Utopia and Hellas basins, Mars: Twins separated at birth

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005je002666, 2006 Utopia and Hellas basins, Mars: Twins separated at birth Mindi L. Searls, 1 W. Bruce Banerdt, 2 and Roger J. Phillips 1 Received 7 December 2005; revised 30 March 2006; accepted 13 April 2006; published 17 August [1] Using topography and gravity data as constraints, we formulate spherical harmonic thin elastic-shell models to determine the subsurface structure of the Hellas and Utopia basins. For Hellas, we show that our model is consistent with the elastic thickness results of McGovern et al. (2002, 2004). The thin elastic lithosphere at the time of formation implies that Hellas is close to isostatic. Since Utopia formed earlier, we argue that an isostatic assumption is justified for the Utopia basin before it was filled. From this supposition, we derive a system of equations that allows us to solve for the amount of fill, the prefill topography, and the amount of flexure due to the fill within the Utopia basin. An analysis of the parameter space shows that the fill density and the amount of fill is strongly dependent on the elastic thickness at the time of infilling. A thinner elastic lithosphere favors a denser fill, while a thicker lithosphere will allow for less dense material. Likewise, larger crustal thickness values lead to smaller fill density values. The presence of quasi-circular depressions, interpreted as impact craters, within the Utopia basin indicates that the majority of the material within Utopia was deposited prior to Ga. The early timing for the deposition combined with the heat imparted by the basin forming event argues for a thinner lithosphere which could, in turn, suggest fill densities that are more consistent with a volcanic load than with pure sediment or ice-rich material. These results are supported using an alternative method of determining the amount of fill and flexure within Utopia. This model assumes that Hellas and Utopia were initially identical and that the only difference in their subsequent evolution was the addition of material in the Utopia basin. The volume of material needed to fill Utopia is immense (on the order of 50 million km 3 or more). The high density obtained for the fill requires that it contain a large igneous component, the source of which is problematic. Relaxing the isostatic assumption to a reasonable degree perturbs the density bound only slightly. Citation: Searls, M. L., W. B. Banerdt, and R. J. Phillips (2006), Utopia and Hellas basins, Mars: Twins separated at birth, J. Geophys. Res., 111,, doi: /2005je Introduction [2] The topographic signature of Mars is dominated by the dichotomy between the old, heavily cratered southern highlands and the smooth low-lying terrain of the northern hemisphere. Part of the topographic low can be explained by the presence of Utopia basin. With a diameter of 3000 km, Utopia is one of the largest impact structures in the solar system [Thomson and Head, 2001]. Despite the large diameter of this basin its topographic signature is marked by a shallow 1 3 km depression [Smith et al., 1999]. Additionally, with a free-air gravity high of several hundred mgal [Lemoine et al., 2001; Yuan et al., 2001], Utopia shows the classical signs of mascon loading (see Figure 1). 1 Department of Earth and Planetary Sciences and McDonnell Center for the Space Sciences, Washington University, Saint Louis, Missouri, USA. 2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. Copyright 2006 by the American Geophysical Union /06/2005JE [3] A great deal of work has been done in determining the resurfacing history of the northern lowlands [e.g., Buczkowski and Cooke, 2004; Frey et al., 2002; Head et al., 2002; Tanaka and Scott, 1987; Tanaka et al., 2003]; however, most of this research has focused on the depth and characteristics of the Hesperian and Amazonian plains units which cover an older, heavily cratered surface. In the present study we use the topography and gravity data from recent Mars missions to analyze the subsurface structure of Utopia basin, focusing on the volume and density of the material that fills the basin. The presence of buried craters within the Utopia basin [Frey et al., 2002] indicates that any appreciable amount of fill within Utopia was deposited in the Noachian; therefore an analysis of the amount and density of the fill within Utopia could provide valuable insight to the depositional environment or intensity of volcanism of the northern lowlands during the earliest epoch of Martian history. [4] The diameter of Utopia is equivalent to that of another ancient impact basin on Mars, Hellas basin. Although Utopia and Hellas are similar in size and age [Tanaka and Leonard, 1995; Thomson and Head, 2001], they differ in other aspects. In contrast with Utopia s subtle features, the 1of13

2 Figure 1. Global view of the observed gravity anomalies (expanded to l = 10) draped over a three-dimensional view of the observed topography centered on 80 E. Image is a sinusoidal projection. Hellas basin is a major topographic structure of the southern highlands of Mars with an overall relief of 9 km[smith et al., 1999]. An analysis of the gravity field highlights another point of contrast between the basins. Utopia displays one of the larger positive gravity anomalies on Mars, while the gravity signal associated with Hellas is a subdued, slightly negative anomaly [Lemoine et al., 2001; Yuan et al., 2001]. The striking differences between the basins can possibly be attributed to differences in the depositional environment. The average elevation of Utopia is 4 km below the reference geoid and, along with the rest of the northern lowlands, this basin was likely a sink for sediment transported via valley networks as well as volcanic and aeolian material [Banerdt and Vidal, 2001; Smith et al., 2001]. Topographically, source regions for the Hellas basin are relatively limited [Banerdt and Vidal, 2001]. [5] In this study, spherical harmonic thin elastic-shell loading models are used to investigate the mechanics of the Martian impact basins Hellas and Utopia using two distinct approaches. For the first model, we begin by exploring the isostatic state of Hellas. Both the Hellas and Utopia basins formed in the early Noachian [Frey, 2006] when the outer part of the planet presumably had a very high temperature gradient [Hauck and Phillips, 2002]. The resulting thin effective elastic lithosphere would likely have allowed for rapid compensation of the originally unfilled basins. The lack of a large-scale free-air gravity anomaly over Hellas indicates that it is presently very close to isostatic equilibrium (as also indicated by spectral admittance studies [McGovern et al. 2002, 2004]), while Utopia s gravity high indicates that it is not. As Hellas is mostly unfilled [e.g., Moore and Edgett, 1993; Smith et al., 1999; Wichman and Schultz, 1989] and is somewhat younger than Utopia [Frey, 2006], it