Ries and Chicxulub: Impact craters on Earth provide insights for Martian ejecta blankets

Abstract— Terrestrial impact structures provide field evidence for cratering processes on planetary bodies that have an atmosphere and volatiles in the target rocks. Here we discuss two examples that may yield implications for Martian craters: 1. Recent field analysis of the Ries crater has revealed the existence of subhorizontal shear planes (detachments) in the periphery of the crater beneath the ejecta blanket at 0.9–1.8 crater radii distance. Their formation and associated radial outward shearing was caused by weak spallation and subsequent dragging during deposition of the ejecta curtain. Both processes are enhanced in rheologically layered targets and in the presence of fluids. Detachment faulting may also occur in the periphery of Martian impacts and could be responsible for the formation of lobe‐parallel ridges and furrows in the inner layer of double‐layer and multiple‐layer ejecta craters. 2. The ejecta blanket of the Chicxulub crater was identified on the southeastern Yucatán Peninsula at distances of 3.0–5.0 crater radii from the impact center. Abundance of glide planes within the ejecta and particle abrasion both rise with crater distance, which implies a ground‐hugging, erosive, and cohesive secondary ejecta flow. Systematic measurement of motion indicators revealed that the flow was deviated by a preexisting karst relief. In analogy with Martian fluidized ejecta blankets, it is suggested that the large runout was related to subsurface volatiles and the presence of basal glide planes, and was influenced by eroded bedrock lithologies. It is proposed that ramparts may result from enhanced shear localization and a stacking of ejecta material along internal glide planes at decreasing flow rates when the flow begins to freeze below a certain yield stress.     

Observations of martian gullies and constraints on potential formation mechanisms

The discovery of presumably geologically recent gully features on Mars (Malin and Edgett, 2000, Science 288, 2330-2335) has spawned a wide variety of proposed theories of their origin including hypotheses of the type of erosive material. To test the validity of gully formation mechanisms, data from the Mars Global Surveyor spacecraft has been analyzed to uncover trends in the dimensional and physical properties of the gullies and their surrounding terrain. We located 106 Mars Orbiter Camera (MOC) images that contain clear evidence of gully landforms, distributed in the southern mid and high latitudes, and analyzed these images in combination with Mars Orbiter Laser Altimeter (MOLA) and Thermal Emission Spectrometer (TES) data to provide quantitative measurements of numerous gully characteristics. Parameters we measured include apparent source depth and distribution, vertical and horizontal dimensions, slopes, orientations, and present-day characteristics that affect local ground temperatures. We find that the number of gully systems normalized to the number of MOC images steadily declines as one moves poleward of 30° S, reaches a minimum value between 60°-63° S, and then again rises poleward of 63° S. All gully alcove heads occur within the upper one-third of the slope encompassing the gully and the alcove bases occur within the upper two-thirds of the slope. Also, the gully alcove heads occur typically within the first 200 meters of the overlying ridge with the exception of gullies equatorward of 40° S where some alcove heads reach a maximum depth of 1000 meters. While gullies exhibit complex slope orientation trends, gullies are found on all slope orientations at all the latitudes studied. Assuming thermal conductivities derived from TES measurements as well as modeled surface temperatures, we find that 79% of the gully alcove bases lie at depths where subsurface temperatures are greater than 273 K and 21% of the alcove bases lie within the solid water regime. Most of the gully alcoves lie outside the temperature-pressure phase stability of liquid CO₂. Based on a comparison of measured gully features with predictions from the various models of gully formation, we find that models involving carbon dioxide, melting ground ice in the upper few meters of the soil, dry landslide, and surface snowmelt are the least likely to describe the formation of the martian gullies. Although some discrepancies still exist between prediction and observation, the shallow and deep aquifer models remain as the most plausible theories. Interior processes involving subsurface fluid sources are generally favored over exogenic processes such as wind and snowfall for explaining the origin of the martian gullies.     

