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    LETTERdoi:10.1038/nature17171

    Late Tharsis formation and implications for

    early MarsSylvain Bouley1,2, David Baratoux3,4, Isamu Matsuyama5, Francois Forget6, Antoine Séjourné1, Martin Turbet6 & Francois Costard1

    The Tharsis region is the largest volcanic complex on Mars andin the Solar System. Young lava flows cover its surface (from theAmazonian period, less than 3 billion years ago) but its growthstarted during the Noachian era (more than 3.7 billion years ago).Its position has induced a reorientation of the planet with respectto its spin axis (true polar wander, TPW), which is responsiblefor the present equatorial position of the volcanic province. It hasbeen suggested that the Tharsis load on the lithosphere influencedthe orientation of the Noachian/Early Hesperian (more than3.5 billion years ago) valley networks1 and therefore that most of thetopography of Tharsis was completed before fluvial incision. Here wecalculate the rotational figure of Mars (that is, its equilibrium shape)and its surface topography before Tharsis formed, when the spin axisof the planet was controlled by the difference in elevation betweenthe northern and southern hemispheres (hemispheric dichotomy).We show that the observed directions of valley networks are alsoconsistent with topographic gradients in this configuration and thusdo not require the presence of the Tharsis load. Furthermore, thedistribution of the valleys along a small circle tilted with respectto the equator is found to correspond to a southern-hemispherelatitudinal band in the pre-TPW geographical frame. Preferentialaccumulation of ice or water in a south tropical band is predictedby climate model simulations of early Mars applied to the pre-TPWtopography. A late growth of Tharsis, contemporaneous with valley

    incision, has several implications for the early geological historyof Mars, including the existence of glacial environments near thelocations of the pre-TPW poles of rotation, and a possible linkbetween volcanic outgassing from Tharsis and the stability of liquidwater at the surface of Mars.

    The Tharsis bulge is the largest volcano-tectonic centre on Mars. Itsgrowth started during the Noachian epoch (>3.7 billion years ago)2 and the associated enormous transfer of mass, energy and release of volatiles from the mantle had implications for the planet’s evolution,including its climate, surface environment and mantle dynamics.The earliest signs of activity are limited to Noachian extensional tec-tonics observed around Claritas Fossae in the ancient Syria Planum,Thaumasia and Tempe Terra regions2. Assuming a 100-km-thick elasticspherical shell, models of the topographic effect of the Tharsis load have

    suggested that most of the bulge was largely in place by the end of theNoachian epoch. If so, it could have influenced the orientation of valleynetworks1. However, the elastic lithosphere thickness at the Noachianaccording to modern estimates3 (

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    formation of Tharsis and TPW (100.5°± 49.5° W, . °− . °+ . °

    71 114 4

    17 5  N; ref. 10).The proximity of the palaeo north pole inferred from the valley net-work distribution and the one inferred from degree-2 spherical har-monic gravity without Tharsis10 is remarkable because these resultsare independent.

    In the pre-TPW configuration, the valley network distributiondefines a latitudinal band of ±14° centred at 24° S, that is, in thesouth tropical regions (Fig. 1b). The incision of valley networksspans the Hesperian–Noachian (>3.5 billion years ago) period14,15 and it is unclear whether the valley network formation or the TPWevent caused by the Tharsis rise occurred first. To investigate whether

    the Tharsis bulge controlled the direction of the valley network, wemodelled the stream network in a latitudinal band (from 40° S to thedichotomy) in the pre-TPW reference frame for a topography withoutTharsis and before TPW at 1° per pixel (available in the SupplementaryInformation; see also Methods) and for a present-day topography withTharsis at the same resolution. The directions of large-scale valleynetworks in the pre-TPW and in the present configuration are bothcompatible with the observed directions of valley network (Extended Data Figs 1 and 2). In both configurations valley networks are orientedtowards the north, reflecting the topographic dichotomy of the Martiansurface. This result indicates that the presence of the Tharsis bulge isnot necessary to explain their orientation. However, the occurrence of

     valley networks within a palaeo tropical band, between the equator and40° S, subject to precipitation (ice, snow or rainfall), supports a post-

    incision Tharsis-driven TPW during the Early/Late Hesperian period.

