Radial variation of lunar crater rim topography

The variation of rim topography as a function of range from the crater rim has been determined for a group of morphologically fresh lunar craters (D = 10–140 km) using the recent series of Lunar Topographic Orthophotomaps. The rate at which exterior crater topography converges with the surrounding surface is highly variable along different radial directions at individual craters as well as between different craters. At several craters, oblique impact appears to have contributed to azimuthal elevation/range variations. The topographic expression of a crater above the surrounding surface typically decreases to one-tenth of the estimated rim height at a range of 1.3R–1.7R, well within the rough-textured ejecta deposit surrounding the crater. Comparisons with terrestrial craters suggest that the topographic crater rim is predominantly a structural feature. In most craters large portions of the hummocky facies and virtually all of the radial facies, in spite of their rough appearance and local topographic variations, provide no significant net topographic addition to the preexisting surface. The extreme variability of crater rim topography strongly suggests that ejecta thicknesses are highly variable and that a unique power-law expression cannot truly represent the radial variation of ejecta deposit thickness.     

The transition from complex crater to peak-ring basin on the Moon: New observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument

Impact craters on planetary bodies transition with increasing size from simple, to complex, to peak-ring basins and finally to multi-ring basins. Important to understanding the relationship between complex craters with central peaks and multi-ring basins is the analysis of protobasins (exhibiting a rim crest and interior ring plus a central peak) and peak-ring basins (exhibiting a rim crest and an interior ring). New data have permitted improved portrayal and classification of these transitional features on the Moon. We used new 128 pixel/degree gridded topographic data from the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter, combined with image mosaics, to conduct a survey of craters >50 km in diameter on the Moon and to update the existing catalogs of lunar peak-ring basins and protobasins. Our updated catalog includes 17 peak-ring basins (rim-crest diameters range from 207 km to 582 km, geometric mean = 343 km) and 3 protobasins (137-170 km, geometric mean = 157 km). Several basins inferred to be multi-ring basins in prior studies (Apollo, Moscoviense, Grimaldi, Freundlich-Sharonov, Coulomb-Sarton, and Korolev) are now classified as peak-ring basins due to their similarities with lunar peak-ring basin morphologies and absence of definitive topographic ring structures greater than two in number. We also include in our catalog 23 craters exhibiting small ring-like clusters of peaks (50-205 km, geometric mean = 81 km); one (Humboldt) exhibits a rim-crest diameter and an interior morphology that may be uniquely transitional to the process of forming peak rings. A power-law fit to ring diameters (D_ring) and rim-crest diameters (D_r) of peak-ring basins on the Moon [D_ring = 0.14 ± 0.10(D_r)^1.21±0.13] reveals a trend that is very similar to a power-law fit to peak-ring basin diameters on Mercury [D_ring = 0.25 ± 0.14(D_rim)^1.13±0.10] [Baker, D.M.H. et al. [2011]. Planet. Space Sci., in press]. Plots of ring/rim-crest ratios versus rim-crest diameters for peak-ring basins and protobasins on the Moon also reveal a continuous, nonlinear trend that is similar to trends observed for Mercury and Venus and suggest that protobasins and peak-ring basins are parts of a continuum of basin morphologies. The surface density of peak-ring basins on the Moon (4.5 × 10⁻⁷ per km²) is a factor of two less than Mercury (9.9 × 10⁻⁷ per km²), which may be a function of their widely different mean impact velocities (19.4 km/s and 42.5 km/s, respectively) and differences in peak-ring basin onset diameters. New calculations of the onset diameter for peak-ring basins on the Moon and the terrestrial planets re-affirm previous analyses that the Moon has the largest onset diameter for peak-ring basins in the inner Solar System. Comparisons of the predictions of models for the formation of peak-ring basins with the characteristics of the new basin catalog for the Moon suggest that formation and modification of an interior melt cavity and nonlinear scaling of impact melt volume with crater diameter provide important controls on the development of peak rings. In particular, a power-law model of growth of an interior melt cavity with increasing crater diameter is consistent with power-law fits to the peak-ring basin data for the Moon and Mercury. We suggest that the relationship between the depth of melting and depth of the transient cavity offers a plausible control on the onset diameter and subsequent development of peak-ring basins and also multi-ring basins, which is consistent with both planetary gravitational acceleration and mean impact velocity being important in determining the onset of basin morphological forms on the terrestrial planets.     