Ejecta emplacement and modes of formation of martian fluidized ejecta craters

From an analysis of 1173 craters possessing single (Type I) and double (Type 2) concentric ejecta deposits, Type 2 craters are found to occur most frequently in areas that have also been described as possessing periglacial features. The frequency of occurence of central peaks and wall failure (terraces plus scallops) within the craters indicate that, by analogy with previous analyses, Type 1 craters form in more fragmental targets than Type 2 craters. The maximum range of the outer ejecta deposits of Type 2 craters, however, consistently extends ～0.8 crater radii further than ejecta deposits of Type 1 craters, suggesting a greater degree of ejecta fluidization for the twin-lobed Type 2 craters. Numerous characteristics of Ries Crater, West Germany, show similarities to craters on Mars, indicating that Martian fluidized ejecta craters may be closer analogs to this terrestrial crater than are lunar craters.     

Martian perched craters and large ejecta volume: Evidence for episodes of deflation in the northern lowlands

Abstract— The northern lowland plains, such as those found in Acidalia and Utopia Planitia, have high percentages of impact craters with fluidized ejecta. In both regions, the analysis of crater geometry from Mars Orbiter Laser Altimeter (MOLA) data has revealed large ejecta volumes, some exceeding the volume of excavation. Moreover, some of the crater cavities and fluidized ejecta blankets of these craters are topographically perched above the surrounding plains. These perched craters are concentrated between 40 and 70°N in the northern plains. The atypical high volumes of the ejecta and the perched craters suggest that the northern lowlands have experienced one or more episodes of resurfacing that involved deposition and erosion. The removal of material, most likely caused by the sublimation of ice in the materials and their subsequent erosion and transport by the wind, is more rapid on the plains than on the ejecta blankets. The thermal inertia difference between the ejecta and the surrounding plains suggests that ejecta, characterized by a lower thermal inertia, protect the underneath terrain from sublimation. This results in a decreased elevation of the plains relative to the ejecta blankets. Sublimation and eolian erosion can be particularly high during periods of high obliquity.     

Distribution of ejecta from small impact craters

The present study focuses both on the influence of impact scale on ejecta expansion and on specific features of ejecta deposits around relatively small craters (i.e., those a few kilometers in width). The numerical model is based on the SOVA multimaterial multidimensional hydrocode, considering subaerial vertical impacts only, applying a 2‐D version of the code to projectiles of 100, 300, and 1000 m diameter. Ejecta can roughly be divided into two categories: “ballistic” ejecta and “convective” ejecta; the ballistic ejecta are the ejecta with which the air interacts only slightly, while the convective ejecta motion is entirely defined by the air flow. The degree of particle/air interaction can be defined by the time/length of particle travel before deceleration. Ejecta size‐distributions for the impacts modeled can be described by the same power law, but the size of maximum fragment increases with scale. There is no qualitative difference between the 100 m diameter projectile case and the 300 m diameter projectile impact. In both cases, fine ejecta decelerate in the air at a small distance from launching point and then rise to the stratosphere by air flows induced by the impacts. In the 1000 m‐scale impact, the mass of ejecta is so large that it moves the atmosphere itself to high altitudes. Thus, the atmosphere cannot decelerate even the fine ejecta and they consequently expand to the rarefied upper atmosphere. In the upper atmosphere, even fine ejecta move more or less ballistically and therefore may travel to high altitudes.     

Areal distribution of Martian rampart craters

A survey of medium- and high-resolution Viking orbital imagery was carried out in order to characterize the areal distribution of Martian rampart craters. Such craters have been identified on nearly every major geologic unit on the planet, at all latitudes and longitudes, and over a wide range of altitudes. Rampart crater formation spans Martian geologic history from at least the formation of the Chryse channels to the present.     

Morphologic classification of Martian craters and some implications

A computer data bank containing information on crater sizes, locations, and morphologies for all craters visible on Mariner 9 wide-angle mapping photography was used to construct a crater morphologic classification. Four general classes were constructed that can be interpreted to represent increasing degrees of crater degradation. Fresh class craters are nearly unmodified and consist of deep bowl-shaped craters and deep, flat-floored craters with terraced walls. The slightly modified class consists of deep flat-floored craters that usually have raised rims, but lack the terracing, central peaks, and hummocky floors indicative of unmodified impact crater morphology. Craters in the modified class are rimless and shallow and those in the ghost class are rimless and extremely shallow. Retention ages for fresh (i.e. unmodified) class craters on equatorial cratered terrain range from millions to billions of years, depending on the impact flux history used. If the trend is toward billions of years, then present degradation rates on Mars are low relative to earlier history and most craters in the degraded classes were probably modified in an early (>3.3 b.y.?) period.     

