Secondary and sesquinary craters on Europa

We address impact cratering on Io and Europa, with the emphasis on the origin of small craters on Europa as secondary to the primary impacts of comets on Io, Europa, and Ganymede. In passing we also address the origin of secondary craters generated by Zunil, a well-studied impact crater on Mars that is a plausible analog to impact craters on Io. At nominal impact rates, and taking volcanic resurfacing into account, we find that there should be 1.3 impact craters on Io, equally likely to be of any diameter between 100 m and 20 km. The corresponding model age of Europa's surface is between 60 and 100 Ma. This range of ages does not include a factor three uncertainty stemming from the uncertain sizes and numbers of comets. The mass of basaltic impact ejecta from Io to reach Europa is found to meet or exceed the micrometeoroid flux as a source of rock-forming elements to Europa's ice crust. To describe impact ejecta in more detail we adapt models for impact-generated spalls and Grady-Kipp fragments originally developed by Melosh. Our model successfully reproduces the observed size-number distributions of small craters on both Mars and Europa. However, the model predicts that a significant fraction of the 200-500 m diameter craters on Europa are not traditional secondary craters but are instead sesquinary craters caused by impact ejecta from Io that had gone into orbit about Jupiter. This prediction is not supported by observation, which implies that high speed spalls usually break up into smaller fragments that make smaller sesquinary craters. Iogenic basalts are also interesting because they provide stratigraphic horizons on Europa that in principle could be used to track historic motions of the ice, and they provide materials suitable to radiometric dating of Europa's surface.     

Thermal-orbital evolution of Io and Europa

Coupled thermal-orbital evolution models of Europa and Io are presented. It is assumed that Io, Europa, and Ganymede evolve in the Laplace resonance and that tidal dissipation of orbital energy is an internal heat source for both Io and Europa. While dissipation in Io occurs in the mantle as in the mantle dissipation model of Segatz et al. (1988, Icarus 75, 187), two models for Europa are considered. In the first model dissipation occurs in the silicate mantle while in the second model dissipation occurs in the ice shell. In the latter model, ice shell melting and variations of the shell thickness above an ocean are explicitly included. The rheology of both the ice and the rock is cast in terms of a viscoelastic Maxwell rheology with viscosity and shear modulus depending on the average temperature of the dissipating layer. Heat transfer by convection is calculated using a parameterization for strongly temperature-dependent viscosity convection. Both models are consistent with the present orbital elements of Io, Europa, and Ganymede. It is shown that there may be phases of quasi-steady evolution with large or small dissipation rates (in comparison with radiogenic heating), phases with runaway heating or cooling and oscillatory phases during which the eccentricity and the tidal heating rate will oscillate. Europa's ice thickness varies between roughly 3 and 70 km (dissipation in the silicate layer) or 10 and 60 km (dissipation in the ice layer), suggesting that Europa's ocean existed for geological timescales. The variation in ice thickness, including both convective and purely conductive phases, may be reflected in the formation of different geological surface features on Europa. Both models suggest that at present Europa's ice thickness is several tens of km thick and is increasing, while the eccentricity decreases, implying that the satellites evolve out of resonance. Including lithospheric growth in the models makes it impossible to match the high heat flux constraint for Io. Other heat transfer processes than conduction through the lithosphere must be important for the present Io.     

Morphology and origin of palimpsests on Ganymede based on Galileo observations

Palimpsests are large, circular, low-relief impact scars on Ganymede and Callisto. These structures were poorly understood based on Voyager-era analysis, but high-resolution Galileo images allow more detailed inspection. We analyze images of four Ganymedean palimpsests targeted by Galileo: Memphis and Buto Faculae, Epigeus, and Zakar. Ganymedean craters and Europan ring structures are used as tools to help better understand palimpsests, based on morphologic similarities. From analysis of Galileo images, palimpsests consist of four surface units: central plains, an unoriented massif facies, a concentric massif facies, and outer deposits. Using as a tie point the location in these structures where secondary craters begin to appear, outer deposits of palimpsests are analogous to the outer ejecta facies of craters; the concentric massif facies of palimpsests are analogous to the pedestal facies of craters; and the unoriented massif facies and central plains are analogous to crater interiors. These analogies are supported by the presence of buried preexisting structure beneath the outer two and absence of buried structure beneath the inner two units. Our observations indicate that palimpsest deposits represent fluidized impact ejecta, rather than cryovolcanic deposits or ancient crater interiors.     