Transitional impact craters on the Moon: Insight into the effect of target lithology on the impact cratering process

We studied a data set of 28 well‐preserved lunar craters in the transitional (simple‐to‐complex) regime with the aim of investigating the underlying cause(s) for morphological differences of these craters in mare versus highland terrains. These transitional craters range from 15 to 42 km in diameter, demonstrating that the transition from simple to complex craters is not abrupt and occurs over a broad diameter range. We examined and measured the following crater attributes: depth (d), diameter (D), floor diameter (D_f), rim height (h), and wall width (w), as well as the number and onset of terraces and rock slides. The number of terraces increases with increasing crater size and, in general, mare craters possess more terraces than highland craters of the same diameter. There are also clear differences in the d/D ratio of mare versus highland craters, with transitional craters in mare targets being noticeably shallower than similarly sized highland craters. We propose that layering in mare targets is a major driver for these differences. Layering provides pre‐existing planes of weakness that facilitate crater collapse, thus explaining the overall shallower depths of mare craters and the onset of crater collapse (i.e., the transition from simple to complex crater morphology) at smaller diameters as compared to highland craters. This suggests that layering and its interplay with target strength and porosity may play a more significant role than previously considered.     

A model of Phobos

A model of the Martian satellite Phobos was constructed at a scale of 1:60 000 using 25 Mariner 9 photorecords and a solar-simulation technique. Measurements of the crater diameters D, depths d, ratios $\text{d}\text{D}$, longitude and latitude locations of the centers, IAU designations, crater shapes, and rim class are given in a catalog of 260 depressions. An open-ended indexing of the craters is based on their locations by octant and diameter magnitude. Six craters were found with sharply defined rims. At least 28 craters have raised rims. The range of the $\text{d}\text{D}$ ratios is from 0.002 to 0.26, with a mean $\text{d}\text{D}$ of 0.10. The mean diameter of Stickney is interpreted to be 11.1 km, its minimum 9.6 km, and the diameter of Hall 5.9 km. A 100-m contour-interval topographic map has been drawn from measurements of the model. This is rendered on an elliptical form of a Lambert equal-area polar projection. The topographic map made it possible to estimate vector lengths from the center of Phobos to vertices on a 6-frequency octahedron that fits the sattelite. A mean radius of 11.0 km results from averaging the vector lengths to the 146 well-distributed vertices of the polyhedron. A volume of 5620 km³ is deduced.     

Pluto—The ninth planet's golden year: A meeting held at New Mexico State University,Las Cruces,New Mexico

The simple-to-complex transition for impact craters on Mars occurs at diameters between about 3 and 8 km. Ballistically emplaced ejecta surround primarily those craters that have a simple interior morphology, whereas ejecta displaying features attributable to fluid flow are mostly restricted to complex craters. Size-dependent characteristics of 73 relatively fresh Martian craters, emphasizing the new depth/diameter (d/D) data of D. W. G. Arthur (1980, to be submitted for publication), test two hypotheses for the mode of formation of central peaks in complex craters. In particular, five features appear sequentially with increasing crater size: first flat floors (3–4 km), then central peaks and shallower depths (4–5 km), next scalloped rims (? km), and lastly terraced walls (～8 km). This relative order indicates that a shallow depth of excavation and an unspecified rebound mechanism, not centripetal collapse and deep sliding, have produced central peaks and in turn have facilitated failure of the rim. The mechanism of formation of a shallow crater remains elusive, but probably operates only at the excavation stage of impact. This interpretation is consistent with two separate and complementary lines of evidence. First, field data have documented only shallow subsurface deformation and a shallow transient cavity in complex terrestrial meteorite craters and in certain surface-burst explosion craters; thus the shallow transient cavities of complex craters never were geometrically similar to the deep cavities of simple craters. Second, the average depths of complex craters and the diameters marking the transition from simple to complex craters on Mars and on three other terrestrial planets vary inversely with gravitational acceleration at the planetary surface, g, a variable more important in the excavation of a crater than in any subsequent modification of its geometry. The new interpretation is summarized diagrammatically for complex craters on all planets.     