Layered ejecta craters and the early water/ice aquifer on Mars

Abstract— A model for emplacement of deposits of impact craters is presented that explains the size range of Martian layered ejecta craters between 5 km and 60 km in diameter in the low and middle latitudes. The impact model provides estimates of the water content of crater deposits relative to volatile content in the aquifer of Mars. These estimates together with the amount of water required to initiate fluid flow in terrestrial debris flows provide an estimate of 21% by volume (7.6 × 10⁷km³) of water/ice that was stored between 0.27 and 2.5 km depth in the crust of Mars during Hesperian and Amazonian time. This would have been sufficient to supply the water for an ocean in the northern lowlands of Mars. The existence of fluidized craters smaller than 5 km diameter in some places on Mars suggests that volatiles were present locally at depths less than 0.27 km. Deposits of Martian craters may be ideal sites for searches for fossils of early organisms that may have existed in the water table if life originated on Mars.     

Impacts into non-polar ice-rich paleodeposits on Mars: Excess ejecta craters, perched craters and pedestal craters as clues to Amazonian climate history

We compare three previously independently studied crater morphologies - excess ejecta craters, perched craters, and pedestal craters - each of which has been proposed to form from impacts into an ice-rich surface layer. Our analysis identifies the specific similarities and differences between the crater types; the commonalities provide significant evidence for a genetic relationship among the morphologies. We use new surveys of excess ejecta and perched craters in the southern hemisphere in conjunction with prior studies of all of the morphologies to create a comprehensive overview of their geographic distributions and physical characteristics. From these analyses, we conclude that excess ejecta craters and perched craters are likely to have formed from the same mechanism, with excess ejecta craters appearing fresh while perched craters have experienced post-impact modification and infilling. Impacts that led to these two morphologies overwhelmed the ice-rich layer, penetrating into the underlying martian regolith, resulting in the excavation of rock that formed the blocky ejecta necessary to armor the surface and preserve the ice-rich deposits. Pedestal craters, which tend to be smaller in diameter, have the same average deposit thickness as excess ejecta and perched craters, and form in the same geographic regions. They rarely have ejecta around their crater rims, instead exhibiting a smooth pedestal surface. We interpret this to mean that they form from impacts into the same type of ice-rich paleodeposit, but that they do not penetrate through the icy surface layer, and thus do not generate a blocky ejecta covering. Instead, a process related to the impact event appears to produce a thin, indurated surface lag deposit that serves to preserve the ice-rich material. These results provide a new basis to identify the presence of Amazonian non-polar ice-rich deposits, to map their distribution in space and time, and to assess Amazonian climate history. Specifically, the ages, distribution and physical attributes of the crater types suggest that tens to hundreds of meters of ice-rich material has been episodically emplaced at mid latitudes in both hemispheres throughout the Amazonian due to obliquity-driven climate variations. These deposits likely accumulated more frequently in the northern lowlands, resulting in a larger population of all three crater morphologies in the northern hemisphere.     

Martian rampart crater ejecta: Experiments and analysis of melt-water interaction

Viking images of Martian craters with rampart-bordered ejecta deposits reveal distinct impact ejecta morphology when compared to that associated with similar-sized craters on the Moon and Mercury. Topographic control of distribution, lobate and terraced margins, cross-cutting relationships, and multiple stratigraphic units are evidence for ejecta emplacement by surface flowage. It is suggested that target water explosively vaporized during impact alters initial ballistic trajectories of ejecta and produces surging flow emplacement. The dispersal of particulates during a series of controlled steam explosions generated by interaction of a thermite melt with water has been experimentally modeled. Preliminary results indicate that the mass ratio of water to melt and confining pressure control the degree of melt fragmentation (ejecta particle size) and the energy and mode of melt-ejecta dispersal. Study of terrestrial, lobate, volcanic ejecta produced by steam-blast explosions reveals that particle size and vapor to clast volume ratio are primary parameters characterizing the emplacement mechanism and deposit morphology. Martian crater ramparts are formed when ejecta surges lose fluidizing vapors and transported particles are deposited en masse. This deposition results from flow yield strength increasing above shear stress due to interparticle friction.     

