Toward Understanding the History and Mechanisms of Martian Faulting: the Contribution of Gravitational Potential Energy Lada L

GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L08202, doi:10.1029/2005GL025307, 2006

Toward understanding the history and mechanisms of Martian faulting: The contribution of gravitational potential energy Lada L. Dimitrova,1 William E. Holt,1 A. John Haines,2 and R. A. Schultz3 Received 23 November 2005; revised 24 February 2006; accepted 8 March 2006; published 28 April 2006.

[1] Current stress solutions for Mars match the long al., 1992, and references therein]. More recently, Banerdt wavelength signal of present day topography and gravity and Golombek [2000] proposed that the seeming need of but fail to match many surface faults, including the normal multiple mechanisms was due to the quality of data avail- faults in northern Claritas Fossae north to Tantalus and Alba able prior to MGS, and Phillips et al. [2001] furthermore Fossae. A deviatoric stress field associated with horizontal argued that the faulting is explained by membrane flexure gradients of gravitational potential energy (GPE) provides alone. an excellent fit, as measured by objective functions, to many [4] Banerdt and Golombek [2000] calculated the deflec- of the normal faults in the western Martian hemisphere as tion of the lithosphere due to the Tharsis load alone while well as wrinkle ridges circumferential to Tharsis; 70% of satisfying the long wavelength signal of present day topog- the faults have a misfit 0.1. The fit of faults to the GPE- raphy and gravity. The resulting stress field has radial derived stress field reflects the thermal state of the planet at compressive stresses throughout Tharsis. Banerdt and the times of faulting, and suggests that at such times elastic Golombek [2000] show only the extensional component thicknesses and membrane stresses were small, and of the strains, which is consistent with normal faulting on topography was supported by buoyancy forces. pre-existing faults radial to Tharsis and away from the load, Citation: Dimitrova, L. L., W. E. Holt, A. J. Haines, and R. for example, Memnonia, Sirenum, Thaumasia, southern A. Schiltz (2006), Toward understanding the history and Claritas, and Tempe Fossae. However, the faulting extend- mechanisms of Martian faulting: The contribution of ing from northern Claritas Fossae north to Tantalus and gravitational potential energy, Geophys. Res. Lett., 33, L08202, Alba Fossae is not well explained by the membrane model, doi:10.1029/2005GL025307. which predicts zero extension in these areas [Banerdt and Golombek, 2000], where the density of normal faults is high [Anderson et al., 2001]. 1. Introduction [5] Therefore, as pointed out by Banerdt and Golombek [2] The quantification of lithospheric dynamics on Mars [2000], these faults may have formed under different con- is of fundamental importance to the understanding of ditions (topography and gravity) than we see today. In Martian geologic history and surface morphology. An particular, while the bulk of the crust formed 4.5 Ga and understanding of the sources of stress, and the expected later additions were volumetrically minor [Nimmo and style, orientation, and magnitudes of stress and associated Tanaka, 2005], gravity and elastic thicknesses are unlikely strain is important for understanding the evolution of fault- to have remained unchanged for the last 4.5 Gy. For ing on Mars and its relationship to loading. The unprece- example, it is conceivable that mantle circulation rather dented volume, quality, and coverage of the data make it than flexure played a significant role in the early support of now possible to apply mature theoretical dynamic models Tharsis, producing a different gravity field during that time (previously applied to Earth) that may help resolve long- [Lowry and Zhong, 2003, and references therein]. standing scientific issues such as the formation and timing [6] In this paper we consider a different source of stress – of extensive graben sets radial to Tharsis and the distribu- stress associated with internal buoyancy forces, i.e., gravi- tion of wrinkle ridges [Banerdt et al., 1992; Banerdt and tational potential energy (GPE), constrained by topography Golombek, 2000; Anderson et al., 2001; Watters, 1993; and crustal thickness models of Zuber et al. [2000] and Head et al., 2002; Schultz, 2000, 2003]. Neumann et al. [2004]. We test the validity of the stress [3] The Tharsis province, due to its large scale and model by comparing it with the strain geometry of the complex deformation, has long been the focus of studies surface faults. on the Martian geologic evolution, and has been intensely studied with Viking, Mariner, and Mars Global Surveyor 2. Methodology (MGS) data. Early models seemed to require more than one mechanism – a combination of lithospheric uplift, isostasy, [7] We solve the 3-D force-balance equations for the and flexure – to explain the region’s evolution [Banerdt et vertically integrated deviatoric stress field associated with topography and crustal thickness variations using the thin- 1Department of Geosciences, Stony Brook University, State University sheet method discussed by Flesch et al. [2001], which is of New York, Stony Brook, New York, USA. appropriate when the horizontal scale of the features is 2Department of Earth Sciences, University of Cambridge, Cambridge, much larger than the layer thickness and horizontal gra- UK. dients in basal tractions are small. The deviatoric stress 3Department of Geological Sciences and Engineering, University of Nevada, Reno, Nevada, USA. solution is the unique solution that balances the body force distribution, in this case GPE differences, while providing a Copyright 2006 by the American Geophysical Union. global minimum of the second invariant of stress. This finite 0094-8276/06/2005GL025307$05.00