is reasonable to assume that prefill Utopia, responding to a hotter planet [Hauck and Phillips, 2002], was at least as close to isostatic equilibrium as Hellas is now. [6] Using the assumption that the initial isostatic state of Utopia is similar to that of Hellas allows us to constrain a model for Utopia that enables investigation of the subsurface structure of Utopia basin. On the basis of the work of Banerdt [1986], we derive a system of equations that will allow us to solve for the original basin shape, the amount of fill within Utopia basin, and the amount of flexure due to the fill material. Given a lithospheric thickness this model also allows us to place constraints on the density of the fill material. [7] We will also present an alternative method of determining the amount of fill and flexure within Utopia. Using the assumptions that the initial depths as well as the initial isostatic state of the basins were identical, we start with the current observed topography of Hellas, fill it with material, and allow the basin to flex in response to the load until the final topography and geoid matches that currently observed for Utopia. 2. Hellas 2.1. Hellas Model [8] As Utopia and Hellas are similar in size and age, an analysis of the isostatic state of Hellas can provide valuable insight into the isostatic state of Utopia prior to infilling. In the modeling of Hellas basin the goal is to determine whether or not an assumption of isostatic equilibrium holds true for an ancient unfilled basin. To achieve this goal, we compare the observed geoid of Hellas to a model geoid derived under the assumption that the Hellas basin reached a state of isostatic compensation shortly after formation. [9] The calculations for the isostatic model geoid are based on the thin elastic-shell model described by Banerdt [1986]. The equations derived are spectral solutions; that is, the equations relate the spherical harmonic coefficients for each degree l and order m. The approach used with the thinshell model yields the model geoid (G lm ), given an isostatic crustal thickness perturbation at the Moho (dc lm ), basin fill (F lm ), and observed surface topography (H lm ). ( ) 3 R ðlþ2þ cr G lm ¼ r rð2l þ 1Þ c ðh lm F lm ÞþDrdc lm þ r R f F lm ; 0 ð1þ where R 0 is the planetary reference radius, R cr is the radius to the base of the crust, and densities, r, are defined in Table 1. All quantities are positive if they lie in a positive spherical coordinate radial direction with the exception of the load which is defined as positive downward. The first term in the model geoid equation describes the contribution of the unfilled basin (H lm F lm ) topography to the geoid, the second term relates to topography on the Moho, and the last term is the contribution of the basin fill (for our calculations for Hellas we set the density of the fill equal to that of the crust, i.e. r f = r c ). Table 1. Nominal Parameter Values Parameter Name Symbol Value Units Crustal density r c 2900 kg/m 3 Mantle density r M 3500 kg/m 3 Density contrast Dr = r M r c 600 kg/m 3 Mean density r 3933 kg/m 3 Young s modulus E Pa Poisson s ratio n 0.25 Planetary radius R km Mean gravitational acceleration g m/s 2 7 2of13

3 where a l ¼ R4 0 ðf l þ 1 nþ ; D fl 3 þ 4fl 2 þ yð1 n 2 Þðf l þ 2Þ f l ð1 þ n f l =yþ g l ¼ a l ; ð5þ f l þ 1 n Figure 2. Degree of compensation as a function of spherical harmonic degree, l. The elastic thickness used, 5 km, is appropriate for the Hellas basin at the time of its formation. [10] In this model we assume Airy compensation. If the basin is completely isostatic, then Airy compensation gives a mass balance of Drdc lm ¼ r c ðh lm F lm Þ; ð2þ where we assume that the crust did not isostatically adjust to the small amount of fill added to the Hellas basin. As the dominant wavelengths of Hellas are comparable to planetary radius, some of the basin will be supported by elastic membrane stresses [Turcotte et al., 1981], and equation (2) must be modified accordingly. In an elasticplate model, mass balance will only be achieved if the elastic thickness and/or Young s modulus are low, the precise values for this depending on wavelength. The same is true for an elastic shell, but now the inclusion of membrane support moves the isostatic support of a load farther away from mass balance for the same set of elastic parameters. This can be expressed by a degree of compensation [Turcotte et al., 1981], C l,anl-dependent measure of the fraction of the load that is in mass balance for a spherical elastic shell. Isostatic equilibrium is now expressed as Drdc lm ¼ r c C l ðh lm F lm Þ ð3þ and mass balance is achieved only when C l! 1. Using Banerdt [1986] as a basis, the degree of compensation is given by where f l = l(l + 1), y =12R 0 2 /T e 2, and D = ET e 3 /[12(1 n 2 )]. [11] The flexure of the lithosphere is denoted by w lm, and T e and T cr are the elastic thickness and the crustal thickness, respectively. McGovern et al. [2002, 2004] estimates that the elastic thickness at the time of formation (T e ) for the Hellas basin is less than 13 km with a best fit of 5 km. In Figure 2 we show, for T e = 5 km, the corresponding degree of compensation, C l, indicating that at the long wavelengths (low l) appropriate for Hellas, the basin is about 97% compensated by mass balance; that is, the Hellas basin is close to being isostatic. [12] In the modeling done here, T cr, and T e cannot be determined uniquely. Our approach is to adopt the T e solution for Hellas of 5 km, as determined by spectral admittance methods of McGovern et al. [2002, 2004]. In comparing the observed and model geoids, if the best fitting solutions yield a T cr value in agreement with the 50 km value found by McGovern et al. [2002, 2004], then the method adopted here is valid and an isostatic prefill assumption can be justified. These authors found that spectral admittance methods yield robust results at Hellas for both T cr, and T e. Our approach can corroborate their spectral results. [13] The method adopted in this study is preferable over the admittance method of McGovern et al. [2002, 2004] for two reasons. First, buried loads that are correlated with topography can be modeled with the admittance method; however, the correlation of the gravity and topography at Utopia is low and the loading models used by McGovern et al. [2002, 2004] cannot account for these low correlation values. Once the validity of the method outlined above is established by a comparison of the Hellas results with published spectral admittance results, then this method can be confidently applied to Utopia. Second, the effect of nonzero basin fill on isostatic equilibrium at Hellas can be tested, an approach highly amenable to the methods adopted here Gravity and Topography [14] The observed geoid used for our modeling is from a spherical harmonic gravity model (JGM95I01) of degree and order 90 that was developed via radio tracking of Mars ð C l ¼ r M r c Þ w lm r c H lm F lm ( " 3 a l 1 rð2l þ 1Þ r c þ Dr R # ) l cr n þ g R l 0 1 n T 1 e R 0 ¼ ( " # ) 1 Drg a 3 l 1 rð2l þ 1Þ Dr þ r R lþ2 cr c þ g h l n i ; r R 0 DrR c 0 1 n T e T cr r M ðt e T cr Þ ð4þ 3of13