    Early Mars climate simulations16–18 assuming the present topogra-phy predict patchy ice/water accumulation in a south tropical band fora cold/icy scenario17,18 and precipitation around Hellas basin and inTharsis region for warm/wet conditions18. Both kinds of simulation failto explain the occurrence of valley networks down to 45° S at the eastof Hellas and down to 60° S at the south of Tharsis. They also predictsubstantial rain/snowfall in the west of Tharsis. This prediction doesnot match the lack of valley networks in this region. We performednew simulations using the same model and conditions (see Methods)using a pre-TPW topography. We found that ice tends to stabilize andaccumulate in a tropical band (Fig. 2) similar to the distribution of

     valley networks (Fig. 1b), as a result of enhanced precipitation inducedby adiabatic cooling when the atmospheric circulation transports water

     vapour southward, up to the highlands. An icy patch is also predicted inthe Tharsis region but recent volcanic flows preclude the preservationof ancient morphologies in this region. Intensity of drainage is affectedby several factors and is not only related to the intensity of precipita-tion. The geological history subsequent to valley network formationmay also be responsible for heterogeneous modifications of the palaeodrainage intensities.

    Can we find any geological clues of a past polar climate at the locationof the palaeo poles? The palaeo north pole is located in Scandia Colles(Extended Data Fig. 4), a knobby terrain that probably represents one ofthe rare Noachian units in the north polar region19. Interestingly, someof the landforms of this region have been attributed to Late Hesperian

    polar ice retreat or melting20,21, which could be the result of the

    Figure 1 | Noachian/Early Hesperian valley networks distribution anddensity 12 before and after TPW. a, In the present reference frame. Thepalaeo pole positions are indicated with a diamond, with the spread in

    longitude and latitude for solutions shaded from black (14°) to red (15°),corresponding to the associated root-mean-square value for each solution,

    as given by equation (16) (see Methods). The white dashed line is thepre-TPW equator. b, In the pre-TPW configuration. Valley networks occurwithin a latitudinal band of ±14° centred at 24° S. The black dashed line is

    the present equator.

    90° N

    60° N

    30° N

    30° S

    60° S

    90° S

    180° 135° W 90° W 45° W 0° 45° E 90° E 135° E 180°

    90° N

    60° N

    30° N

    30° S

    60° S

    90° S

    a

    b

    180° 135° W 90° W 45° W 0° 45° E 90° E 135° E 180°

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    early degassing and progressive depletion of volatiles in the mantlesource. The calculated pre-Tharsis topographic map of Mars providesa framework within which to examine the first billion years of itsgeological history.

    Online Content Methods, along with any additional Extended Data display items andSource Data, are available in the online version of the paper; references unique tothese sections appear only in the online paper.

    Received 16 July 2015; accepted 27 January 2016.

    Published online 2 March 2016.

    1. Phillips, R. J. et al. Ancient geodynamics and global-scale hydrology on mars.Science 291, 2587–2591 (2001).

    2. Anderson, R. C. et al. Primary centers and secondary concentrations of tectonicactivity through time in the western hemisphere of Mars. J. Geophys. Res. 106, 20563–20586 (2001).

    3. Grott, M. et al. Long-term evolution of the martian crust-mantle system. SpaceSci. Rev. 174, 49–111 (2013).

    4. Grott, M. Late crustal growth on Mars: evidence from lithospheric extension.Geophys. Res. Lett. 32, L23201 (2005).

    5. Nahm, A. L. & Schultz, R. A. Evaluation of the orogenic belt hypothesis for theformation of the Thaumasia highlands, Mars. J. Geophys. Res. 115, E04008(2010).