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.     

Use of equivalency in estimating the historical size distribution of impact craters

A previous analysis of a stochastic model of lunar-type impact cratering is extended to utilize geological age data by defining a more general statistic $\text{Ω}{}_{\mathrm{i}}\text{(t)}$ to be the number of equivalent whole craters of original diameter d_i and age ≤t in an observational area A; each crater is taken to be equivalent to the fraction of its rim (or area) that is in A and not occluded by later craters. By integration of a new gain-loss differential equation, a generalization of the previous basic equation is obtained that relates the expected value $\text{ω}{}_{\mathrm{i}}\text{(t) = E[Ω}{}_{\mathrm{i}}\text{(t)]}$ to the process functions specifying the size distribution and flux of craters (primary or secondary) as they form. The results are specialized to the plausible case in which the cratered body can be subdivided into geological provinces of increasing ages t₁, t₂, …, t_i … and the size probability distribution can be approximated as constant within each of the periods t_i+1 - t_i. It is shown that use of the $\text{Ω}{}_{\mathrm{i}}$ permits, in principle, a reconstruction of the historical values of the process functions and correctly compensates for the effect of overlap by removing the false bias favoring large craters that results from the usual method of crater counting. Possible generalizations of the gain-loss equation are indicated.     

Interplanet variations in scale of crater morphology—Earth,Mars, Moon

Craters on the Earth, Mars, and the Moon show a spectrum of morphologies with diameter increasing from simple, bowl-shaped craters through craters with increasingly complex central peaks, to craters with “peak rings” and basins with multiple concentric scarps. In each category there is a range of diameters, centered around a characteristic diameter, D_c. It is found that D_c decreases as the size of the planet increases. Several possible explanations are considered. It is suggested that the effect results from a gravity scaling law derived here and having approximately from the D_c∂ 1/g^1.25, where g is the surface gravity. All geological structures in which gravity is the dominant parameter affecting the morphology should follow such a law.     

Structural uplift and ejecta thickness of lunar mare craters: New insights into the formation of complex crater rims

We investigate the elevated crater rims of lunar craters. The two main contributors to this elevation are a structural uplift of the preimpact bedrock and the emplacement of ejecta on top of the crater rim. Here, we focus on five lunar complex mare craters with diameters ranging between 16 and 45 km: Bessel, Euler, Kepler, Harpalus, and Bürg. We performed 5281 measurements to calculate precise values for the structural rim uplift and the ejecta thickness at the elevated crater rim. The average structural rim uplift for these five craters amounts to S_RU = 70.6 ± 1.8%, whereas the ejecta thickness amounts to E_T = 29.4 ± 1.8% of the total crater rim elevation. Erosion is capable of modifying the ratio of ejecta thickness to structural rim uplift. However, to minimize the impact of erosion, the five investigated craters are young, pristine craters with mostly preserved ejecta blankets. To quantify how strongly craters were enlarged by crater modification processes, we reconstructed the dimensions of the transient crater. The difference between the transient crater diameter and the final crater diameter can extend up to 11 km. We propose reverse faulting and thrusting at the final crater rim to be one of the main contributing factors of forming the elevated crater rim.     

