Abstract
Introduction
Background
Experimental Setup
Procedure
Variables
Results
Phase 1
Phase 2
Phase 3
Discussion
Experimental Errors
Application to the Moon
Summary
References
Tables
Figures

de ~ 0.084 Dr

(1)

and for complex craters (D_r > 19 km),

de ~ 0.15 Dr0.85

(2)

These equations yield a first order approximation of the thickness of the overlying deposits, within an error ±15%.
       In Chapter 1, this technique was applied to a study area on the western limb of the Moon, where average minimum thicknesses of cryptomafic deposits were found to range from 600-950 meters, which is consistent with mare thicknesses on the western limb [De Hon, 1979; Head, 1982]. These translated into an estimate of 5 x 10⁵ km³ for the volume of cryptomafic material on the western limb, representing an increase of 5% to the total volume of known volcanic deposits on the lunar surface.
       This method, however, only provides a first-order approximation of the thicknesses and volumes of cryptomafic deposits, since depth of excavation is not an accurate measure of the stratigraphic layer depths. Consider Figure 3, which schematically illustrates how d_e overestimates the thickness of the overlying deposits. The minimum dark-haloed crater represents the smallest possible dark-haloed crater that can form, occurring when enough mafic material has been excavated and deposited beyond the crater rim to make a dark halo just barely visible. Figure 3 schematically shows how the crater must excavate the mafic substrate to some depth (d_m) before sufficient mafic material is excavated to produce this barely visible dark halo. The depth of excavation, therefore, does not measure the exact thickness of the overlying ejecta (t_m), but rather the ejecta thickness plus the value d_m. The maximum dark-haloed crater in Figure 3 represents the largest possible dark-haloed crater that can form, occurring when the dark halo is still barely visible despite the fact that it is partially obscured by pristine highland material that has been excavated from beneath the cryptomafic layer. Here, the depth of excavation can penetrate into the underlying highland crust by some maximum depth (d_h) before sufficient highland material is excavated in order to completely obscure the dark halo. Again, the depth of excavation measures not only the thickness of the overlying layers (t_h), but it also includes d_h. The values d_m and d_h can potentially have a significant effect on cryptomafic thickness estimates: d_m by overestimating the thickness of the overlying regional ejecta deposit, as determined from the smallest observed dark-haloed craters; and d_h by overestimating the depth to the base of the cryptomafic deposit, as determined by the largest dark-haloed craters, but only if these craters are indeed tapping the bottom of the cryptomafic deposits. In order to evaluate the magnitudes of d_m and d_h and their effect on the reliability of cryptomafic thickness and volume estimates, a series of impact experiments that simulate dark halo formation was begun.



Experimental Setup

        Procedure
       A series of vertical impacts into a layered half-space was conducted at the NASA-Johnson Space Center Vertical Gun Lab. Targets were constructed of colored, resin-coated sand, arranged in a round aluminum container 7 cm deep and 25 cm in diameter. For each target, the sand was placed inside the container in three layers. One unit of dark-colored sand was interleaved between two layers of light-colored sand to simulate the configuration of a cryptomafic deposit.
       The prepared target was placed inside a special, plexiglass platform apparatus, from which a 25 cm diameter round hole had been cut away, allowing the top of the platform to lay flush with the top of the container and layered sand surface (Figure 4). This arrangement allowed the experimental surface area to be extended, while at the same time conserving the volume of sand that was required. The platform top had previously been sprayed with adhesive glue, sprinkled with light-colored sand and allowed to dry, in order to simulate the sand surface of the layered target as much as possible, and to keep individual grains of ejecta from sliding along a smooth plexiglass surface. This entire apparatus was placed in the impact chamber of the vertical gun. A thin layer of light-colored sand was then sprinkled over the platform surface, further increasing the resemblance to the layered target by the presence of free-moving sand grains. Next, several small, plastic vials were placed into a series of holes, which had been drilled in the platform at 2.54-cm intervals (Figure 4). These vials acted as catchers during the experiment, allowing us to obtain samples of the ejected material for later study of its volume and composition. The range of these catchers was extended closer to the impact point by placing two small plastic vial lids in the sand target, spaced at the same interval (Figure 4). These two catchers, however, were expected to provide less reliable results because of the potential for ejecta grains to bounce out of these shallow catchers.
       Impacts were normal to the target surface and took place in a chamber atmosphere of 3 torr. All projectiles in this study were spheres, 6.35 mm in diameter.
       Spectra of the resulting crater and ejecta were obtained after some shots with the Mini PS II personal spectrometer. A removable apparatus that allowed the aperture unit of the spectrometer to be moved, at a fixed height, radially across the crater was set up in the impact chamber. Reflectance spectra were taken at the crater center and at 2.54-cm intervals starting from the crater rim.
       The target was then removed from the impact chamber and the resulting crater was photographed. One set of photographs was taken under high-angle illumination, simulating a high-sun view, in order to emphasize the albedo of the ejecta. Another set was taken under low-angle illumination, emphasizing crater topography. After the target surface had been photographed, the contents of the catcher vials were collected, labeled, and stored for study at a later time (analysis of the catcher results will not be discussed in this paper). The target container was removed from the platform apparatus and baked in a low-temperature oven, allowing the resin to harden and solidify the crater. The solid target was then sawed in half ( Figure 5), permitting accurate measurements of the crater's morphometric parameters to be made ( Figure 6).
       This procedure was repeated for a total of 46 targets.