Crater geometry and ejecta thickness of the Martian impact crater Tooting

Abstract— We use Mars Orbiter Laser Altimeter (MOLA) topographic data and Thermal Emission Imaging System (THEMIS) visible (VIS) images to study the cavity and the ejecta blanket of a very fresh Martian impact crater ?29 km in diameter, with the provisional International Astronomical Union (IAU) name Tooting crater. This crater is very young, as demonstrated by the large depth/diameter ratio (0.065), impact melt preserved on the walls and floor, an extensive secondary crater field, and only 13 superposed impact craters (all 54 to 234 meters in diameter) on the ?8120 km² ejecta blanket. Because the pre‐impact terrain was essentially flat, we can measure the volume of the crater cavity and ejecta deposits. Tooting crater has a rim height that has >500 m variation around the rim crest and a very large central peak (1052 m high and >9 km wide). Crater cavity volume (i.e., volume below the pre‐impact terrain) is ?380 km³ the volume of materials above the pre‐impact terrain is ?425 km³. The ejecta thickness is often very thin (<20 m) throughout much of the ejecta blanket. There is a pronounced asymmetry in the ejecta blanket, suggestive of an oblique impact, which has resulted in up to ?100 m of additional ejecta thickness being deposited down‐range compared to the up‐range value at the same radial distance from the rim crest. Distal ramparts are 60 to 125 m high, comparable to the heights of ramparts measured at other multi‐layered ejecta craters. Tooting crater serves as a fresh end‐member for the large impact craters on Mars formed in volcanic materials, and as such may be useful for comparison to fresh craters in other target materials.     

Morphology and geometry of the distal ramparts of Martian impact craters

Abstract— We used Mars Orbiter Laser Altimeter (MOLA), Thermal Emission Imaging System visible light (THEMIS VIS), and Mars Orbiter Camera (MOC) data to identify and characterize the morphology and geometry of the distal ramparts surrounding Martian craters. Such information is valuable for investigating the ejecta emplacement process, as well as searching for spatial variations in ejecta characteristics that may be due to target material properties and/or latitude, altitude, or temporal variations in the climate. We find no systematic trend in rampart height that would indicate regional variations in target properties for 54 ramparts at 37 different craters 5.7–35.9 km in diameter between 52.3°S to 47.6°N. Rampart heights for multi‐lobe and single‐lobe ejecta are each normally distributed with a common standard deviation, but statistically distinct mean values. Ramparts range in height from 20–180 m, are not symmetric, are typically steeper on their distal sides, and may be as much as ?4 km wide. The ejecta blanket proximal to parent crater from the rampart may be very thin (<5 m). A detailed analysis of two craters, Toconao crater (21°S, 285°E) (28 measurements), and an unnamed crater within Chryse Planitia (28.4°N, 319.6°E) (20 measurements), reveals that ejecta runout distance increases with an increase in height between the crater rim and the rampart, but that rampart height is not correlated with ejecta runout distance or the thickness of the ejecta blanket.     

Preservation of layered paleodeposits in high-latitude pedestal craters on Mars

An outstanding question in Mars’ climate history is whether or not pedestal craters represent the armored remnants of ice-rich paleodeposits. We address this question using new high-resolution images; in a survey of several hundred high-latitude pedestal craters, we have identified 12 examples in which visible and/or topographically expressed layers are exposed on the marginal scarp of the pedestal. One example, located on the south polar layered deposits, preserves ice-rich layers that have otherwise been completely removed from the polar cap. These observations provide empirical evidence that the pedestal crater formation mechanism is capable of armoring and preserving ice-rich layered paleodeposits. Although layered exposures have not yet been observed in mid-latitude pedestal craters, high-latitude instances of discontinuous, partially covered layers suggest that layers can be readily concealed, likely through mantling and/or mass wasting processes along the marginal scarp. This interpretation is supported by the observation that high-latitude pedestals with exposed layers along their margins are, on average, taller than mid-latitude examples, and have larger, steeper marginal scarps, which may help to maintain layer exposures. These observations favor the interpretation that mid- to high-latitude pedestal craters represent the armored remnants of ice- and dust-rich paleodeposits, which occurred transiently due to changes in the climate regime. Preservation of fine-scale layering of ice and dust at these latitudes implies that the climate change did not involve regional melting conditions.     