4 Figure 3. Comparison of (a) the observed geoid with (b) a best fit for the model geoid for Hellas Basin (Mercator projection from latitude 65 to 10 and longitude 30 E to 110 E). The model geoid shown includes 1 km of fill, and an elastic thickness of 5 km and yields a regional crustal thickness of 87 km. Both images have been filtered using a high-pass filter with a cosine taper from 2 to 5 and have been cut off at degree 50. Global Surveyor (MGS), Odyssey, Pathfinder, and the Viking 1 Lander (G. L. Tyler et al., JGM95I01.SHA, in MGS RST Science Data Products, USA_NASA_JPL_ MORS_1024, edited by R.A. Simpson, Data set MGS-M- RSS-5 SDP-V1.0, 2004, NASA Planetary Data System, available at rsdata.html). An unfiltered view of the Hellas region shows that the Arabia bulge dominates the long-wavelength geoid signal [Phillips et al., 2001]; therefore filtering of the data is required in order to isolate the desired Hellas basin signal. The Arabia bulge and Tharsis trough, manifested in both the shape and geoid of the Mars, are due to the effects of the Tharsis load globally deforming the planet [Phillips et al., 2001]. The diameter of the Hellas basin corresponds by a half-wavelength argument to spherical harmonic degree l = 5; thus Hellas can be represented predominantly by degrees l 5. A high-pass filter with a cosine taper from 2 to 5 is applied here to effectively subtract off the longer-wavelength effect of Tharsis loading while leaving the shorter-wavelength basin. The geoid model is complete to degree and order 95; however, owing to the long wavelength nature of Hellas, a lowpass filter with a degree cutoff of l = 50 is also applied. The spherical harmonic coefficients for topography (gtm090aa) were derived from the Mars Orbiter Laser Altimeter (MOLA) 0.5-degree gridded data set and can be found through NASA s Planetary Data System at pds-geosciences.wustl.edu/missions/mgs/shadr.html. It is important to note that the topographic coefficients used throughout this paper are referenced to the center of mass and not to the geoid. The same filters that were used for the geoid are applied to the topographic spherical harmonic coefficients Hellas Results [15] With these geoid and topography data sets, we carried out the analysis described in section 2.1 to find a best fitting crustal thickness based on equations (1), (3), (4), and (5), T e = 5 km, r f = r c, and other parameters the same as in work by McGovern et al. [2002]. The amount of fill, F lm, within Hellas is not well constrained. There have been several studies attempting to describe the basin deposits. Leonard and Tanaka [2001] outlined a history of volcanic, aeolian, and fluvial deposition and erosion within the Hellas region. Kargel and Strom [1992] suggested that Hellas was modified by glacial activity that scoured the basin resulting in 200 m of erosion. On the basis of the high wind velocities within the basin, Moore and Edgett [1993] concluded that Hellas basin would undergo net dust erosion. Moreover, Wichman and Schultz [1989] believe that there is 1 km of basaltic fill covering the basin floor. For our model we allowed the amount of fill within Hellas to vary. The fill term was initially created as a latitude/longitude grid with spacing of 0.25 degrees. All values outside of Hellas were assigned a value of zero while all data values inside of the basin were assigned a one. This allowed us to easily create a grid with any amount of fill required. Once the data values for each latitude and longitude are known, the spherical harmonic coefficients representing the fill were computed via numerical integration. For the calculations done here, I allowed for fill thicknesses ranging from 0 km to 1 km. [16] In order to quantify the mean (or reference) crustal thickness that provides the best fit between the observed and modeled geoid, the spectral geoids were converted into the spatial domain and the error between the geoids was calculated as a function of T cr. Data and model values for 4of13

5 Figure 4. Schematic view of the structure of Utopia basin. All quantities are defined in the text. They are positive if they lie in a positive spherical coordinate radial direction, with the exception of the load which is defined as positive downward. The solid lines represent the prefill topography, while the dashed lines represent the postfill structure, which accounts for flexure of the lithosphere. each latitude (q) and longitude (j) over a quarter degree grid were used to calculate a root-mean square error E 2 ðt cr Þ ¼ 1 X Jmax J max j¼1 h i 2; G q j ; j j ; T cr G obs q j ; j j ð6þ where J max is the number of data points. For T e = 5 km, the minimum error in comparing the model geoid and the observed geoid occurred with crustal thickness values of 43 km and 87 km, given the end-members of no basin fill and 1 km of basin fill, respectively. With a fill of 160 m we can match the 50 km crustal thickness value of McGovern et al. [2002, 2004] exactly. A comparison of the observed geoid and a best fit for the modeled geoid is given in Figure 3. The slight mismatch in the eastern portion of Hellas basin is most likely the result of spatial variations in fill thickness, which is not accounted for in this model. [17] The values for crustal thickness that were calculated based on the assumption of initial spherical isostatic compensation are consistent, over the assumed range of possible fill, with the 50-km value of crustal thickness used in the spectral admittance modeling by McGovern et al. [2002, 2004]. The agreement between the results presented here and spectral admittance results validates the approach adopted in this study and supports an isostatic assumption for an ancient unfilled basin. 3. Utopia 3.1. Utopia Model [18] On the basis of the work of Banerdt [1986], we derive a suite of equations that will allow us to explore the subsurface structure of the Utopia basin. This system of six equations solves for the original basin topography before infilling occurred, the amount of fill within the basin, and the amount of flexure in response to this added load, as well as the vertical load, the horizontal load potential, and the geoid at the crust-mantle boundary. In the modeling of Utopia, the observed geoid and topography are used as boundary conditions. This allows solution for flexural/ membrane deflection plus an additional subsurface parameter, which in the work by Banerdt [1986] was either a crustal perturbation on the Moho or a density anomaly in the upper mantle. Here we are able to solve for both the original basin configuration and amount of fill within the Utopia basin by introducing a new equation: the geometrical relationship between the observed topography, the original basin topography, the amount of fill, and the amount of flexure. [19] As discussed earlier, the assumption of isostatic equilibrium prior to fill is reasonable to apply to Utopia, as it is somewhat older than Hellas. On the basis of our results at Hellas, the geoid of the original Utopia basin before infilling occurred can be expressed as ( " # ) 3 R lþ2 cr G iso;lm ¼ r rð2l þ 1Þ c O lm C l r c O lm ; ð7þ R 0 where O lm is the topography of the original basin before fill and by analogy to Hellas, C l is calculated with a prefill elastic thickness value of 5 km. As before, the equations are spectral. A schematic representation of the Utopia model is presented in Figure 4. The solid lines in this figure represent the prefill basin geometry while the dashed lines show the basin configuration after basin infilling and flexure. 5of13