Scaling of melt production in hypervelocity impacts from high-resolution numerical simulations

The volume of melt produced in hypervelocity planetary impacts and the size and shape of the melted region are key to understanding the impact histories of solid planetary bodies and the geological effects of impacts on their surfaces and interiors. Prior work of Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) gave the first estimates of impact melt production in geological materials using a modern hydrocode and equation of state. However, computational limits at the time forced use of low resolution, which may have resulted in low melt volumes. Our simulations with 50 times higher resolution provide independent confirmation of the Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) melt volumes in aluminum, iron, dunite, and granite impacts at velocities between 20 and 80 km/s. In ice/ice impacts, we find that melt volumes depend on target temperature and are lower than predicted by Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423). Our melt volumes are directly proportional to impact energy for all materials, over a wide range of impact velocity. We also report new data for melt volume scalings for ice/dunite and iron/dunite impacts and the size and shape of melted region, valuable for interpretation of cratering records and studies of impact-induced differentiation.     

Large impacts detected by the Apollo seismometers: Impactor mass and source cutoff frequency estimations

Meteoroid impacts are important seismic sources on the Moon. As they continuously impact the Moon, they are a significant contribution to the lunar micro-seismic background noise. They also were associated with the most powerful seismic sources recorded by the Apollo seismic network. We study in this paper the largest impacts. We show that their masses can be estimated with a rather simple modeling technique and that high frequency seismic signals have reduced amplitudes due to a relatively low (about 1 s) corner frequency resulting from the duration of the impact process and the crater formation. If synthetic seismograms computed for a spherical model of the Moon are unable to match the waveforms of the observations, they nevertheless provide an approximate measure of the energy of seismic waves in the coda. The latter can then be used for an estimation of the mass of the impactors, when the velocity of the impactor is known. This method, for the artificial impacts of the LM and SIVB Apollo upper stages, allows us to retrieve the mass within 20% of relative error. The estimated mass of the largest impacts observed during the 7 years of activity of the Apollo seismic network provides an explanation for the non-detection of surface waves on the seismograms. The specifications of future Moon seismometers, in order to provide the detection of surface waves, are given in conclusion.     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

Initial condensate composition during asteroid impacts

A model has been developed for the chemical composition of early-time condensates forming during planetary impacts at velocities sufficient for complete evaporation of the impactor (). Hydrodynamics is approximated as hemispheric expansion of a chondritic impactor described with the help of a new semi-analytic equation of state. The gas phase is a mixture of a large number of molecular and mono-atomic species, whereas the Helmholtz free energy of the condensed phase is approximated as sum of a zero-temperature contribution and an Einstein-Debye solid for the thermal part. Interpolation of the free energy between the states of dense solids and molecular gases is used over the wide range of densities and pressures. Chemical equilibrium calculations, performed in a post-processing step, begin at conditions near the coexistence curve as obtained during hydrodynamic simulations, then the condensed phase contains 31 compound species, among them the most important oxides, sulphides, silicates as well as pure elements occurring in a liquid phase at sufficiently high temperature. The composition of the resulting liquid condensate in terms of major elements is compared to that of spinel inclusions in spherules found worldwide at the K-P boundary.     

