Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Carr et al., 1998; Greenberg et al., 1999], or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 2000]. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.
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 Of Europa's many unique terrain types, probably the most intriguing is chaos terrain [Carr et al., 1998]. Chaos on Europa (Figure 1a) involves the breakup of older ridged plains units into polygonal “blocks” up to a few 10's of km across and its replacement by newer “matrix” material, which typically has a coarse, unorganized texture [Pappalardo et al., 1998]. Chaos is relatively young [e.g., Greenberg et al., 1999] and can occur as large irregular areas a few hundred km across or as ovoidal regions only a few km across (sometimes referred to as lenticulae). The two end-member models for chaos formation are complete melt-through from a subsurface ocean and subsequent refreezing of the “lake” to form matrix [Carr et al., 1998; Greenberg et al., 1999], or solid-state intrusion by warm-ice diapirs, upwellings triggered by convection of the ice shell, where matrix material represents uplifted and exposed material from the lower shell [Head and Pappalardo, 1999; Collins et al., 2000]. Hybrid models involving intrashell melting and partial melting over diapirs have been proposed [Collins et al., 2000] but for purposes of testing models using topographic data, these can be considered with their respective end-member models.
 Resolution of the debate over diapirism versus melt-through has relevance for understanding the state and thickness of the Europa's outer ice shell. In turn, constraining Europa's ice shell thickness is important to understanding the means of exchange of material between the surface and ocean and potential habitability of Europa [Greenberg et al., 2000; Chyba, 2000]. The melt-through model is commonly linked to an ice shell <5 km or so thick [Greenberg et al., 2000; O'Brien et al., 2002] because of the difficulty of melting through thicker ice. Indeed, melt-through is plausible only if the shell is thin, otherwise rapid lateral flow of the warm base of the shell would preclude melting [Stevenson, 2000; Nimmo et al., 2003]. A melt-through origin implies that near-surface life plausibly might be sustained by photosynthesis [Greenberg et al., 2000] and that surface oxidants could be delivered directly to an ocean to support biota [Chyba, 2000]. Conversely, solid-state ice convection is likely to be thermally driven and the ice shell must be of significant thickness (>10–25 km) to become unstable to convection [McKinnon, 1999]. This would imply that any communication of nutrients and/or organisms between the surface and ocean occurs through the intermediary of convecting ice, and would make oceanic material more difficult to sample directly.
2. Topography of Chaos
 Local and regional topographic digital elevation models (DEMs) of selected chaos sites have been produced using two techniques separately and in combination: stereo image analysis, shape-from-shading (photoclinometry, or PC), and PC-DEMs controlled by coincident stereo-derived elevation data [Schenk, 2002]. The latter technique preserves high-resolution information while effectively eliminating the long-wavelength imprecision that can affect PC topographic mapping. Conamara Chaos (Figures 1a and 1b), at 10°N, 273°W, is the archetypal example of chaos and has the best topographic coverage available. Conamara Chaos is roughly 125 by 75 km across and ∼60% matrix and 40% remnant blocks of older ridged plains [Spaun et al., 1998]. Two stereo-controlled PC DEMs have been produced: a regional map of all of Conamara Chaos at 180 m resolution and an east-west swath at 55 m resolution (Figures 1a, 1b, 2a and 2b). Stereo data at 11 m resolution is also available over a very small portion of the chaos interior.
 The regional map shows that Conamara Chaos is elevated above surrounding terrains, but not uniformly (Figure 1). A number of domical areas 5 to 30 km across and a few 10's to 250 m high can be resolved within this terrain. The east-west 55-m swath (Figures 2a and 2b) confirms that matrix material by itself (excluding individual remnant blocks) is variable in elevation with up to 300 m of total relief, sometimes over distances of less than 10 km (Figure 3). At least three large broad domical rises and three smaller rises can be mapped (Figures 2a and 2b). One of these topographic domes extends beyond the western margin of the chaos into surrounding ridged plains (Figure 2b). In this and the high-resolution stereo DEM, several tilted blocks are lower in elevation by up to 100 m compared to matrix ≤5 km away.
 Most (but not all) of the lenticulae in the regional Conamara DEM (Figures 1a and 1b) are elevated 100–200 m above surrounding terrain, the highest rising 250 m above the local datum (and 320 m above its own margin). High-resolution stereo southeast of Tyre (Figures 4a and 4b) includes one oblong lenticula 5 by 10 km across and about half of a chaos unit 20 by 25 km across [Kadel et al., 2000]. The smaller oblong lenticula has a domical surface that rises ∼150 m above adjacent ridged plains units. Matrix material within the chaos unit varies by at least 100 m in elevation, with the center rising ≤50 m above surrounding ridged plains. In some locations, the outer margin of this matrix material lies nearly 100 m below adjacent ridged plains, forming a moat-like depression (Figures 4a and 4b). Additional sites of elevated chaos material have been identified using photoclinometry near 0°N, 230°W; 45°S, 295°W; 88°N, 125°W; and 29°S, 219°W.