6 [20] After isostasy is achieved, the basin is loaded with material of density r f. As the fill load is substantial in Utopia, this formulation will treat the fill rigorously in the equations of mechanical equilibrium. The weight of the fill will cause a downward displacement of the shell (w lm ), which will equally depress the Moho, where there is a density contrast of Dr = r M r c. The downward displacements at the top and bottom of the lithosphere lead to a downward displacement of the geoid, while the additional mass of the load causes an upward displacement of the geoid; therefore the perturbation of the geoid due to the loading and the resulting flexure can be expressed as follows: ( " # ) 3 R lþ2 cr DG lm ¼ r rð2l þ 1Þ f F lm þ r c w lm þ Drw lm : ð8þ R 0 The total geoid is a combination of the original basin and the effect of the fill, G lm ¼ G iso;lm þ DG lm ( 3 ¼ r rð2l þ 1Þ c ðo lm þ w lm Þþr f F lm " þ ðdrw lm C l r c O lm Þ R #) lþ2 cr : ð9þ R 0 The geoid at the Moho, G c,lm, is defined as the departure of the gravitational equipotential surface from its hydrostatic value at the base of the crust and can be derived in a similar fashion, giving ( 3 h G c;lm ¼ r rð2l þ 1Þ c ðo lm þ w lm Þþr f F lm i : R cr R 0 þ Drw lm C l r c O lm ): ð10þ [21] The overall load on the Utopia system is a combination of surface and interior loads. Any boundary representing a density contrast which has been vertically displaced will result in a load. The original basin shape, flexure and fill all contribute to the surface loading of the planet, q s;lm ¼ r c go ð lm þ w lm G lm Þþr f F lm : ð11þ The subsurface load consists of flexure at the bottom of the lithosphere and the upward movement of the Moho that occurred in response to the original basin formation, q b;lm ¼ Drg w lm G c;lm rc gc l O lm : ð12þ Combining (11) and (12) gives us a net load of q lm ¼ r c go ð lm C l O lm þ w lm G lm Þþr f gf lm þ Drg w lm G c;lm : ð13þ [22] The horizontal forces acting on the lithosphere also need to be accounted for. The horizontal load potential (W lm ) as defined by Banerdt [1986] serves to describe the effect of l the horizontal load due to slopes in density boundaries. We have rederived the horizontal load potential to be consistent with the geometry shown in Figure 4, W lm n 1 n r H lm cgt e þ n R 0 1 n r Flm f gt e n R 0 1 n gt ð e T cr Þ C lr c O lm þ ½r R c gt cr þ r m gt ð e T cr ÞŠ w lm : ð14þ 0 R 0 The vertical displacement of the lithospheric shell is related to both the vertical load and the horizontal load potential via the following relationship [Banerdt, 1986]: w lm ¼ a l q lm þ g l W lm ; ð15þ where a l and g l are defined in equation (5) and now incorporate values of elastic thickness, T e, at the time of infilling. Subsequent discussions of elastic thickness, now a model parameter, refer to this later value. To complete the system a sixth equation is needed. The observed topography is a combination of the original basin, the amount of fill, and the flexure; therefore H lm ¼ O lm þ F lm þ w lm : ð16þ [23] We now have a solvable system of six equations (equations (9), (10), and (13) (16)) and six unknowns (O lm, F lm, w lm, G c,lm, q lm, W lm ) with boundary conditions of observed topography (H lm ) and geoid (G lm ). Because Hellas and Utopia are similar in size, the same filters that were used in analysis of Hellas are employed in the modeling of Utopia Utopia Results [24] Combining crustal thickness estimates derived from viscous relaxation studies [Nimmo and Stevenson, 2001; Zuber et al., 2000], a thorium mass balance calculation [McLennan, 2001], a spectral-admittance study [McGovern et al., 2002], and geoid-to-topography ratios, Wieczorek and Zuber [2004] found that these estimates are consistent with a mean crustal thickness of 50 ± 12 km. Applying a regional crustal thickness of 35 km for the northern lowlands (consistent with the results of Neumann et al. [2004]), an elastic thickness at time of basin infilling of 70 km, a fill density of 2900 kg/m 3 and other parameters as given in Table 1, the model results for Utopia show that prior to infilling the original basin shape is characterized by a depth of 5 km for this choice of model parameters (see Figure 5). After basin formation, the Utopia impact structure is subsequently modified with 20 km of basin fill. In response to this basin fill, we calculate an associated 14 km of lithospheric flexure. However, these results will vary depending on the chosen model parameters. [25] An exploration of the model parameter space was made in order to understand the relationships between the parameters and the output of the model. In Figure 6, we present an analysis of how the elastic thickness at the time of infilling affects the prefill basin depth and the amount of fill for various values of fill densities. These values represent the deepest point spatially in the original basin and the maximum amount of fill within the basin. In this analysis 6of13

7 Figure 5. Modeled (a) prefill basin shape, (b) depth of fill, and (c) lithospheric flexure of Utopia Basin (sinusoidal projection from latitude 5 to 80 and longitude 60 E to 165 E). For this example the crustal thickness is 35 km, the elastic lithosphere thickness is 70 km, and the fill density is 2900 kg/m 3. These results will vary depending on the model parameters. we first set the crustal thickness to 35 km (Figures 6a and 6b) while all other parameters are as outlined in Table 1. Since we assume that Utopia, like Hellas, was compensated before infilling, the deepest the prefill basin could have been is 6.2 km for this set of model parameters after accounting for membrane support (the degree of compensation, C l, factor). If the basin was any deeper than that, the basin could not have been in spherical isostatic equilibrium because not enough crustal material could have been displaced at the Moho to compensate for the missing topography. In effect, mantle flow would have shallowed the basin to 6.2 km in a drive toward mechanical equilibrium (a quasi-minimum stress state). In Figure 6, the regions that violate this criterion are shaded, while the valid portions of the graph are unshaded. If the crust in the lowlands is thicker