A conceptual model for explanation of Albedo changes in Martian craters

We propose a conceptual model to interpret AM/PM high albedo events (HAEs) in crater interiors at the Martian seasonal polar caps. This model consists of two components: (1) a relatively permanent high-albedo water–ice body exposed in a crater interior and (2) a variable crater albedo in response to aerosol optical depth, dust contamination, and H₂O/CO₂ frost deposits or sublimes in four phases, based on temperature and solar longitude changes. Two craters (Korolev crater of fully exposed water–ice layer and ‘Louth’ crater of partially exposed water–ice layer) are used to demonstrate the model. This model explains the HAEs and their seasonal changes and suggests that many crater-like features formed in the last episodic advance of the polar ice cap in the last high obliquity period should have water–ice exposed or covered. For the AM-only HAEs craters, there seems no need of a water–ice layer to be fully exposed, but a subsurface water–ice layer (or ice-rich regolith) is a necessary condition.     

Impact craters in the northern hemisphere of Mars: Layered ejecta and central pit characteristics

Abstract— Mars Global Surveyor (MGS) and Mars Odyssey data are being used to revise the Catalog of Large Martian Impact Craters. Analysis of data in the revised catalog provides new details on the distribution and morphologic details of 6795 impact craters in the northern hemisphere of Mars. This report focuses on the ejecta morphologies and central pit characteristics of these craters. The results indicate that single‐layer ejecta (SLE) morphology is most consistent with impact into an ice‐rich target. Double‐layer ejecta (DLE) and multiple‐layer ejecta (MLE) craters also likely form in volatile‐rich materials, but the interaction of the ejecta curtain and target‐produced vapor with the thin Martian atmosphere may be responsible for the large runout distances of these ejecta. Pancake craters appear to be a modified form of double‐layer craters where the thin outer layer has been destroyed or is unobservable at present resolutions. Pedestal craters are proposed to form in an icerich mantle deposited during high obliquity periods from which the ice has subsequently sublimated. Central pits likely form by the release of vapor produced by impact into ice‐soil mixed targets. Therefore, results from the present study are consistent with target volatiles playing a dominant role in the formation of crater morphologies found in the Martian northern hemisphere.     

Dust formation and survival in supernova ejecta

The presence of dust at high redshift requires efficient condensation of grains in supernova (SN) ejecta, in accordance with current theoretical models. Yet observations of the few well-studied supernovae (SNe) and supernova remnants (SNRs) imply condensation efficiencies which are about two orders of magnitude smaller. Motivated by this tension, we have (i) revisited the model of Todini & Ferrara for dust formation in the ejecta of core collapse SNe, and (ii) followed, for the first time, the evolution of newly condensed grains from the time of formation to their survival – through the passage of the reverse shock – in the SNR. We find that  0.1–0.6  M_⊙  of dust form in the ejecta of 12–40 M_⊙ stellar progenitors. Depending on the density of the surrounding interstellar medium, between 2 and 20 per cent of the initial dust mass survives the passage of the reverse shock, on time-scales of about  4–8 × 10⁴  yr  from the stellar explosion. Sputtering by the hot gas induces a shift of the dust size distribution towards smaller grains. The resulting dust extinction curve shows a good agreement with that derived by observations of a reddened QSO at   z = 6.2  . Stochastic heating of small grains leads to a wide distribution of dust temperatures. This supports the idea that large amounts (∼0.1 M_⊙) of cold dust  ( T ∼ 40   K)  can be present in SNRs, without being in conflict with the observed infrared emission.     

Meteoritical and dynamical constraints on the growth mechanisms and formation times of asteroids and Jupiter