    6. Roberts, J. H. & Zhong, S. The cause for the north south orientation of thecrustal dichotomy and the equatorial location of Tharsis on Mars. Icarus 190, 24–31 (2007).

    7. Melosh, H. J. Tectonic patterns on a reoriented planet: Mars. Icarus 44, 745–751 (1980).

    8. Willemann, R. J. Reorientation of planets with elastic lithospheres. Icarus 60, 701–709 (1984).

    9. Rouby, H., Greff-Lefftz, M. & Besse, J. Rotational bulge and one plumeconvection pattern: influence on Martian true polar wander. Earth Planet.Sci. Lett. 272, 212–220 (2008).

    10. Matsuyama, I. & Manga, M. Mars without the equilibrium rotational figure,Tharsis, and the remnant rotational figure. J. Geophys. Res. 115, E12020 (2010).

    11. Carr, M. H. The Martian drainage system and the origin of valley networks andfretted channels. J. Geophys. Res. 100, 7479–7507 (1995).

    12. Hynek, B. M., Beach, M. & Hoke, M. R. T. Updated global map of Martian valleynetworks and implications for climate and hydrologic processes. J. Geophys.Res. 115, E09008 (2010).

    13. Irwin, R. P., III, Craddock, R. A., Howard, A. D. & Flemming, H. L. Topographicinfluences on development of Martian valley networks. J. Geophys. Res. 116, E02005 (2011).

    14. Fassett, C. I. & Head, J. W. III. The timing of Martian valley network activity:constraints from buffered crater counting. Icarus 195, 61–89 (2008).

    15. Bouley, S. & Craddock, R. A. Age dates of valley network drainage basins andsubbasins within Sabae and Arabia Terrae, Mars. J. Geophys. Res. 119, 1302–1310 (2014).

    16. Forget, F. et al. 3D modelling of the early Martian climate under a denser CO2 atmosphere: temperatures and CO2 ice clouds. Icarus 222, 81–99 (2013).

    17. Wordsworth, R. et al. Global modelling of the early Martian climate under adenser CO2 atmosphere: water cycle and ice evolution. Icarus 222, 1–19(2013).

    18. Wordsworth, R. D. et al. Comparison of “warm and wet” and “cold and icy”scenarios for early Mars in a 3D climate model. J. Geophys. Res. 120, 1201–1219 (2015).

    19. Tanaka, K. & Kolb, E. Geologic history of the polar regions of Mars based onMars Global Surveyor data. I. Noachian and Hesperian Periods. Icarus 154, 3–21 (2001).

    20. Fishbaugh, K. & Head, J. North polar region of Mars: topography ofcircumpolar deposits from Mars Orbiter Laser Altimeter (MOLA) data andevidence for asymmetric retreat of the polar cap. J. Geophys. Res. 105, 22455–22486 (2000).

    21. Tanaka, K. L. et al. History of plains resurfacing in the Scandia region of Mars.Planet. Space Sci. 59, 1128–1142 (2011).

    22. Putzig, N. E. et al. SHARAD soundings and surface roughness at past,present, and proposed landing sites on Mars: reflections at Phoenix may

    be attributable to deep ground ice. J. Geophys. Res. 119, 1936–1949(2014).

    23. Kress, A. M. & Head, J. W. Late Noachian and early Hesperian ridge systems inthe south circumpolar Dorsa Argentea Formation, Mars: evidence for twostages of melting of an extensive late Noachian ice sheet. Planet. Space Sci. 109–110, 1–20 (2015).

    24. Feldman, W. C. et al. Global distribution of near-surface hydrogen on Mars. J. Geophys. Res. 109, E09006 (2004).

    25. Head, J. W. & Pratt, S. Extensive Hesperian-aged south polar ice sheet on Mars:evidence for massive melting and retreat, and lateral flow and ponding ofmeltwater. J. Geophys. Res. Planets 106, 12275–12299 (2001).