than 35 km, then the isostatic prefill basin depth could be deeper (9 km with a crustal thickness of 50 km) and still satisfy the isostatic assumption. Given that the crust in the northern hemisphere is on average thinner than that of the southern hemisphere [Neumann et al., 2004; Zuber et al., 2000], the uncertainties in calculating the crustal thickness allow that the crust beneath Utopia basin could be as much as 50 km. Figures 6c and 6d show minimum prefill basin depth and the maximum amount of fill for a background crustal thickness of 50 km. From Figure 6 we can see that the fill density and the amount of fill is strongly dependent on the elastic thickness at the time of infilling. Lower values of fill density are allowed only at higher values of T e, while higher fill densities are permissible at all values of elastic thickness if we allow for a shallow prefill basin depth at higher values of T e. Given a range of elastic thickness from 0 to 150 km, fill densities range from >3400 to 2400 kg/m 3. Fill densities greater than 3300 kg/m 3 would imply extremely shallow initial basin depths of less than 3 km at the deepest point. If we increase the crustal thickness in the northern lowlands to 50 km in our model, the range of fill densities would increase to allow for fill densities as low as 2300 kg/m 3 for large values of T e. [26] Neumann et al. [2004] suggested that the morphology of the uplifted Moho under Utopia is indicative that the entire crust was excavated during basin formation. If this was the case, the depth of the prefill isostatic basin would have been 6.2 km with an assumed background crustal thickness of 35 km and other parameters as given in Table 1. If this constraint is applied, we can relate the elastic thickness (T e ) at the time of basin infilling with the density of the fill and the amount of fill within the basin (Figures 6a and 6b). For example, if we assume an elastic thickness of 75 km, then the density of the fill is 2800 kg/m 3 and at the deepest point in the basin there is 20 km of fill material. [27] We have also examined how the assumed crustal density affects the mechanics of the basin, in particular, the depth of the basin before infilling and the amount of fill. If we allow a range in crustal densities from 2700 to 3100 kg/m 3, the prefill basin depth will vary by only ±0.6 km and the amount of fill will vary by ±1.5 km. Thus the crustal density as well as the density contrast between the crust and mantle play minor roles when compared to the effect that the elastic thickness has on the model results. 4. Alternative Approach [28] In this section we present an alternative, yet complimentary, method to calculate the amount of fill and corresponding flexure associated with Utopia basin. We start with the explicit assumption that Utopia and Hellas formed at approximately the same time and were initially identical, and that the only difference in their subsequent evolution was the addition of material to the Utopia basin. This does not mean that no other processes were active, just that the only difference in their modification history after formation was the filling of Utopia. Our goal is to determine which combinations of fill density (r f ), crustal density (r c ), crustal thickness (T cr ), and elastic lithosphere thickness (T e ) are consistent with this model with the observed boundary conditions of topography and gravity. [29] We start with the current observed topography and geoid of Hellas and for each spherical harmonic fill it with 7of13

8 Figure 6. Dependence of the prefill basin depth and the basin fill on the elastic thickness at the time of infilling for various values of fill density. (a, b) Calculated using a regional crustal thickness of 35 km. (c, d) Calculated using a regional crustal thickness of 50 km. All other parameters as shown in Table 1. The unshaded region represents portions of the graph that are physically possible, while the shaded regions violate the prefill isostatic assumption. These values represent the lowest point in the original basin and the corresponding fill amount at the deepest point. material of some density r f, allowing flexural response of a structure with an assumed T e, T cr, and r c, until the final topography matches that currently observed for Utopia. As before, we base our calculations on the thin shell formulation of Banerdt [1986]. For this analysis we include harmonics l = The resulting geoid signature is then calculated (which includes contributions from the unfilled Hellas anomaly, fill and crustal flexure) and compared to the observed Utopia anomaly (note that the amplitude of the observed anomaly with respect to the regional level is about 150 m). If the geoid amplitudes match, the combination of parameters is considered permissible. Figure 7 shows an example of one such calculation. [30] This procedure was used to investigate the (T e, T cr, r f, r c ) parameter space by fixing two parameters, varying the other two, and calculating the resulting geoid amplitudes as described above. Figure 8 shows contours of geoid as a function of T e and r f for T cr = 50 km and r c = 2900 kg/m 3.In general, the size of the geoid anomaly increases with both elastic lithosphere thickness and fill density. In fact, the geoid signature will vanish for sufficiently low values of these parameters. Using the geoid contour that best matches the observed anomaly (150 ± 25 m), we find that for a range of lithosphere thicknesses from 25 to 100 km, the fill density is between 2450 and 2900 kg/m 3. For this set of model parameters high fill densities corresponding to volcanic material (>2750 kg/m 3 ) are permissible only for lithosphere thicknesses less than 50 km. Conversely, very low fill densities that would be characteristic of a high water fraction require excessive lithosphere thicknesses, in excess of 100 km. [31] Similar to the previous model in section 3, an analysis of the parameter space shows that this model is also relatively insensitive to the crustal parameters. The dashed line in Figure 8 shows how doubling the crustal thickness to 100 km would affect the model. The assumption that the initial basin depth of Hellas and Utopia were identical places a lower limit of about 35 km on the range of 8of13