Impact cratering and break up of the small bodies of the Solar System

We consider the largest impact craters observed on small satellites and asteroids and the impact disruption of such bodies. Observational data are considered from 21 impact-like structures on 13 satellites and 8 asteroids (target body radii in the range 0.7-265 km). If the radius of the target body is R and the diameter of the largest crater observed on this body D, the ratio D/R is then the main observational parameter of interest. This is found on the observed bodies and compared to data obtained in the laboratory. Taking the largest observed value for D/R as a proxy for the ratio Dc/R (where Dc is the diameter of the largest crater that can be formed on a body without shattering it) it was found that for the observed icy satellites Dc,icy≈1.2R and for the asteroids and the rocky satellites Dc,rocky≈1.6R. In laboratory experiments with ice targets at impactor speeds of 1 to 3 km s⁻¹ we obtained Dc,icy≈1.64R.     

Morphology of Lonar Crater,India: Comparisons and implications

Lonar Crater is a young meteorite impact crater emplaced in Deccan basalt. Data from 5 drillholes, a gravity network, and field mapping are used to reconstruct its original dimensions, delineate the nature of the pre-impact target rocks, and interpret the emplacement mode of the ejecta. Our estimates of the pre-erosion dimensions are: average diameter of 1710 m; average rim height of 40 m (30–35 m of rim rock uplift, 5–10 m of ejected debris); depth of 230–245 m (from rim crest to crater floor). The crater's circularity index is 0.9 and is unlikely to have been lower in the past. There are minor irregularities in the original crater floor (present sediment-breccia boundary) possibly due to incipient rebound effects. A continuous ejecta blanket extends an average of 1410 m beyond the pre-erosion rim crest.In general, fresh terrestrial craters, less than 10 km in diameter, have smaller depth/diameter and larger rim height/diameter ratios than their lunar counterparts. Both ratios are intermediate for Mercurian craters, suggesting that crater shape is gravity dependent, all else being equal. Lonar demonstrates that all else is not always equal. Its depth/diameter ratio is normal but, because of less rim rock uplift, its rim height/diameter ratio is much smaller than both fresh terrestrial and lunar impact craters. The target rock column at Lonar consists of one or more layers of weathered, soft basalt capped by fresh, dense flows. Plastic deformation and/or compaction of this lower, incompetent material probably absorbed much of the energy normally available in the cratering process for rim rock uplift.A variety of features within the ejecta blanket and the immediately underlying substrate, plus the broad extent of the blanket boundaries, suggest that a fluidized debris surge was the dominant mechanism of ejecta transportation and deposition at Lonar. In these aspects, Lonar should be a good analog for the fluidized craters of Mars.     

Fractal properties of outflows from Venusian impact craters

This article presents fractal analyses of 28 outflow margins from 18 Venusian impact craters. The fractal dimensions of the second parts of R-plots of the outflow outlines were measured by a three-step method. The fractality values for the same outflow measured from images which have only a small difference in resolution are very similar, while large differences in image resolution may result in differences in fractality, possibly due to the fact that we are actually studying geological processes on different scales. The outflows were classified into three general categories: single outflows, multiple outflows and outflow fields. Three conclusions were drawn on the relations between fractality and crater diameter, which may be related to the greater effects caused by the immediate local environment on the outflows from small craters than on those from larger craters. Investigation of the relations between the regional topography and fractality indicates that there are substantially less effects on outflows originating from large craters than on those from small craters. The smooth bending in the R-plot and the higher D-value for the multiple outflows could result from the mixing of various fractal or non-fractal units. When comparing our results with the fractality of terrestrial lava flows, outflows from craters of diameter greater than 50 km seem to resemble aa-type lava flows in their fractal dimensions and outflows from craters of diameter below 50 km tend to be more pahoehoe-like. This preliminary result is based on 28 outflows, however, and the pattern should be investigated more carefully by further more extensive work.     

The terrestrial cratering record: II. The crater production rate

The terrestrial cratering record for the Phanerozoic has a size-frequency distribution of NαD^?2.05 for D > 22.6 km and NαD^?0.24 for D < 11.3 km. This shallowing of the distribution slope at D > 22.6 km reflects the removal of small terrestrial craters by erosion. The number of large craters on the North American and East European cratons provide estimated terrestrial crater production rates for D > 20 km of 0.36 ± 0.1 and 0.33 ± 0.2 × 10^?14 km^?2 year^?1, respectively. These rates are in good agreement with previous estimates and astronomical observations on Apollo bodies. Comparisons with the lunar rate, taking account of the effects of variations in impact velocity, surface gravity, and gravitational cross section, indicate that the lunar and terrestrial rates overlap, if the cratering flux has been constant during the last 3.4 by. If the early (pre 4.0 by) high-flux rate did not decay to a constant value until 3.0 to 2.5 by then the rates differ by a factor of 2 and the Phanerozoic can be interpreted as a period of higher than normal cratering.     