X-ray probes of magnetospheric interactions with Jupiter's auroral zones, the Galilean satellites, and the Io plasma torus

Remote observations with the Chandra X-ray Observatory and the XMM-Newton Observatory have shown that the jovian system is a source of X-rays with a rich and complicated structure. The planet's polar auroral zones and its disk are both powerful sources of X-ray emission. Chandra observations revealed X-ray emission from the Io plasma torus and from the Galilean moons Io, Europa, and possibly Ganymede. The emission from the moons is due to bombardment of their surfaces by highly energetic magnetospheric protons, and oxygen and sulfur ions. These ions excite atoms in their surfaces leading to fluorescent X-ray emission lines. These lines are produced against an intense background continuum, including bremsstrahlung radiation from surface interactions of primary magnetospheric and secondary electrons. Although the X-ray emission from the Galilean moons is faint when observed from Earth orbit, an imaging X-ray spectrometer in orbit around one or more of these moons, operating from 200 eV to 8 keV with 150 eV energy resolution, would provide a detailed mapping of the elemental composition in their surfaces. Surface resolution of 40 m for small features could be achieved in a 100-km orbit around one moon while also remotely imaging surfaces of other moons and Jupiter's upper atmosphere at maximum regional resolutions of hundreds of kilometers. Due to its relatively more benign magnetospheric radiation environment, its intrinsic interest as the largest moon in the Solar System, and its mini-magnetosphere, Ganymede would be the ideal orbital location for long-term observational studies of the jovian system. Here we describe the physical processes leading to X-ray emission from the surfaces of Jupiter's moons and the properties required for the technique of imaging X-ray spectroscopy to map the elemental composition of their surfaces, as well as studies of the X-ray emission from the planet's aurora and disk and from the Io plasma torus.     

Geophysical consequences of planetary-scale impacts into a Mars-like planet

All planetary bodies with old surfaces exhibit planetary-scale impact craters: vast scars caused by the large impacts at the end of Solar System accretion or the late heavy bombardment. Here we investigate the geophysical consequences of planetary-scale impacts into a Mars-like planet, by simulating the events using a smoothed particle hydrodynamics (SPH) model. Our simulations probe impact energies over two orders of magnitude (2 × 10²⁷-6 × 10²⁹ J), impact velocities from the planet’s escape velocity to twice Mars’ orbital velocity (6-50 km/s), and impact angles from head-on to highly oblique (0-75°). The simulation results confirm that for planetary-scale impacts, surface curvature, radial gravity, the large relative size of the impactor to the planet, and the greater penetration of the impactor, contribute to significant differences in the geophysical expression compared to small craters, which can effectively be treated as acting in a half-space. The results show that the excavated crustal cavity size and the total melt production scale similarly for both small and planetary-scale impacts as a function of impact energy. However, in planetary-scale impacts a significant fraction of the melt is sequestered at depth and thus does not contribute to resetting the planetary surface; complete surface resetting is likely only in the most energetic (6 × 10²⁹ J), slow, and head-on impacts simulated. A crater rim is not present for planetary-scale impacts with energies >10²⁹ J and angles ?45°, but rather the ejecta is more uniformly distributed over the planetary surface. Antipodal crustal removal and melting is present for energetic (>10²⁹ J), fast (>6 km/s), and low angle (?45°) impacts. The most massive impactors (with both high impact energy and low velocity) contribute sufficient angular momentum to increase the rotation period of the Mars-sized target to about a day. Impact velocities of >20 km/s result in net mass erosion from the target, for all simulated energies and angles. The hypothesized impact origin of planetary structures may be tested by the presence and distribution of the geochemically-distinct impactor material.     

Early-stage ejecta velocity distribution for vertical hypervelocity impacts into sand

The ejecta dynamics during main-stage excavation flow in a cratering event have previously been well characterized, particularly for vertical impacts. In this experimental study, we present new results addressing the early-time, low-angle, high-speed component of the ejecta velocity distribution as a function of time for hypervelocity vertical impacts into sand. Although this regime represents a very small portion of total ejected mass in laboratory experiments, it comprises a greater percentage of growth for larger craters.     