    26. Kargel, J. S. & Strom, R. G. Ancient glaciation on Mars. Geology  20, 3–7(1992).

    27. Leonard, G. J. & Tanaka, K. L. Geologic map of the Hellas region of Mars. USGSSurv. Misc. Invest. Ser. Map I–2694 (scale 1:4,336,000) http://pubs.usgs.gov/imap/i2694/ (USGS, 2001).

    28. Costard, F. The spatial distribution of volatiles in the martian hydrolithosphere.Earth Moon Planets 45, 265–290 (1989).

    29. Weiss, D. K. & Head, J. W. Formation of double-layered ejecta craters on Mars:a glacial substrate model. Geophys. Res. Lett. 40, 3819–3824 (2013).

    30. Grimm, R. E. & Solomon, S. C. Tectonic tests of proposed polar wander pathsfor Mars and the Moon. Icarus 65, 110–121 (1986).

    31. Tsai, V. C. & Stevenson, D. J. Theoretical constraints on true polar wander. J. Geophys. Res. 112, B05415 (2007).

    32. Chan, N. H. et al. Time-dependent rotational stability of dynamic planets withelastic lithospheres. J. Geophys. Res. 119, 169–188 (2014).

    33. Bibring, J. P. et al. Global mineralogical and aqueous Mars history derived fromOMEGA/Mars Express data. Science 312, 400–404 (2006).

    Supplementary Information is available in the online version of the paper.

    Acknowledgements  This research was funded by the GEOPS laboratory, theProgramme National de Planétologie of INSU-CNRS and the Centre Nationald’Etude Spatiale (CNES).

    Author Contributions S.B. conceived the project. S.B and D.B. drafted themanuscript with contributions from all authors and performed calculations of

    palaeo poles from valley networks distribution. I.M. performed the calculation ofthe rotational figure of Mars and its surface topography before TPW and Tharsis.F.F. and M.T. performed early Mars climate model simulations applied to thepre-TPW topography. A.S. and S.B. performed calculations of stream networkfor a topography of Mars with and without Tharsis.

    Author Information Reprints and permissions information is availableat www.nature.com/reprints . The authors declare no competing financialinterests. Readers are welcome to comment on the online version of thepaper. Correspondence and requests for materials should be addressed toS.B. ([email protected] ).

    © 2016 Macmillan Publishers Limited. All rights reserved

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    METHODSTopography model. The topography without Tharsis and rotational deformationdue to TPW was calculated using gravity and topography data10. We adopt theexpected rotation pole location before the emplacement of Tharsis (259.5° E, 71.1°N), the expected elastic lithosphere thickness at the time of loading (58 km), andthe expected Tharsis gravity and shape coefficients (tables 3–5 in ref. 10).

    The gravitational potential external to Mars, at a point with spherical coordi-nates (r , θ, φ), where θ is co-latitude andφ is longitude, can be expanded in spher-ical harmonics with unnormalized expansion coefficients C lm and Slm as follows

    (see, for example, refs 34 and 35):

    ∑ ∑θ φ

    θ φ φ

    ( ) = + 

    × ( ) ( ) + ( )=

    =

    U r   GM 

    GM 

    R

    P C m S m

    , ,

    cos [ cos cos ]

    l m

    l l 

    lm lm lm

    2 0

     

    (1)

    whereG is the gravitational constant,  M  and R are the mass and mean radius ofMars, and P lm are unnormalized associated Legendre functions given by:

    µ µµ

    µ( ) = ( − ) ( )   ( )/P P 1  d

    d2lm

      mm

    m  l 

    2 2

    where P l  are Legendre polynomials35,36. We do not include the Condon–Shortey

    phase factor of (−1)m. The unnormalized coefficients are related to the normalizedexpansion coefficients,C lm and lm:

    δ 

     =

    ( − )( + )

    ( − )!

    ( + )!