Thermal models and radiometric ages for meteorites show that the peak temperatures inside their parent bodies were closely linked to their accretion times. Most iron meteorites come from bodies that accreted <0.5 Myr after CAIs formed and were melted by ²⁶Al and ⁶⁰Fe, probably inside 2 AU. Rare carbon-rich differentiated meteorites like ureilites probably also come from bodies that formed <1 Myr after CAIs, but in the outer part of the asteroid belt. Chondrite groups accreted intermittently from diverse batches of chondrules and other materials over a 4 Myr period starting 1 Myr after CAI formation when planetary embryos may already have formed at ∼1 AU. Meteorite evidence precludes accretion of late-forming chondrites on the surface of early-formed bodies; instead chondritic and non-chondritic meteorites probably formed in separate planetesimals. Maximum metamorphic temperatures in chondrite groups are correlated with mean chondrule age, as expected if ²⁶Al and ⁶⁰Fe were the predominant heat sources. Because late-forming bodies could not accrete close to large, early-formed bodies, planetesimal formation may have spread across the nebula from regions where the differentiated bodies formed. Dynamical models suggest that the asteroids could not have accreted in the main belt if Jupiter formed before the asteroids. Therefore Jupiter probably reached its current mass >3-5 Myr after CAIs formed. This precludes formation of Jupiter via a gravitational instability <1 Myr after the solar nebula formed, and strongly favors core accretion. Jupiter probably formed too late to make chondrules by generating shocks directly, or indirectly by scattering Ceres-sized bodies across the belt. Nevertheless, shocks formed by gravitational instabilities or Ceres-sized bodies scattered by planetary embryos may have produced some chondrules. The minimum lifetime for the solar nebula of 3-5 Myr inferred from the total spread of CAI and chondrule ages may exceed the median lifetime of 3 Myr for protoplanetary disks, but is well within the 1-10 Myr observed range. Shorter formation times for extrasolar planets may help to explain their unusual orbits compared to those of solar giant planets.     

The formation of fluidized ejecta on Mars by granular flows

Abstract— A simple granular flow model is used to investigate some of the conditions under which ejecta may flow as a granular media. The purpose of this investigation is to provide some bounds as to when either volatiles or an atmosphere are required to explain the fluid‐like morphology of many Martian ejecta deposits. We consider the ejecta deposition process from when an ejecta curtain first strikes a target surface via ballistics and possibly flows thereafter. A new finding is that either hard‐smooth surfaces or slightly erodible surfaces allow ejecta to flow readily as a granular medium. Neither volatiles nor an atmosphere are required to initiate flow. A low friction coefficient between ejecta grains can also generate flow and would be analogous to adding volatiles to the ejecta. The presence of either a rough or a densely packed erodible surface does not permit easy ejecta flow. High friction coefficients between ejecta grain also prevent flow, while changes in the coefficient of restitution (a measure of how much energy is retained after collisions between particles) plays a minor role in the flow dynamics of ejecta. A hard smooth or a somewhat erodible surface could be generated by past fluvial activity on Mars, which can either indurate a surface, erode and smooth a surface, or generate sedimentary terrains that are fairly easy to erode. No ramparts or layered ejecta morphologies are generated by our model, but this may be because several simplifying assumptions are used in our model and should not be construed as proof that either volatiles or an atmosphere are required to form fluidized ejecta morphologies.     

Hypervelocity impacts on dry and wet sandstone: Observations of ejecta dynamics and crater growth

Abstract– This study deals with the investigation of highly dynamic processes associated with hypervelocity impacts on porous sandstone. For the impact experiments, two light‐gas accelerators with different calibers were used, capable of accelerating steel projectiles with diameters ranging from 2.5 to 12 mm to several kilometers per second. The projectiles impacted on dry and water‐saturated Seeberger Sandstone targets. The study includes investigations of the influence of pore water on the shape of the ejecta cloud as well as transient crater growth. The results show a significant influence of pore water on ejecta behavior. Steeper ejecta cone angles are observed if the impacts are conducted on wet sandstones. The transient crater grows at a faster rate and reaches a larger diameter if the target is water saturated. In our experiments, target porosity leads to smaller crater sizes compared with nonporous targets. Water within the pore space reduces porosity and counteracts this process. Power law fits were applied to the crater growth curves. The results show an increase in the scaling exponent μ with increasing pore space saturation.     

Preflow stresses in Martian rampart ejecta blankets: A means of estimating the water content

Measurements of extents of rampart ejecta deposits as a function of the size of the parent craters support models which, for craters larger than about 6 km diameter, constrain ejecta blankets to all have a similar maximum thickness regardless of the crater size. These volatile-rich ejecta blankets may have failed under their own weights, then flowed radially outward. Assuming this to be so, we can then determine some of the physicomechanical properties of the ejecta deposits at the time of their emplacement. Finite-element studies of the stress magnitudes, distributions, and directions in hypothetical Martian rampart ejecta blankets reveal that the material most likely failed when the shear stresses were less than 500 kPa and the angle of internal friction was between 26 and 36°. These figures imply that the ejecta has a water content between 16 and 72%. Whether the upper limit or the lower limit is more appropriate depends on the mode of failure which one presumes; namely, viscous flow or plastic deformation.