Transient crater growth in granular targets: An experimental study of low velocity impacts into glass sphere targets

We experimentally studied the formation and collapse processes of transient craters. Polycarbonate projectiles with mass of 0.49 g were impacted into the soda-lime glass sphere target (mean diameters of glass spheres are ∼36, 72, and 220 μm, respectively) using a single-stage light-gas gun. Impact velocity ranged from 11 to 329 m s⁻¹. We found that the transient crater collapses even at laboratory scales. The shape (diameter and depth) of the transient crater differs from that of the final crater. The depth-rim diameter ratios of the final and transient craters are 0.11-0.14 and 0.26-0.27, respectively. The rim diameter of both the transient and final crater depends on target material properties; however, the ratio of final to transient crater diameter does not. This suggests that target material properties affect the formation process of transient craters even in the gravity regime, and must be taken into account when scaling experimental results to planetary scales. By observing impacts into glass sphere targets, we show that although the early stage of the excavation flow does not depend on the target material properties, the radial expansion of the cavity after the end of vertical expansion does. This suggests that the effect of target material properties is specifically important in the later part of the crater excavation and collapse.     

Scaling of oblique impacts in frictional targets: Implications for crater size and formation mechanisms

Almost every meteorite impact occurs at an oblique angle of incidence, yet the effect of impact angle on crater size or formation mechanism is only poorly understood. This is, in large part, due to the difficulty of inferring impactor properties, such as size, velocity and trajectory, from observations of natural craters, and the expense and complexity of simulating oblique impacts using numerical models. Laboratory oblique impact experiments and previous numerical models have shown that the portion of the projectile’s kinetic energy that is involved in crater excavation decreases significantly with impact angle. However, a thorough quantification of planetary-scale oblique impact cratering does not exist and the effect of impact angle on crater size is not considered by current scaling laws. To address this gap in understanding, we developed iSALE-3D, a three-dimensional multi-rheology hydrocode, which is efficient enough to perform a large number of well-resolved oblique impact simulations within a reasonable time. Here we present the results of a comprehensive numerical study containing more than 200 three-dimensional hydrocode-simulations covering a broad range of projectile sizes, impact angles and friction coefficients. We show that existing scaling laws in principle describe oblique planetary-scale impact events at angles greater than 30° measured from horizontal. The displaced mass of a crater decreases with impact angle in a sinusoidal manner. However, our results indicate that the assumption that crater size scales with the vertical component of the impact velocity does not hold for materials with a friction coefficient significantly lower than 0.7 (sand). We found that increasing coefficients of friction result in smaller craters and a formation process more controlled by impactor momentum than by energy.     

Pits and uplifts on Europa

A survey of depression and uplift features on Europa, based on Galileo regional mapping images, shows that these features come in a wide range of sizes, with numbers increasing greatly with decreasing size, down to the limits of resolution. Size distributions are similar in the northern leading and southern trailing hemispheres, where they are distinctly different from the southern leading and northern trailing hemispheres, suggesting an oblique, antipodal symmetry pattern, similar to that of chaotic and tectonic terrain. This pattern is suggestive of polar wander. Uplifts are usually polygonal or irregular in shape and rarely are cracked. Patches of chaotic terrain, which we had surveyed earlier, are not included in the current study because their topography is generally unclear, and because there is no a priori known genetic linkage with the pits and uplifts.These results contradict generalizations based on the earlier “pits, spots, and domes” (PSD) taxonomy. Most of the type examples for PSDs were simply patches of chaotic terrain selected from a limited portion of their full size range. The use of the term lenticula to collectively describe PSDs is inconsistent with the IAU definition of lenticula: a small dark spot seen at low resolution. Pits and uplifts do not correlate with lenticulae, although chaos often does. Properties of PSDs that have been widely cited as primary evidence for convective upwelling in thick ice (e.g., that uplifts are generally dome-shaped and often cracked; that pits and domes are regularly spaced; that there is a typical diameter of ∼10 km) were premature and not supported by subsequent data. Most pits and uplifts are less than 10 km across so, if they formed by diapirism or convective upwelling, the sources must have been very shallow, less than 5 km deep. How they actually formed remains unknown.     