    ( )/

    Sl 

      l m

    l m

    S2 2 1   3

    lm

    lm

    mlm

    lm

    0

    1 2

    where δ m0 is the Kronecker delta function.We expand the geoid, N , and shape, S, in spherical harmonics with unnormal-

    ized expansion coefficients as:

    ∑ ∑

    θ φ φ

    θ

    = ( ) ( ) + ( )

    − − (π/ )

    =

    =

    =

    N R P C m S m

    w R

    GM R P C 

    cos [ cos sin ]

    1

    2cos 2

    l m

    lm lm lm

    l l 

    2 0

    2 42

    2

    0 0

     

    (4)

    where the equipotential is chosen to be the mean potential at the equator, and:

    ∑ ∑   θ φ φ= ( ) ( ) + ( ) ( )=

    =

    S P c m s mcos [ cos sin ] 5

    l m

    lm lm lm

    2 0

    where clm and slm are the shape expansion coefficients. We use the Jet PropulsionLaboratory Mars gravity field MRO95A37 and the Mars Orbiting Laser Altimetry(MOLA) shape model38. The topography is given by T  ≡ S − N .

    We remove rotational deformation contributions associated with the changein the rotational potential due to TPW. Given the location of the rotation pole,(θR , φR ), the rotational potential expansion coefficients are:

    θ φ

    θ φδ 

      Ω θ

    φ

    φ

    ( )

    ( )

    =−( − )

    ( − )!

    ( + )!× × ( )

    ( )

    ( )

    S

    m

    m

    R

    GM P 

    m

    m

    ,

    ,2

      2

    2

    1

    3cos

    cos

    sin

    m

    m

    m m

    2

    R R    R 

    2

    R R    R 

    0

    2 3

    2 R R 

      (6)

    whereΩ  is the rotation rate. The gravity expansion coefficients associated withrotational deformation due to TPW can be written as:

    θ φ

    θ φ

    θ φ

    θ φ

    =

    ( )

    ( )

    ( )

    ( )

    ( )C 

    S

    kC 

    S

    kC 

    S

    ,

    ,

    ,

    ,7

    m

    m

    m

    m

    m

    m

    2TPW

    2TPW

      22R 

    R,f    R,f 

    2R 

    R,f    R,f 

    22R 

    R,i   R,i

    2R 

    R,i   R,i

    where k2 is the degree-2 tidal Love number describing the long-term gravity defor-mation due to the change in the rotational potential, and (θR,f , φR,f ) and (θR,i, φR,i)are the final (present) and initial (before TPW) spherical coordinates of the rota-tion pole respectively. Similarly, the shape expansion coefficients associated withrotational deformation due to TPW can be written as:

    θ φ

    θ φ

    θ φ

    θ φ

    =

    ( )

    ( )

    ( )

    ( )

    ( )c

    s

    RhC 

    S

    RhC 

    S

    ,

    ,

    ,

    ,

    8m

    m

    m

    m

    m

    m

    2TPW

    2

    TPW  2

    2R 

    R,f    R,f 

    2

    R,f    R,f 

    22R 

    R,i   R,i

    2

    R,i   R,i

    where h2 is the degree-2 tidal displacement Love number describing the long-termshape deformation due to the change in the rotational potential.

    The dimensionless k2 and h2 Love numbers depend on Mars’ interior struc-ture and rheology. We assume the five-layer internal structure model describedin table 2 of ref. 10, and use the classical propagator matrix method (for example,ref. 39) to calculate their values. For the expected elastic lithosphere thickness of58 km, k2 = 1.10 and h2 = 2.00. These Love numbers are not sensitive to elasticlithosphere thickness. For example, k2 = 1.19 and h2 = 2.19 for a model withoutan elastic lithosphere.