The effect of interplanetary acceleration on the propagation of energetic solar particles in prompt events

Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyD _TT is allowed to be either independent of radial distance,R(AU), or follow the lawD _TT=D₀T²R ₀ ² /(A²+R²) in either case with the 1 AU value ofD _TT at 10 MeV ranging between 10^?4 (MeV)² s^?1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ_‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofD _TT and the spatial diffusion coefficientK _r=K₀R^?2 forR«1 andK _r=K₀R^0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofD _TT chosen within the above range. Experimental determination of the decay constant is difficult.     

The coronal hole at the 7 March 1970 solar eclipse

Coronal interferograms in the lines of Fe xiv 5303 Å, He i 5876 Å and Fe x 6374 Å were obtained during the total solar eclipse of 10 July, 1972 (see Figure 2). He i emission was found in the chromosphere only. The upper limit of the D₃ equivalent width in terms of the coronal continuous background is 0.013 Å in the inner corona (r=1.15 R⊙). The λ6374 negative was taken with low contrast. The half width of 16374 is 1.0–1.08 Å for a limited area of the corona (P=88?104°, r=1.30?1.44 R⊙). A detailed photometry of the 5303 Å line was carried out and the behaviour of the half widths and equivalent widths were studied in different regions of the corona. The half width of λ5303 increases with distance from the Sun's center in almost all the studied regions (1.2 R⊙ ? r ? 1.7 R⊙). This increase corresponds to an increase of the non-thermal velocities with a gradient of 1–2 km s^-1 per 0.1 R⊙. The equivalent widths, expressed in the coronal continuous background intensity remain constant on the average.     

Wind-blown streaks,splotches, and associated craters on Mars: Statistical analysis of Mariner 9 photographs

Crater morphology and size play a major role in determining whether wind-blown streaks emanating from craters or dark splotches within craters will form. Both bright and dark streaks emanate almost exclusively from bowl-shaped craters. Dark splotches are found mainly in flat-floored craters, especially those that are deep and have high rim relief. Trends of dark splotches in the northern to southern midlatitudes closely follow those of bright streaks, suggesting both were formed by similar winds. In the high southern latitudes, on the other hand, dark splotch trends closely follow those of dark streaks.Qualitative models of streak and splotch formation have been derived from these data and results of Sagan et al. (1972, 1973). Bright streaks probably form by trapping and simultaneous streaming of bright dust downwind. Dark splotched craters in regions with bright streaks usually have upwind bright patches, suggesting these features form by dumping of bright dust over crater rims with some minor redistribution of dark materials toward the downwind sides of craters. Data are consistent with dark streaks forming by erosion or nondeposition of bright material or by trapping of dark material. Dark splotches in these regions are probably mainly the result of trapping of dark sand in the downwind sides of crater floors. Craters with dark splotches and dark streaks are usually rimless and shallow. This is consistent with ponded dark sands easily washing over crater walls and extending downwind.Plots of streak length versus crater diameter suggest a complex history of streak formation for most regions.Bright streak trends and latitudinal distributions are consistent with return flow of dust to the southern hemisphere. Some dark streaks may be direct relics of passing sand and dust storms. Trends of dark streaks and splotches away from the south pole are consistent with the spreading of a debris mantle from the polar regions toward the equator.     