9 Figure 7. Comparison of the observed geoid of Utopia with a matching one calculated from the model for a filled Hellas. For this example the crustal thickness, T cr,is 50 km, lithosphere thickness, T e, is 100 km, crustal density is 2900 kg/m 3, and fill density is 2450 kg/m 3. crustal thickness that can be allowed in this model, on the basis of the assumption that the unfilled depth is equal to the observed depth of Hellas. If the crust is thinner than this lower bound, it will not be possible to uplift the Moho enough to match the initial isostatic state of Hellas. This constraint is similar to that discussed in the previous section. 5. Discussion [32] A comparison of the two Utopia models (Figures 6c and 8) show similarities in the relationship between elastic thickness and fill density for an initial depth of 9 km. The fill densities obtained using the method in section 3 are slightly higher than the values obtained using the other approach (on average 120 kg/m 3 higher). This difference can be partly negated by using a thinner lithosphere at the time of basin formation. For the calculations in section 3, the lithospheric thickness at the time of basin formation was set at 5 km; as mentioned, this is based on the admittance estimate of McGovern et al. [2002, 2004]. Decreasing the lithospheric thickness at the time of basin formation increases the degree of compensation, C l, allowing the prefill basin to become closer to mass balance; that is, the Moho rises slightly higher. The effect of this would be to decrease the density of the fill providing a closer match between the models. [33] These models for the formation of the Utopia basin imply that it is an extremely deep structure. For a fill thickness of 18 km, nearly km 3 of material is required to fill it to the present level. This is a huge amount, equivalent to the volume of a 350-m layer covering the entire planet. From another perspective, the entire volume of an ocean filling the northern plains to the putative Contact 2 shoreline [Head et al., 1999; Parker et al., 1993] would fill only one quarter of Utopia. [34] This huge volume of material filling Utopia begs the question of where it came from, and how it was transported to this location. This problem is compounded by the short timeframe for this process. The presence of quasi-circular depressions (QCDs), interpreted as mostly buried impact craters, throughout the northern lowlands and Utopia Planitia indicates that the visible smooth plains surface is only a thin veneer of material that covers a basement of early Noachian terrain [Frey, 2006; Frey et al., 2002]. The areal density of QCDs in the Utopia basin is not particularly different than elsewhere in the northern lowlands, suggesting that the emplacement of the Utopia basin fill must have occurred rapidly and relatively early in Martian history, before the end of heavy bombardment. On the basis of correlations between N(200) crater retention ages and the Hartmann-Neukum model chronology [Hartmann and Neukum, 2001], Frey [2006] has suggested a formation age of > Ga for the Utopia basin and a formation time of > Ga for the buried lowlands. This suggests that the majority of the basin material was deposited prior to 4.04 Ga, and that this infilling occurred relatively quickly. The Hartmann-Neukum timescale that these absolute ages are based on contains a high level of uncertainty [Frey, 2006]; however, as it is unlikely that all craters larger than 200 km were included in the N(200) age, the absolute ages are most likely older than these values [Frey, 2006]. [35] Since the fill densities in our models are dependent on the thickness of the elastic lithosphere at the time of basin filling, Frey s [2006] work leads us to analyze how Figure 8. Geoid anomaly amplitude calculated for varying values of elastic lithosphere thickness and fill density. Crustal thickness and density are held constant at 50 km and 2900 kg/m 3, respectively. The best fitting geoid amplitude (150 ± 25 m) is denoted by the blue contour. The dashed line shows the equivalent 150-m contour for a crustal thickness of 100 km. 9of13

10 Figure 9. Steady state conductive model of the temperature profile of Mars at 4 Ga given a surface heat flux of 65 mw/m 2, a coefficient of thermal conductivity of 3 W/mK for the crust and 4 W/mK for the mantle, a surface temperature of 220 K, a crustal thickness of 35 km, and a mantle composition of depleted peridotite. The dashed line assumes a crust of basalt (surface type 1), while the solid line is appropriate for a crust of basaltic-andesite (surface type 2). The base of the elastic lithosphere (900 K isotherm) is at 34 km depth for surface type 1 and 70 km for surface type 2. thick the elastic lithosphere in the Utopia region would be at 4.04 Ga. A basic approach to this problem is to assume that the elastic lithosphere at 4 Ga in the Utopia region will not be thicker than the average global value at that time. Using a simple steady state heat conduction model with volumetric heat production [e.g., Turcotte and Schubert, 2002], we can estimate the thickness of the elastic lithosphere based on an assumption of its basal temperature value. To do this we need to know the composition of the Martian crust; however, this has been a subject of recent debate [McSween et al., 2003; Wyatt and McSween, 2002; Wyatt et al., 2004]. The surface lithology of Mars has been broken into two types: surface type 1 is interpreted as having a basaltic composition, while surface type 2 has been interpreted as either basaltic-andesite or altered basalt [Wyatt et al., 2004]. As the amount of heat producing elements within type 1 is less than that of type 2 (assuming type 2 is basaltic-andesite, which provides a bounding value of heat source content), we will model both types of crust using the radiogenic element concentrations as outlined by Nimmo and Tanaka [2005]. Given that the composition of the Martian mantle is likely similar to that of the Earth [Wanke and Dreibus, 1994], we assume an upper mantle composition of depleted peridotite for our model. With a surface heat flux at 4 Ga of 65 mw/m 2 [Hauck and Phillips, 2002], a coefficient of thermal conductivity of 3 W/m-K for the crust and 4 W/m-K for the mantle, and a surface temperature of 220 K, we can calculate the depth to the 900 K isotherm, which can be used as a reasonable proxy for the base of the elastic lithosphere [Anderson, 1995; Watts, 2001]. For a 35-km crust, the base of the elastic lithosphere is 34 km for surface type 1 and 70 km for surface type 2 (see Figure 9). For an elastic thickness of <70 km, the density of the fill within Utopia basin would be >2850 kg/m 3 (see Figure 6a). For the same range of lithospheric thickness, a 50-km crust would allow for a less dense fill of >2700 kg/m 3 for the model presented in section 3 (see Figure 6c) and an ever lower value of >2600 kg/m 3 for the model presented in section 4 (see Figure 8). As with most thermal models, this model is sensitive to the input parameters. Increasing the crustal thickness or allowing for higher radiogenic element concentrations than type 2 within the crust would result in an increase in the elastic thickness (and allow for lower fill densities). However, this simple model does not account for the energy imparted by the impactor during basin formation. The heat from the impact would have caused a regional thinning of the lithosphere. This line of reasoning argues for denser fill materials and greater amounts of fill to create the large gravity anomaly that is seen over Utopia. [36] If the Utopia fill is primarily volcanic, it would be the second largest volcanic feature on Mars, after Tharsis. It