        Variables
       The experiments were conducted in three distinct phases. The goal of the first phase was to study the formation of simple dark halos. Therefore, for this phase of experiments, the dark-colored layer was kept relatively thick, ensuring that the projectile did not penetrate to the underlying light-colored layer. The experimental setup for phase 1 is illustrated in Figure 7. The thickness of the overlying light layer (t) was varied between shots in order to find the thickness at which a sufficient quantity of dark material is excavated to produce a barely visible dark halo. Identification of barely visible, or minimum, dark-haloed craters was accomplished by visual inspection of the targets and high-angle illumination photographs. We define a barely visible dark-haloed crater by the presence of a tenuous, but relatively symmetrical, halo of dark material around the rim of the experimental crater. Spectral measurements of the craters and their ejecta deposits were taken for some craters, using the portable Mini PS II personal spectrometer. The intent of these measurements was to determine if the spectral and visible definitions of a minimum dark-haloed crater coincide for these experiments.
       The targets of phase 1 were impacted at velocities of 1, 1.5 and 2 km/s, allowing the variation in dark halo formation to be studied as a function of impactor velocity, while remaining within range of comfortable performance of the vertical gun. The projectiles used were mainly glass spheres, but similar-sized spheres of nylon and aluminum were used for some shots in this first phase to consider the effects of impactor density. The findings from phase 1 were used to constrain the experimental variables used in subsequent phases.
       Our goal in the second phase was to simulate dark halo obscuration. This was accomplished by constructing targets in which the top two layers were kept relatively thin, allowing material from the bottom, light-colored layer to be excavated. Experimental setup for phase 2 is illustrated in Figure 8. The combined thickness (t) of the top light layer and the dark layer was varied in order to permit ejection of sufficient quantities of the lower light layer to obscure the dark halo. Identification of an obscured dark halo was accomplished by visual inspection of the targets and photographs taken at high-angle illumination. We define an obscured dark halo by the absence of a distinct albedo variation between the pre-impact surface and the ejecta of the experimental crater. However, the physical constraints of these experiments, namely the maximum crater size that could be produced and the minimum layer thickness that could be constructed, prevented us from forming a completely obscured dark halo. For this phase of experiments, only glass projectiles were used. An impact velocity of 1.5 km/s was used for most shots, but some targets were impacted at velocities of 2 km/s in an attempt to increase penetration and improve the possibility of producing an obscured dark halo. Spectral measurements were not obtained for any craters from phase 2 of the experiments.
       The third phase of experiments involved an attempt to improve the analogy between the experimental setup and the Moon by making the top layer less pristine. When a large ejecta deposit is emplaced on top of a mafic unit, forming a cryptomafic deposit, some mafic material is incorporated into the ejecta deposit during the emplacement process [Oberbeck, 1975; Bell and Hawke, 1984]; therefore, the layer overlying a cryptomafic unit is composed of a mixture of highland and mafic materials [Bell and Hawke, 1984]. Furthermore, all lunar materials tend to darken as they mature [Adams and McCord, 1973], therefore, the layer overlying a cryptomafic unit will become darker with time. To simulate this darker nature of the obscuring layer, the top light layer in the target and platform setup from phase 1 of the experiments (Figure 7) was replaced with a layer of mixed light and dark material. The thickness of this mixed layer was varied until the underlying pure dark layer was excavated in sufficient quantities to produce a visible dark-haloed crater. Dark-haloed craters were identified and defined in the same way as for phase 1 of the experiments. The percentage of dark material in the mixed layer was also varied, using 10, 20, and 30% dark material, in order to study the effects of albedo differences on dark halo formation. Only glass projectiles were used, and the velocity was maintained at 1.5 km/s. Spectral measurements were not obtained for this phase of experiments.