3. Implications for Melt-Through and Diapiric Models
 While the global topography (and hence the true geoidal level) of Europa is unknown, it is clear that matrix material can be elevated several hundred meters above nearby terrains, and can vary by several hundred meters over distances of as little as 5 km, forming multiple adjacent domical rises. These characteristics do not compare favorably to first-order predictions of the melt-through hypothesis [Carr et al., 1998; Greenberg et al., 1999]. Refreezing of the ice shell could produce positive relief over chaos only if the effective density of the refrozen shell is less than that of the original adjacent ice shell. Because rapid lateral flow of the basal shell is expected to effectively eliminate basal shell topography [Stevenson, 2000; Nimmo et al., 2003], we assume that surface topography across the refrozen zone is controlled by Pratt isostasy. A density contrast between the refrozen section and the original shell of 5% or greater is required to produce elevations of ∼250 m in a shell ≤5 km thick. Such a large density contrast would require either a high porosity or emplacement of relatively clean ice in the refrozen areas [cf. Nimmo et al., 2003]. We estimate that an excess of ∼10–15% void space in the upper 1/3 to 1/4 of the ice column (porosity in the lower sections closes due to thermal annealing [Nimmo et al., 2003]) would be needed to produce such density contrasts. If chaos refreezes to relatively pure ice, then the older ice shell would have to be composed of 7–10% by weight (depending on composition) of denser impurities such as hydrated sulfates (likely candidate non-ice materials [e.g., McCord et al., 1998]) in order to produce sufficient density differences. Such scenarios cannot be ruled out, but the new topographic data challenge the melt-through model and place tight constraints on how melt-through and refreezing could proceed on Europa.
 Post-freezing deformation could alter the final topographic expression of chaos, but the domical expression we see is inconsistent with the imposition of simple lateral stress fields such as tidal deformation, and is not easily explained in the melt-through model. Refreezing of a water pocket enclosed within a thin ice shell is also an implausible mechanism, requiring a pocket 7–20 km thick to produce the observed 100–300 m of topography.
 Producing positive relief through diapirism has also proved challenging. Diapirism driven by simple thermal convection does not appear capable of producing topography on Europa greater than a few 10s of meters [Showman and Han, 2004]. However, compositional buoyancy induced by thermal segregation of non-ice phases during plume ascent could produce uplifts of several hundred meters [Pappalardo and Barr, 2004]. In this case, a density difference of only ∼10–15 kg m−3 (low-eutectic impurity volume fraction ∼2%) is required to produce relief of 200–300 m in a region of clean ice ∼20 km thick. A general lack of large blocks in Conamara Chaos on local topographic highs (Figure 3) is consistent with the hypothesis [Head and Pappalardo, 1999] that blocks are preferentially disrupted and destroyed in situ above local centers of intense diapiric upwelling. Relief of several hundred meters and the observation that some blocks are lower than adjacent matrix material (Figure 3) and hence unflooded suggest that block rotation [Spaun et al., 1998] did not occur in a liquid medium, consistent with diapir related deformation.
 The broadly undulating topography of Conamara Chaos with several prominent domical rises supports a model in which large chaos areas form over regions of diapiric upwelling, with coalescence of several individual diapirs in the shallow sub-surface [Spaun et al., 1998]. Mottled terrains may represent broad areas of convective instability within the ice shell. Formation of chaos as a result of diapirism favors a relatively thick ice shell [e.g., McKinnon, 1999], consistent with thermal equilibrium calculations [e.g., Hussmann et al., 2002] suggesting a shell thickness ≥25 km, and analysis of impact crater depth/diameter measurements [Schenk, 2002], indicating a minimum shell thickness of 19–25 km.
 A relatively thick ice shell implies indirect communication between Europa's surface and ocean through diapiric transport. It would be very difficult for a landed spacecraft to directly sample frozen ocean water, while the hazard of contaminating a subsurface ocean with terrestrial organisms [Task Group on the Forward Contamination of Europa, 2000] is greatly reduced relative to the thin shell model. The elevated topography and especially the domical undulations associated with chaos (and lenticulae) on Europa are most consistent with formation by solid-state diapirism, while challenging the melt-through model. Global topographic data from orbiting spacecraft are required to determine whether the topographic characteristics of chaos inferred here are uniform globally or characterize a specific time in Europa's history. Whatever the details of chaos formation, the data presented here place important constraints on any future models developed to explain resurfacing on Europa.