would require the extraction of enough melt from the interior to decrease Mars radius by 350 m (although the flexure of the basin would largely compensate for the lost volume). This is an enormous amount of melting, but still small compared to Tharsis (about 15% [Phillips et al., 2001]). On the moon, flood basalts from subsurface dikes are the main contributors to the resurfacing and infilling of the lunar basins and similar processes may have been at work in the Utopia region. Within the Utopia region there is evidence for intrusive volcanism. Lava flows are seen emanating from linear features that are interpreted to be the surface expression of dikes, and Ernst et al. [2001] suggested that the Elysium fossae may be part of a giant radiating dike swarm. The proximity of the Elysium volcanic rise to Utopia could also provide a key source of material. [37] It has been suggested that basin forming impacts could be the root cause of large-scale flood basalts [e.g., Rampino, 1987; Elkins-Tanton and Hager, 2005; Reese et al., 2004]. Work done by Elkins-Tanton and Hager [2005] estimates that a million cubic kilometers of magma can be produced via decompression melting under a 300-km impact basin. This volume of magma production is consistent with the large amount of fill that we estimate is responsible for the large gravity high over Utopia basin. However, if impact induced volcanism is responsible for the fill within Utopia basin, the problem exists of how Hellas avoided volcanic infilling. A possible solution to this dilemma could 10 of 13

11 Figure 10. Dependence of (a) the minimum prefill basin depth and (b) the maximum basin fill on the elastic thickness at the time of infilling for various values of fill density for a crustal thickness of 35 km (all other parameters as shown in Table 1). The lines represent values calculated assuming 120% mass balance prior to infilling. The unshaded region represents portions of the graph that are physically possible. lie with the elastic thickness at the time of basin formation. One theory for the formation of the northern lowlands is that a degree-one plume thinned the crust [McGill and Dimitriou, 1990]. If this is the case, we would expect to see a thinner lithosphere under the Utopia region. Decompression melting due to crater excavation is extremely sensitive to the elastic thickness [Elkins-Tanton and Hager, 2005]. If the lithosphere in the northern lowlands was thinner than that in the highlands, it is conceivable that decompression melting would have occurred under the Utopia basin and not under Hellas; however, no studies have been done on basins of this magnitude. [38] If we allow for a thicker lithosphere and less dense fill material, a comparison to sedimentary basins on Earth can show that in a dynamic environment the deposition of 20 km of basin fill can occur rapidly. For example, in the Carpathians bend zone in Romania approximately 13 km of sediments were deposited in the Focsani Depression in less than 16.5 Myr [Tarapoanca et al., 2003]. If early Mars had abundant water and high erosion rates, it is possible that Utopia could have been filled with sediments eroded from the highlands and transported into the low-lying basin by runoff. There is evidence for extensive fluvial erosion on Mars during the early Noachian [e.g., Craddock and Howard, 2002; Solomon et al., 2005]. Craddock and Howard [2002] suggested that erosion of the highlands could have averaged hundreds of meters. However, if the material filling Utopia originated only in the southern highlands, then more than 700 m on average would have had to have been stripped and transported into the basin. [39] Another dilemma is how Hellas avoided Utopia s fate. It cannot be related to depth alone, as the floor of Hellas is well below Utopia s filled level. Part of the solution to this problem may be Hellas itself. Ejecta from the Hellas impact dominates a large portion of the southern highlands. Since Utopia formed prior to Hellas, it is likely that part of the material filling Utopia is ejecta from the Hellas impact. However, as the ejecta from Hellas would have put down a fairly uniform blanket of ejecta over the Utopia region, this may have been the equivalent to thickening the crust rather than filling the basin. Another possible explanation for relatively pristine condition of Hellas as compared to Utopia is the disparity between the potential source areas. The average elevation of Utopia is 4 km below the reference geoid and, along with the rest of the northern lowlands, this basin was likely a sink for sediment transported via valley networks as well as volcanic and aeolian material [Banerdt and Vidal, 2001; Smith et al., 2001]. Topographically, source regions for the Hellas basin are relatively limited [Banerdt and Vidal, 2001]. Tectonic patterns [Banerdt and Golombek, 2000] and paleo-flow directions [Phillips et al., 2001] indicate that gross topography has not changed significantly since at least the Early to Mid-Noachian. But even if the erosional event predated Tharsis, a marked difference in elevation between the rim levels of Hellas and Utopia could be sufficient to strongly affect their relative susceptibility to infilling by surface transport. One drawback to this line of reasoning is that although Utopia is the lowest topographic point, it would be difficult to transport material over the saddle points that adjoin nearby drainage basins. [40] The results presented in sections two and three are dependent on the initial assumption that Utopia and Hellas were isostatically compensated prior to basin infilling. This assumption was based on the similar size and relative ages of the Hellas and Utopia basins; however, Isidis, a younger and smaller basin located in the northern lowlands, shows evidence for possible superisostatic uplift [Neumann et al., 2004]. How would our model of Utopia be affected by relaxing the initial isostatic assumption to allow the prefill basin to reach a super-isostatic state? In Figure 10, we address this issue by allowing the Utopia basin to reach 120% mass balance (C l = 1.2) prior to loading. As discussed previously, prefill basin depths greater than 6.2 km are not physically possible given the prefill isostatic assumption 11 of 13