Results

        Phase 1
       The resulting craters from phase 1 of these experiments can be divided into four distinct types: dark-haloed craters, minimum dark-haloed craters, incipient dark-haloed craters, and non-haloed craters (Figure 9). As previously noted, minimum dark-haloed craters where defined by the presence of tenuous, but relatively symmetrical, halos of dark material (Figure 9b). Dark-haloed craters were defined by well-developed symmetrical halos of dark material (Figure 9a). Incipient dark-haloed craters were defined as those craters that had no visible halo, but which showed the presence of some dark grains beyond the rim of the experimental crater (Figure 9c). These craters demonstrate the emergent excavation of dark material and so represent potential, or incipient, dark-haloed craters. Non-haloed craters were defined as those craters where no dark material was excavated beyond the crater rim (Figure 9d). The classification of these craters was completed before any other crater analysis, in order to minimize bias.
       The morphometric parameters were measured for each experimental crater as defined in Figure 6. These results are presented in Table 1. The ratio of the top layer thickness and crater depth (t/d_r) was then calculated and plotted as a function of crater type and projectile composition (Figure 10). As expected, the value of t/d_r varies as a function of the crater type, increasing as the quantity of excavated dark material decreases. Dark-haloed craters, which excavate large quantities of dark material, have low t/d_r ratios. Minimum dark-haloed craters, which excavate small quantities of dark material, have intermediate t/d_r ratios. Incipient dark-haloed craters, which are only beginning to excavate dark material, have high t/d_r ratios. Non-haloed craters, which excavate no dark material, have the highest t/d_r ratios. There is insufficient data to resolve any trends that might be related to the projectile density (Figure 10). Small but inconsistent variations in t/d_r can be observed when the results from glass projectiles are plotted as a function of velocity (Figure 11). The boundary between incipient and minimum dark-haled craters appears to occur at lower t/d_r values with higher velocity impacts. A factor of 10 increase in velocity could affect the results by no more than 10%. However, the precise variations of this boundary are not clear, because of the sparseness of this type of data.
       Spectral measurements were obtained for 10 of the impact craters produced in phase 1 of the experiments (Table 1). The spectra were obtained by using a rigid rod apparatus, which allowed us to move the aperture unit of the spectrometer across the crater at a fixed height. However, the inflexible nature of this apparatus meant that the traverse, along which spectra were collected, was fixed. Spectra could only be obtained in a straight line from the center of the crater out towards the impact chamber door. The implication of this limitation was that a traverse, which would eliminate any effects that might result from variations in halo symmetry, could not be specifically chosen.
       Locations comprising part of a sample traverse are shown in Figure 9c. Examples of spectral traverses are shown in Figure 12. Both the light and dark sand that was used in these experiments are compositionally similar, predominantly quartz. Thus, spectral properties of the sand could not be used as diagnostic tools to differentiate between the light and dark material. However, the overall photometry and brightness of the materials could be used to differentiate between the two sand types.
       For each traverse, the spectra were plotted and crater type determined. Three different crater types were identified on the basis of their spectral traverse: dark-haloed craters, minimum dark-haloed craters, and incipient dark-haloed craters. Sample traverses for each type are shown in Figure 12. Dark-haloed craters were defined by the similarity between the rim and center spot spectra, indicating the presence of large quantities of dark material on the crater rim, and by the systematic change in brightness as a function of distance from the crater rim, denoting an orderly decrease in the percentage of dark material in the ejecta (Figure 12a). Minimum dark-haloed craters were defined by a significant brightness difference between the rim and crater center, indicating that smaller quantities of dark material were present on the crater rim than in the center, and also by a systematic change in brightness as a function of distance from the crater rim, again denoting that an orderly decrease in the percentage of dark material is occurring (Figure 12b). Incipient dark-haloed craters were spectrally defined by a large difference between brightness at the rim and at the center, and by the lack of a systematic change in brightness as a function of distance from the crater rim, indicating that the quantity of dark material outside the crater rim is too small to be reliably differentiated by the spectrometer (Figure 12c). The results of this analysis are shown in Table 1. We point out that no spectral traverses of non-haloed type craters were obtained in this study. However, we suspect that non-haloed craters would be spectrally indistinguishable from incipient dark-haloed craters. In all other respects, the crater definitions, determined from the spectral traversed, appear to correspond extremely well with the visual definitions of crater types. This is interpreted to indicate that, in the confines of these experiments, the definition of a minimum dark-haloed crater is constant, regardless of whether craters are identified visually or with digital instruments.
       By definition, incipient dark-haloed craters represent the very beginning of excavation of the dark layer. Therefore, the thickness of the top layer corresponds to the depth of excavation for these craters and the results from incipient dark-haloed craters can be used to assess the validity of these experimental results. From Table 1 and Figure 10, it can be seen that, for the incipient craters, t/d_r ranges from 0.26 to 0.39. In order to eliminate any possible effects due to projectile density, we consider only the results for glass projectiles and find the average t/d_r for incipient craters to be 0.33. Since t = d_e for incipient craters, these experiments show that d_e/d_r = 0.33. Comparing this value to the results of Stöffler et al. [1975], where d_e/d_r was also found to be 0.33, it is clear that our value agrees very well with the previously published findings, giving us confidence in our experimental results.
       Minimum dark-haloed craters represent the minimum amount of dark material that must be excavated before a dark halo becomes visible. Therefore, the difference between the depth of excavation (d_e) for these craters and the thickness (t) of the overlying light layer corresponds to the value d_m, which is the minimum penetration into the dark layer that is required for a dark-haloed crater to form (Figure 7). This relationship can be expressed as d_m = d_e - t or, normalized to the rim-to-floor depth of experimental craters, as