L08202 1of5 L08202 DIMITROVA ET AL.: FAULTING ON MARS—GPE CONTRIBUTION L08202 element thin-sheet approach does not require detailed descriptions of the lithosphere rheology, but only a decision of whether we choose to treat the lithosphere as generally viscous or elastic. The solution is computed over a global grid of 2.5 2.5 resolution, which is based on the ability of current gravity models to resolve crustal thickness differences down to wavelengths of 300 km. The integrated vertical stress, whose gradients need to be balanced by the gradients of the integrated horizontal deviatoric stresses, has units of potential energy per unit area. We assume rcrust = 3 3 2 2900 kg/m , rmantle = 3500 kg/m ,andg =3.7m/s, consistent with the values used by Neumann et al. [2004] Figure 2. Predicted fault style, as defined in equation (1) in estimating the crustal thickness model. from the deviatoric stress field in Figure 1. Global map is [8] GPE is calculated by integrating to a depth, L, as the given in Figure S5. base of the thin shell [Molnar and Lyon-Caen, 1988], which corresponds to the highest point within the lithosphere consider greater depths L, i.e., thicker coupled layers (see where decoupling occurs below the elastic layer. For exam- 1 ple, if there is decoupling between the brittle upper crust Figure S4 ). and ductile lower crust, this depth is the brittle-ductile [10] We calculate the expected fault styles associated with transition. On the other hand, if there is coupling between the dynamic model. Anderson [1951] showed how styles of the brittle and ductile lithosphere, this depth is the contact faulting in the upper crust relate to principal stress magni- between the mantle lithosphere and the convecting mantle. tudes and orientations, connecting the three major fault Assuming no brittle-ductile lithospheric decoupling, the types to tectonic regimes. Since the Martian surface is a shallowest choice for such uniform depth is the deepest free surface and the vertical stress is a principal stress, we extent of the crust on the planet (L 92.84 km below zero can define a normalized parameter topography level at Arsia Mons). Although estimates of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi elastic thickness have shown variability [Banerdt et al., 2 2 A0 ¼ ðÞt1 þ t2 = t1 þ t2 ð1Þ 1992; Nimmo and Tanaka, 2005, and references therein], such effects are likely to be of second order as long as L to discriminate among the three major geologic fault styles encompasses the elastic layer in all regions. associated with the styles of the deviatoric stress field from the dynamic solution. Here t1 and t2 are the principal 3. Results horizontal deviatoric stresses, and the vertical deviatoric [9] The Martian deviatoric stress field associated with stress is À(t1+t2). Apart from the exceptions already noted horizontal GPE gradients shows, to first order, deviatoric in connection with low topography and thin crust, normal extension over topographically high areas transitioning to faulting is predicted as the dominant fault style for deviatoric compression at topographically low areas topographically high areas, thrust faulting for topographi- (Figure 1) due to the large degree 1 signal of the topo- cally low areas, and strike-slip faulting potentially in graphic and crustal dichotomy. A notable exception to this between (Figure 2). pattern is areas with low topography but thin crust, which [11] We develop objective measures for the fit of stresses exhibit propensity for deviatoric extension, for example, and associated strains with surface fault data (fault strike q, Isidis Plantitia and to a smaller extent Utopia, Argyre, rake l, dip d, and slip magnitude u). For each area k,we perform a Kostrov [1974] moment tensor summation to and Acidalia Planitae. This effect is amplified if we k estimate the total strain tensor, eij, in which it is assumed k that the unit moment tensor mij(q,l,d) and the slip magnitude uk do not vary with depth within the faulted layer [Schultz, 2003]. [12] We define objective functions that measure the correlation and misfit between the dynamically predicted stress field and the strain from fault observations as Cfull ¼ ðÞe Á t =ðÞET ; Mfull ¼ 0:51À Cfull ; ð2Þ

where the metrics E and T and the inner product e Á t are defined as Figure 1. Vertically integrated (L = 92.8 km) deviatoric pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi eijeij; T ¼ tijtij; e Á t ¼ eijtij: ð3Þ lithospheric stresses associated with GPE variations calculated from MOLA topography and inferred crustal thickness Here e is the 3-D strain from the Kostrov [1974] [Neumann et al., 2004], and assuming Poisson’s ratio of 0.5. ij summation of fault data, and t is the vertically integrated Red arrows represent deviatoric extension, while black ij arrows represent deviatoric compression. Global map is 1Auxiliary material is available at ftp://ftp.agu.org/apend/gl/ given in Figure S3. 2005gl025307.