12 (denoted by the shaded region). For the 120% compensation case, the area of the shaded region would increase to allow only original basin depths of less than 5.1 km. An increase in the degree of compensation will result in a decrease (150 kg/m 3 ) in the fill densities obtained; however, this decrease is largely offset by the physical limits of the original basin depth. For example, if the elastic thickness at the time of infilling is <70 km, then we would expect fill densities to be greater than 2850 kg/m 3 if we allow the prefill basin to reach a state of isostatic equilibrium (see Figure 6a). Increasing the mass balance to 120% would give fill densities of >2825 kg/m 3 for the same lithospheric thickness (see Figure 10). 6. Summary and Conclusions [41] Utopia and Hellas basins are similar in many aspects. The method and time of formation are almost identical and the overall areal extent of these basins is also similar. We infer that both basins quickly reached an isostatic state via Airy compensation. Subsequently, these twin basins began to follow separate geological paths. Hellas basin remained relatively pristine and unfilled, while Utopia basin was significantly modified by a massive amount of infilling. [42] We first showed that an isostatic assumption for an ancient unfilled basin was justified. We then discussed two different approaches for constraining the amount and nature of the fill within Utopia Basin. The first model assumes that Utopia basin, like Hellas, was isostatically compensated prior to infilling. Using this assumption, we presented a system of equations that allow us to solve for the prefill basin shape, the amount of fill within Utopia and the amount of corresponding flexure. The second model assumes that Hellas and Utopia basin were isostatically identical (but not necessarily compensated) and adds an additional assumption that the basin depths prior to infilling were identical. Given the same set of parameters, the two models give similar results (see Figures 6c and 8). For both models, the specific values for both fill and flexure depend on such parameters as effective elastic thickness at the time of infilling, crustal density, crustal thickness and fill density. We found that the fill density required to produce the observed gravity anomaly of the Utopia basin depends strongly on the assumed lithosphere thickness, but only weakly on crustal density and thickness. Lower values of fill density are allowed only at higher values of T e while higher fill densities are permissible at all values of elastic thickness if we allow for a shallow prefill basin depth at higher values of T e. The crater retention ages of Frey [2006] indicate that the fill was deposited prior to Ga. The early timing for the deposition combined with the heat imparted by the basin forming event argues for a thinner lithosphere which could, in turn, suggest fill densities that are more consistent with a volcanic load than with pure sediment or ice-rich material. The source of the fill material in Utopia is problematic, and the volume of material needed is immense. Given a fill depth of 18 km, this corresponds to about 50 million cubic km of material, equivalent to a global layer 350 m thick. Additional effort is required to address these major issues. Relaxing the isostatic assumption to a reasonable degree perturbs the density bound only slightly. [43] Acknowledgments. The authors thank Sue Smrekar and Patrick McGovern for their thoughtful and constructive reviews. This research was supported by a McDonnell Center for the Space Sciences Edward H. White II Fellowship and by grant NAG from the NASA Planetary Geology and Geophysics Program and grant NNG05GQ81G from the NASA Mars Data Analysis program. References Anderson, D. L. (1995), Lithosphere, asthenosphere, and perisphere, Rev. Geophys., 33(1), Banerdt, W. B. (1986), Support of long-wavelength loads on Venus and implications for internal structure, J. Geophys. Res., 91(B1), Banerdt, W. B., and M. P. Golombek (2000), Tectonics of the Tharsis region of Mars: Insights from MGS topography and gravity, Proc. Lunar Planet. Sci. Conf., 31, Abstract Banerdt, W. B., and A. Vidal (2001), Surface drainage on Mars, Proc. Lunar Planet. Sci. Conf., 32, Abstract Buczkowski, D. L., and M. L. Cooke (2004), Formation of double-ring circular grabens due to volumetric compaction over buried impact craters: Implications for thickness and nature of cover material in Utopia Planitia, Mars, J. Geophys. Res., 109, E02006, doi: / 2003JE Craddock, R. A., and A. D. Howard (2002), The case for rainfall on a warm, wet early Mars, J. Geophys. Res., 107(E11), 5111, doi: / 2001JE Elkins-Tanton, L. T., and B. H. Hager (2005), Giant meteoroid impacts can cause volcanism, Earth Planet. Sci. Lett., 239, Ernst, R. E., E. B. Grosfils, and D. Mège (2001), Giant dike swarms: Earth, Venus, and Mars, Annu. Rev. Earth Planet. Sci., 29, Frey, H. V. (2006), Impact constraints on, and a chronology for, major events in early Mars history, J. Geophys. Res., doi: / 2005JE002449, in press. Frey, H. V., J. H. Roark, K. M. Shockey, E. L. Frey, and S. E. Sakimoto (2002), Ancient lowlands on Mars, Geophys. Res. Lett., 29(10), 1384, doi: /2001gl Hartmann, W. K., and G. Neukum (2001), Cratering chronology and the evolution of Mars, Space Sci. Rev., 96, Hauck, S. A., and R. J. Phillips (2002), Thermal and crustal evolution of Mars, J. Geophys. Res., 107(E7), 5052, doi: /2001je Head, J. W., H. Hiesinger, M. A. Ivanov, M. A. Kreslavsky, S. Pratt, and B. J. Thomson (1999), Possible ancient oceans on Mars: Evidence from Mars Orbiter Laser Altimeter Data, Science, 286, Head, J. W., M. A. Kreslavsky, and S. Pratt (2002), Northern lowlands of Mars: Evidence for widespread volcanic flooding and tectonic deformation in the Hesperian Period, J. Geophys. Res., 107(E1), 5003, doi: /2000je Kargel, J. S., and R. G. Strom (1992), Ancient glaciation on Mars, Geology, 20, 3 7. Lemoine, F. G., D. E. Smith, D. D. Rowlands, M. T. Zuber, G. A. Neumann, D. S. Chinn, and D. E. Pavlis (2001), An improved solution of the gravity field of Mars (GMM-2B) from Mars Global Surveyor, J. Geophys. Res., 106(E10), 23,359 23,376. Leonard, G. J., and K. L. Tanaka (2001), Geologic map of the Hellas region of Mars, USGS Geol. Invest. Ser. I-2694, U.S. Geol. Surv., Boulder, Colo. McGill, G. E., and A. M. Dimitriou (1990), Origin of the Martian global dichotomy by crustal thinning in the late Noachian or early Hesperian, J. Geophys. Res., 95(B8), 12,595 12,605. McGovern, P. J., S. C. Solomon, D. E. Smith, M. T. Zuber, M. Simons, M. A. Wieczorek, R. J. Phillips, G. A. Neumann, O. Aharonson, and J. W. Head (2002), Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution, J. Geophys. Res., 107(E12), 5136, doi: /2002je McGovern, P. J., S. C. Solomon, D. E. Smith, M. T. Zuber, M. Simons, M. A. Wieczorek, R. J. Phillips, G. A. Neumann, O. Aharonson, and J. W. Head (2004), Correction to Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution, J. Geophys. Res., 109, E07007, doi: / 2004JE McLennan, S. M. (2001), Crustal heat production and the thermal evolution of Mars, Geophys. Res. Lett., 28(21), McSween, H. Y., T. L. Grove, and M. B. Wyatt (2003), Constraints on the composition and petrogenesis of the Martian crust, J. Geophys. Res., 108(E12), 5135, doi: /2003je Moore, J. M., and K. S. Edgett (1993), Hellas Planitia, Mars: Site of net dust erosion and implications for the nature of basin floor deposits, Geophys. Res. Lett., 20(15), Neumann, G. A., M. T. Zuber, M. A. Wieczorek, P. J. McGovern, F. G. Lemoine, and D. E. Smith (2004), Crustal structure of Mars from gravity and topography, J. Geophys. Res., 109, E08002, doi: / 2004JE of 13