Analysis of EUV limb-brightening observations from ATM

Limb-brightening curves for EUV resonance lines of O vi and Mg x have been constructed from spectroheliograms (5″ resolution) of quiet limb regions observed with the Harvard experiment on Skylab. The observations are interpreted with a simple model for the transition layer and the corona. A comparison of theoretical and observed limb-brightening curves indicates that the lower boundary of the corona, where T _e= 10⁶K, is at a height of about 8000 km in typical quiet areas. For 1.01 R _⊙?r1.25 R _⊙, the corona can be represented by a homogeneous model in hydrostatic equilibrium with a temperature of 10₆K for 1.01 R _⊙?r<1.1 R _⊙ and 1.1 × 10₆K for r?1.1 R _⊙. The model for the transition layer is inhomogeneous, with the temperature gradient a factor of 3 shallower in the network than in the intranetwork regions. It appears that spicules should be included in the model in order to account for the penetration into the corona of cool (T _e<10⁶K) EUV-emitting material to heights up to 20000 km above the limb.     

Observable Parameters of Solar Microwave Pulsating Structure and Their Implications for Solar Flare

From the observations with the Chinese Solar Broadband Radiospectrometer (SBRS/Huairou) in the frequency range of 1.10?–?2.06 GHz and 2.60?–?3.80 GHz during 2004?–?2006, we select 14 flare events which were associated with numerous fast microwave subsecond pulsating structures (period: P<0.5 s). In order to describe these subsecond pulsating structures comprehensively, we defined a set of observable parameters including emission frequency (f ₀), bandwidth (b _w), polarization degree (r), period (P), duration (D), modulation depth (M), quality factor (Q), single pulse frequency drifting rate (R _spfd), global frequency drifting rate (R _gfd), and symmetrical factor of the pulse profile (S). Then based on a detailed analysis of the spectrograms of the fast pulsations which occurred in one of these flares (an X3.4 flare/CME event occurred on 13 Dec. 2006), we discuss the possible relations among these observable parameters and their physical implications for the dynamical processes of solar eruptive events, and applied them to interpret the nature of the pulsations in the flare/CME event. Such study of microwave periodic pulsations provides us with a useful tool to probe the details of the flare kernels, and understand the physical mechanism of solar eruptive processes.     

Extreme sensitivity of the YORP effect to small-scale topography

Radiation recoil (YORP) torques are shown to be extremely sensitive to small-scale surface topography, using numerical simulations. Starting from a set of “base objects” representative of the near-Earth object population, random realizations of three types of small-scale topography are added: Gaussian surface fluctuations, craters, and boulders. For each, the expected relative errors in the spin and obliquity components of the YORP torque caused by the observationally unresolved small-scale topography are computed. Gaussian power, at angular scales below an observational limit, produces expected errors of order 100% if observations constrain the surface to a spherical harmonic order l?10. For errors under 10%, the surface must be constrained to at least l=20. A single crater with diameter roughly half the object's mean radius, placed at random locations, results in expected errors of several tens of percent. The errors scale with crater diameter D as D² for D>0.3 and as D³ for D<0.3 mean radii. Objects that are identical except for the location of a single large crater can differ by factors of several in YORP torque, while being photometrically indistinguishable at the level of hundredths of a magnitude. Boulders placed randomly on identical base objects create torque errors roughly 3 times larger than do craters of the same diameter, with errors scaling as the square of the boulder diameter. A single boulder comparable to Yoshinodai on 25143 Itokawa, moved by as little as twice its own diameter, can alter the magnitude of the torque by factors of several, and change the sign of its spin component at all obliquities. Most of the total torque error produced by multiple unresolved craters is contributed by the handful of largest craters; but both large and small boulders contribute comparably to the total boulder-induced error. A YORP torque prediction derived from groundbased data can be expected to be in error by of order 100% due to unresolved topography. Small surface changes caused by slow spin-up or spin-down may have significant stochastic effects on the spin evolution of small bodies. For rotation periods between roughly 2 and 10 h, these unpredictable changes may reverse the sign of the YORP torque. Objects in this spin regime may random-walk up and down in spin rate before the rubble-pile limit is exceeded and fissioning or loss of surface objects occurs. Similar behavior may be expected at rotation rates approaching the limiting values for tensile-strength dominated objects.