the south polar region. Thomas et al. (1997a) suggested that the feature is a crater, with a size comparable to that of Vesta. More recent images from the Dawn mission revealed the feature to be two large impact craters in the south polar region of the asteroid (Fig. 2), with the younger Rheasilvia (diameter of ~500 km) largely overprinting about half of the older Veneneia (diameter ~400 km). These impact basins are the most prominent geologic features on the surface of this asteroid, yet aspects of these craters are unusual.

92 80 Figure 1. An image taken during the Dawn mission. The rotational bulge at the equator and flattening at poles are evident. Courtesy of NASA/JPL-Caltech/UCLA/MPS/DLR/IDA. Figure 2. The topographic map of the southern hemisphere of the asteroid Vesta. The two large craters, Rheasilvia and Veneneia, are shown on the map with their centers marked with white and red signs, respectively. Courtesy of NASA/JPL-Caltech/UCLA/MPS/DLR/IDA.