Geologic mapping of the Zal region of Io

We produced a regional geologic map of the Zal region of Io's antijovian hemisphere using Galileo mission data. We discuss the geologic features, summarize the map units and structures that are present, discuss the nature of volcanic activity, and present an analysis of the volcanic, tectonic, and gradational processes that affect the region. The Zal region consists of five primary types of geologic materials: plains, mountains, paterae floors, flows, and diffuse deposits. The flows and patera floors are similar, but are subdivided based on uncertainties regarding emplacement environments and mechanisms. The Zal region includes two hotspots detected by Galileo: one along the western scarp of the Zal Patera volcano and one at the Rustam Patera volcano (name submitted to IAU). A third hotspot at the nearby At'am Patera volcano (name submitted to IAU) is the source of diffuse and pyroclastic materials that blanket north Zal Mons. The western bounding scarp of Zal Patera is the location of a fissure vent that is the source of multiple silicate lava flows. The floor of Zal Patera has been partially resurfaced by dark lava flows, although portions of the patera floor appear bright and unchanged during the Galileo mission. This suggests that the floor did not undergo complete resurfacing as a flooding lava lake but does contain a compound flow field. Mountain materials exhibit stages of degradation; lineated material degrades into mottled material. We have explored the possibility that north and south Zal Mons were originally one structure. We propose that strike-slip faulting and subsequent rifting separated the mountain units, opened a fissure which serves as a vent for lava flow, and created a depression which, by further extension during the rifting event, became Zal Patera. With comparison to other regional maps of Io, this work provides insight into the general geologic evolution of Io.     

Detection of sporadic impact flashes on the Moon: Implications for the luminous efficiency of hypervelocity impacts and derived terrestrial impact rates

We present the first redundant detection of sporadic impact flashes on the Moon from a systematic survey performed between 2001 and 2004. Our wide-field lunar monitoring allows us to estimate the impact rate of large meteoroids on the Moon as a function of the luminous energy received on Earth. It also shows that some historical well-documented mysterious lunar events fit in a clear impact context. Using these data and traditional values of the luminous efficiency for this kind of event we obtain that the impact rate on Earth of large meteoroids (0.1-10 m) would be at least one order of magnitude larger than currently thought. This discrepancy indicates that the luminous efficiency of the hypervelocity impacts is higher than 10⁻², much larger than the common belief, or the latest impact fluxes are somewhat too low, or, most likely, a combination of both. Our nominal analysis implies that on Earth, collisions of bodies with masses larger than 1 kg can be as frequent as 80,000 per year and blasts larger than 15-kton could be as frequent as one per year, but this is highly dependent on the exact choice of the luminous efficiency value. As a direct application of our results, we expect that the impact flash of the SMART-1 spacecraft should be detectable from Earth with medium-sized telescopes.     

Geologic mapping of the Hi’iaka and Shamshu regions of Io

We produced regional geologic maps of the Hi’iaka and Shamshu regions of Io’s antijovian hemisphere using Galileo mission data to assess the geologic processes that are involved in the formation of Io’s mountains and volcanic centers. Observations reveal that these regions are characterized by several types of volcanic activity and features whose orientation and texture indicate tectonic activity. Among the volcanic features are multiple hotspots and volcanic vents detected by Galileo, one at each of the major paterae: Hi’iaka, Shamshu, and Tawhaki. We mapped four primary types of geologic units: flows, paterae floors, plains, and mountains. The flows and patera floors are similar, but are subdivided based upon emplacement environments and mechanisms. The floors of Hi’iaka and Shamshu Paterae have been partially resurfaced by dark lava flows, although portions of the paterae floors appear bright and unchanged during the Galileo mission; this suggests that the floors did not undergo complete resurfacing as flooding lava lakes. However, the paterae do contain compound lava flow fields and show the greatest activity near the paterae walls, a characteristic of Pele type lava lakes. Mountain materials are tilted crustal blocks that exhibit varied degrees of degradation. Lineated mountains have characteristic en echelon grooves that likely formed as a result of gravitational sliding. Undivided mountains are partially grooved but exhibit evidence of slumping and are generally lower elevation than the lineated units. Debris lobes and aprons are representative of mottled mountain materials. We have explored the possibility that north and south Hi’iaka Mons were originally one structure. We propose that strike-slip faulting and subsequent rifting separated the mountain units and created a depression which, by further extension during the rifting event, became Hi’iaka Patera. This type of rifting and depression formation is similar to the mechanism of formation of terrestrial pull-apart basins. With comparison to other regional maps of Io and global studies of paterae and mountains, this work provides insight into the general geologic evolution of Io.     