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Figure 3. (a) Normal faults as identified by Anderson et al. [2001] (stage 1 – Noachian, stage 2 – Late Noachian-Early Hesperian, stage 3 – Early Hesperian, stage 4 – Late Hesperian-Early Amazonian, stage 5 – Middle-Late Amazonian). Areas discussed in the text include Alba Fossae (AF), Alba Patera (AP), Claritas Fossae (CF), Lunae Planum (LP), Mareotis Fossae (MaF), Memnonia Fossae (MeF), Margaritifer Terra (MT), Olympus Mons (OM), Sirenum Fossae (SF), Solis Planum (SP), Tantalus Fossae (TaF), Tempe Fossae (TeF), Thaumasia Fossae (ThF), and Valles Marineris (VM). (b) The misfit Mfull as defined in (2) between the faults in Figure 3a) and the full deviatoric stress field from Figure 1. (c) The misfit Mpre-existing as defined in the text between the faults in Figure 3a and the deviatoric stress field from Figure 1 while ignoring along fault-strike components of stress. (d) Histograms of the percent and length of faults fitted for various values of the misfits in Figures 3b and 3c.

3-D deviatoric stress (or strain) tensor obtained from the normal faults (69% of the faults have Mfull 0.1). The solution to the force-balance equations. This objective exceptions are areas in Margaritifer Terra, Olympus Mons function is minimized when the tensor solution of stress or and north of Alba Patera. Since the misfit measure in strain from the dynamic calculations is consistent with the equation (2) reflects both misfit to the fault strike and the formation of faults with the same strike and style as the fault fault style, we need a second measure to explain the cause data; thus, it accounts for fault strike and fault style, defined of the misfit. by the relative magnitudes of the principal axis of the stress [14] A second measure of misfit between the fault data tensor. The misfit function has values from 0 to 1, with 0 and stress data can be obtained if we consider whether the misfit indicating a perfect fit. stress field is consistent with the strike and style of pre- [13] Figure 3b shows the misfit of 19,897 normal fault existing faults. That is, we rotate the horizontal coordinates segments as identified by Anderson et al. [2001] with the for fault strain and model stress such that the x0 direction is GPE model from Figure 1. We have assumed a uniform aligned with the fault, and the metric and inner products are amount of slip for each fault as a first approximation. defined as Although fault displacements scale primarily with length, qffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi mechanical length depends on fault segmentation, spacing E ¼ e0 e0 ; T ¼ t0 t0 ; e Á t ¼ e0 t0 : ð4Þ and linkage, which are not recognized in the data set at the iy iy iy iy iy iy scale of the study. Thus, our eij reflects the simplest and least biased approach to incorporating fault-related strain to Using these in equation (2), we define a misfit Mpre-existing of compare with the stress model. Furthermore, the strain the model stress to the pre-existing faults, which measures tensor is linearly proportional to the slip, and the misfit whether the model stress field is aligned with the prescribed function Mfull is insensitive to scalar multiples of either the fault strike such as to produce the style of faulting, in our strain or stress tensor, and thus it is insensitive to the actual case normal faulting, and ignores any along strike stresses. value of uk. The GPE model fits a large fraction of the This new misfit is plotted in Figure 3c, and overall a slight

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flexural stresses were small, a combination of brittle and ductile deformation was likely to be widespread, and GPE stresses dominated. [18] Normal faults and wrinkle ridges are not synchro- nous, according to the inferred stratigraphic ages [Anderson et al., 2001]. Our model considers the time- averaged effect of internal buoyancy forces on the deviatoric lithospheric stresses. These buoyancy forces, together with radial basal tractions, supported the topography during the times of faulting. Perhaps the timing of faulting, as well as the misfit of existing models with the faulting in some regions, could be explained by systematic modeling of time-dependent sources of stress. Such sources include sub- and intra- lithospheric volcanic loads [McGovern et al., 2001], as well as localized reduction in elastic strength (and membrane and flexural stresses) due to heating associated with volcanism, against a background of progressive cooling and thickening of the lithosphere resulting in increase of membrane and Figure 4. Wrinkle ridge structures with transects roughly flexural stresses. For example, it is possible that the GPE perpendicular to the ridges in (a) Solis Planum and (b) associated stresses, during times of low elastic strength, northern flank of Alba Patera [Montesi and Zuber, 2003, may be responsible for most of the normal faults in the and references therein] overlain by the GPE deviatoric stress Tharsis province and the wrinkle ridges in the northern field from Figure 1. Additional maps are given in Figures plains, while a time-dependent combination of stress S7 and S8. sources may explain the normal faults in Tantalus and Tempe Fossae and the wrinkle ridge structures in Lunae and Solis Planae. improvement to the fit is observed (Figure 3d, 71% of the faults have Mpre-existing 0.1). A few areas show a marked [19] Acknowledgments. We acknowledge helpful suggestions by two improvement (much lower M than M ), for anonymous reviewers. This work was supported by NSF grant EAR- pre-existing full 0310193 to WEH, and NASA Mars Data Analysis Program grants to RAS. example, the east-west fault at 170–157.5W, À15S, indicating that there we largely misfit the relative References magnitudes of the along-strike stress as compared to the Anderson, E. M. (1951), The Dynamics of Faulting and Dike Formation fault-normal stress. 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