    We compute the expansion coefficients for the topography without Tharsis andthe rotational deformation associated with TPW by removing these contributionsfrom the observed gravity and shape coefficients. The Tharsis gravity and shapecoefficients are taken from tables 3–5 of  ref. 10, and the gravity and shape coeffi-cients for the rotational deformation associated with TPW are given by equations(6) and (7). Finally, we compute the spherical harmonic coefficients in the pre-TPW frame using Wigner-D functions.Determination of the palaeo poles. The palaeo pole positions are calculated froma least-squares adjustment of the valley network density to a small circle on thesphere. (A small circle is given by the intersection of the sphere with a plane.)Considering the plane equation in Cartesian coordinates:

    = + +   ( )z ax by c   9

    and the conversion equation of spherical coordinates (r , λ,ϕ) into Cartesian coor-dinates, where r  is the average radius of Mars, λ is the longitude, andϕ the latitude:

    λ ϕλ ϕ

    ϕ

    ==

    =

    ( )

    x r 

     y r 

    z r 

    cos cos

    sin cos

    sin

    10

    the equation of a small circle is given by:

    ϕ λ λϕ

    = + +   ( )a b  c

    r tan cos sin

    cos  11sc   sc sc

    sc

    This equation may be solved with u = cos(ϕsc) and by extracting the roots of thesecond-degree polynomial in u. We thus have:

    ϕ∆

    =

    − ±

    +

    ( )

     Aarccos

    2[ 1]12

     A

    sc

    2

    2

    where:

    λ λ= +   ( ) A a bcos sin   13sc sc

    and:

    ∆ = 

      − 

      − 

    ( + )   ( )

     Ac

    c

    r  A

    24 1 1   14

    2   2

    2

    2

    The parameters a, b and c are determined by minimizing of the sum of the weightedresiduals between calculated latitudes and observed latitudes of the valley networkdensity map:

    ∑   ϕ λ ϕ= ( ) − ( )v d [ ] 15i

    i   i   isc2   2

    where λi and ϕi are coordinates of the valley network density map and d i is thecorresponding density of valley networks12. Adjustment is achieved by directexploration of the three-dimensional parameter space. This approach is useful

    to determine the best solution corresponding to the minimum of v , but also todetermine the spread of solutions (a, b, c) corresponding to any chosen residualgreater than the minimum value. The residual may be expressed as a root meansquare (r.m.s.) in latitude using:

    ∑. . . =

    ( )v 

    d r m s

    16

    i

    i

    min

    2

    The palaeo pole positions are then given from parameters a and b and the followingequations:

    ϕ

    λ

    = −

      + +

    ( )a b

    b

    a

    90 arccos  1

    1

    arctan

    17

    pole 2 2

    pole

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    LETTERRESEARCH

    The best solution is found at 24° S and corresponds to a r.m.s. in latitude of 14°that is equal to the spread of valley networks in a direction perpendicular tothe small circle. The best palaeo pole positions are indicated with a diamond inFig. 1a, together with the spread in longitude and latitude. Colours from black tored correspond to the associated r.m.s. value for each solution, as given by equation(16), and vary from 14° (black) to 15° (red).Determination of the stream network before and after Tharsis emplacement. The relief controls the direction of runoff processes. To investigate whether theemplacement of the Tharsis bulge controlled the direction of the valley network,

    the stream network was modelled for a topography of Mars without Tharsis andfor a topography with Tharsis with the same resolution of 1° per pixel. We usedthe Arc Hydro tool in ArcGIS (http://downloads.esri.com/archydro/archydro/ )that includes different functions to extract hydrological parameters (that is, theflow direction, the flow accumulation and the stream definition40). The digitalelevation model (DEM) can contain artefacts of DEM construction, but these havebeen corrected.

    The flow direction is based exclusively on topography. For each cell, the flowdirection corresponds to the direction of the steepest slope between the cell andthe eight neighbouring cells. The result is a raster with the value of every cell cor-responding to one of the eight possible flow directions. Then, based on the flowdirection raster, for each cell, the flow accumulation is calculated as the total num-ber of cells drained upstream of each cell. The flow accumulation approximatelyrepresents the drainage network.