Time-resolved studies of hypervelocity vertical impacts into porous particulate targets: Effects of projectile density on early-time coupling and crater growth

The depth and duration of energy and momentum coupling in an impact shapes the formation of the crater. The earliest stages of crater growth (when the projectile transfers its energy and momentum to the target) are unrecoverable when the event is described by late stage parameters, which collapse the initial conditions of the impact into a singular point in time and space. During the coupling phase, the details of the impact are mapped into the ejecta flow field. In this experimental study, we present new experimental and computational measurements of the ejecta distribution and crater growth extending from early times into main-stage ballistic flow for hypervelocity impacts over a range of projectile densities. Specifically, we assess the effect of projectile density on coupling depth and location in porous particulate (sand) targets. A non-invasive high-speed imaging technique is employed to capture the velocity of individual ejecta particles very early in the cratering event as a function of both time and launch position. These data reveal that the effects of early-stage coupling, such as non-constant ejection angles, manifest not only in early-time behavior but also extend to main-stage crater growth. Time-resolved comparisons with hydrocode calculations provide both benchmarking and insight into the parameters controlling the ejection process. Measurements of the launch position and metrics for the transient diameter to depth ratio as a function of time demonstrate non-proportional crater growth throughout much of excavation. Low-density projectiles couple closer to the surface, thereby leading to lower ejection angles and larger effective diameter to depth ratios. These results have implications for the ballistic emplacement of ejecta on planetary surfaces, and are essential to interpreting temporally resolved data from impact missions.     

Non-intrusive measurements of crater growth

An experimental technique to measure crater growth is presented whereby a high speed video captures profiles of a crater forming after impact obtained using a vertical laser sheet centered on the impact point. Unlike previous so called “quarter-space experiments,” where projectiles were launched along a transparent Plexiglas sheet so that growth of half a crater could be viewed, the use of the laser sheet permits viewing changes in crater shape without any physical interference to the cratering process. This technique indicates that for low velocity impacts (<300 m/s) into 220 μm glass beads that are without cohesion and where the projectile is not disrupted, craters initially grow somewhat proportionally, but that later their depths remain essentially constant while their diameters continue to expand. In addition, these experiments indicate that as the impact velocity increases, the rate of growth and the transient depth to diameter ratio at the end of ejecta excavation decreases. These last two observations are probably due to the large time of penetration of the projectile, which becomes a significant fraction of the time of crater formation. This is contrary to the expectations for the scaling rules, which assumes a point source. Very high curtain angles (>45°) are also seen, and could be due to the low friction angle of the target. Significant crater modification, which is rarely seen in “quarter-space experiments,” is also observed and appears to be controlled by the dynamic angle of repose of the target. These latter observations indicate that differences in target friction angles may need to be considered when determining near rim ejecta-mass distributions and large-scale crater modification processes on the planets.     

Segmented lineaments on Europa: Implications for the formation of ridge complexes and bright bands

We describe several segmented lineaments on Europa’s surface. These lineaments are extensive, stretching for 100s-1000s of km, and have ridge complex or bright band morphologies. The geometries of the segmented portions of these features are diagnostic of the remote normal and shear stress environment in which they formed and, therefore, constrain ridge complex and bright band formation mechanisms. Analysis of four ridge complexes indicates that they formed in a remote normal stress environment that was tensile and isotropic (or nearly so) and that these lineaments may have formed in a manner more analogous to bands on Europa than to ridges. The stress environment associated with these ridge complexes may also explain the anastomosing nature of their interior morphology. Analysis of two bright bands indicate that one formed in a remote normal stress environment that was tensile and the other was reactivated under a combination of remote tensile normal stress and remote sinistral shear stress. Aspects of the morphologies of these features also indicate that bright bands likely have complex deformation histories that can include multiple episodes of reactivation.