    Finally, the stream network is defined, based on the flow accumulation networkand on a user-defined river threshold value (Extended Data Fig. 2). For each cell, if

    the value is greater than this threshold, it is defined as a stream. A smaller thresholdwill result in a denser stream network and usually in a greater number of delineatedcatchments, which may hinder delineation performance. For both DEMs, in orderto achieve general flow directions, which are not meant to correspond directly tothe actual valley network, we chose a river threshold value of 15 cells.

    The orientation of the stream network was calculated by using an ArcGIS tool41.This orientation was calculated with respect to the north (azimuth). The data werecompiled in a rose diagram representing the orientation of the stream network forthe DEM without Tharsis (total number of measurements N  = 702; Extended DataFig. 3a) and with Tharsis (N  = 698; Extended Data Fig. 3b).

    The distributions of the stream network for both topographies (before and afterTharsis emplacement and TPW) are similar (Extended Data Fig. 2). The streamnetwork is mainly oriented towards the north in both configurations (Extended Data Fig. 3). The calculation shows that the flow direction in the highlands was

    primarily controlled by the dichotomy and limits the possible influence of theTharsis bulge.Global climate model simulations. We use the Laboratoire de MétéorologieDynamique Early Mars 3D global climate model16,17. It includes the modellingof the CO2 cycle (condensation and sublimation on the surface and in the atmos-phere), a water cycle (transport of water vapour and clouds, precipitation andevaporation) and a detailed radiative transfer code adapted to a thick CO2 atmos-phere and both CO2 and H2O clouds. Here we used the ice equilibration algorithmfrom ref. 17 designed to calculate the location where the ice deposits stabilize

    at equilibrium under early Mars conditions, after the equivalent of thousands ofyears of evolution. This algorithm was shown to be insensitive of the assumedinitial state and in particular to the location of the ice reservoir at the beginningof the simulation.

    Figure 2 presents a map of the permanent ice deposits predicted for themost likely conditions for early Mars, that is, with an obliquity of 45° (ref. 42) anda mean pressure of 0.2 bar of CO2 (ref. 16). Similar results were obtained with amean pressure of 1 bar.

    34. Kaula, W. M. An Introduction to Planetary Physics: the Terrestrial Planets (JohnWiley & Sons, 1968).

    35. Wieczorek, M. A. in Treatise on Geophysics 165–206 (2007).36. Arfken, G. & Weber, H. Mathematical Methods for Physicists 4th edn (Academic

    Press, 1995).37. Lemoine, F. G., Konopliv, M. & Zuber, M. T. MRO Derived Gravity Science Data

    Products, MRO-M-RSS-5-SDP-V1.0, NASA Planetary Data System, https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0 (2008).

    38. Smith, D. E. MOLA initial experiment gridded data record, MGS-M-MOLA-5-IEGDR-L3-V1.0, NASA Planetary Data System, https://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0 (1999).

    39. Sabadini, R. & Vermeersen, B. Global Dynamics of the Earth: Applications ofNormal Mode Relaxation Theory to Solid-Earth Geophysics (Kluwer Academic,2004).

    40. ESRI. Arc Hydro Tools Overviewhttp://downloads.esri.com/blogs/hydro/ah2/arc_ hydro_tools_2_0_overview.pdf (Environmental Systems Research Institute, 2004).

    41. Jenness, J. S. Some thoughts on analyzing topographic habitat characteristics.In Remotely Wild http://www.jennessent.com/downloads/topographic_ analysis_online.pdf  (GIS, Remote Sensing, and Telemetry Working Group ofThe Wildlife Society, June 2005).

    42. Laskar, J. et al. Long term evolution and chaotic diffusion of the insolationquantities of Mars. Icarus 170, 343–364 (2004).

    43. Tanaka, K. L. et al. Geologic map of Mars: U.S. Geological Survey ScientificInvestigations Map 3292, scale 1:20,000,000 http://dx.doi.org/10.3133/sim3292 (2014).

    © 2016 Macmillan Publishers Limited. All rights reserved

    http://-/?-http://downloads.esri.com/archydro/archydro/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0https://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0https://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0https://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0https://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0http://downloads.esri.com/blogs/hydro/ah2/arc_hydro_tools_2_0_overview.pdfhttp://downloads.esri.com/blogs/hydro/ah2/arc_hydro_tools_2_0_overview.pdfhttp://www.jennessent.com/downloads/topographic_analysis_online.pdfhttp://www.jennessent.com/downloads/topographic_analysis_online.pdfhttp://www.jennessent.com/downloads/topographic_analysis_online.pdfhttp://dx.doi.org/10.3133/sim3292http://dx.doi.org/10.3133/sim3292http://dx.doi.org/10.3133/sim3292http://dx.doi.org/10.3133/sim3292http://www.jennessent.com/downloads/topographic_analysis_online.pdfhttp://www.jennessent.com/downloads/topographic_analysis_online.pdfhttp://downloads.esri.com/blogs/hydro/ah2/arc_hydro_tools_2_0_overview.pdfhttp://downloads.esri.com/blogs/hydro/ah2/arc_hydro_tools_2_0_overview.pdfhttps://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0https://pds.nasa.gov/ds-view/pds/viewDataset.jsp?dsid=MGS-M-MOLA-5-IEGDR-L3-V1.0https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0https://pds.nasa.gov/ds-view/pds/viewProfile.jsp?dsid=MRO-M-RSS-5-SDP-V1.0http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://downloads.esri.com/archydro/archydro/http://-/?-

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    Extended Data Figure 1 | Map of Tharsis region with 0 m, 3,000 m and 6,000 m isoaltitude lines. Noachian terrains are mapped in light red for terrainslower than 3,000 m and in dark red for terrains higher than 3,000 m. Hesperian and Amazonian terrains are in grey. Age units are taken from the mostrecent geological map of this region43. The black cross on Tharsis Montes is the location of the centre of mass of the Tharsis dome.

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    Extended Data Figure 2 | Modelled stream network before and after Tharsis emplacement. a, b, Digital Elevation Model (DEM) with 1° per pixel

    resolution without Tharsis (a) and with Tharsis (b). The stream network was modelled using the Arc Hydro tool in ArcGIS.

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    Extended Data Figure 3 | Rose diagram of orientations of the modelled stream network. a , Before Tharsis emplacement (N  = 702). b, After Tharsisemplacement (N  = 698). The orientation values are grouped into 45° sectors. N  is the total number of orientation measurements.

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    Extended Data Figure 4 | Geological map of the north polar region. The red cross indicates the location of the palaeo north pole (PNP), inferred fromthe valley network distribution. Figure modified from ref. 43; US Geological Survey.

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    Extended Data Figure 5 | Orthographic projection of lower-limit concentrations of water abundance at latitudes poleward of 50° N. The red crossindicates the location of the palaeo north pole, inferred from the valley network distribution. Figure modified with permission from figure 5 of Feldman,W. C. et al .24, J. Geophys. Res., John Wiley and Sons, copyright 2004 by the American Geophysical Union.

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    Extended Data Figure 6 | Predicted global-scale stress and tectonicpatterns due to the Tharsis-driven TPW event. Solid circles indicatethe locations of the palaeo poles. In the stress pattern (a), crosses indicatedirections and relative magnitudes of principal stresses, and orange andblue lines correspond to extensional and compressive stresses, respectively.

    In the tectonic pattern (b), the orange, blue, and light grey lines indicatethe strike of the expected normal, thrust and strike–slip faults, respectively.Contours correspond to the deviator stress in units of MPa. Solid blacklines mark the boundaries between different tectonic regions.