dm/dr = de/dr - t/dr

(3)

It can be seen from Table 1 and Figure 10 that, for minimum craters, t/d_r ranges from 0.22 to 0.30. Again, considering only the results for glass projectiles, the average t/d_r for minimum craters is found to be 0.26. Recalling that d_e/d_r = 0.33 from incipient craters, and substituting these values into equation (3) we find that

dm = 0.07 dr

(4)

or

dm = 0.2 de

(5)

Clearly, d_m is a significant quantity, corresponding to 20% of the value of d_e. At greater velocities, the value of d_m is expected to increase, becoming more significant.
       It is obvious that any thickness estimates obtained from the depths of excavation of minimum dark-haloed craters without taking into account d_m will be considerably exaggerated. Therefore, equations that incorporate d_m are derived to calculate a better thickness estimate (t_m) for the layer overlying a cryptomafic deposit (Figure 3). Knowing from the experiments that the average t/d_r value for minimum craters is 0.26, we can say that

tm = 0.26 dr

(6)

In order to express this relationship in terms of crater variables that can be directly measured from lunar images, such as the rim-crest diameter, equations (1) and (2), along with the relation d_e/d_r = 0.33 from Stöffler et al. [1975] can be rearranged to provide

tm ~ 0.066 Dr

(7)

for simple craters and

tm ~ 0.12 Dr0.85

(8)

for complex craters. Equations (7) and (8) should be used to calculate an improved thickness estimate (t_m) for the layer overlying a cryptomafic deposit, since they incorporate the d_m correction. Variations in impactor velocity may have a small effect on these equations, corresponding to an error of less than 10% over a factor of 10 increase in velocity. However, the error associated with equations (1) and (2) is ±15%. Thus, equations (7) and (8) should be accurate to within an error of 15%.


        Phase 2
       Craters from phase 2 of these experiments were divided into two distinct types: light-haloed craters and incipient light-haloed craters. We defined light-haloed craters as those craters that had excavated sufficient quantities of underlying light material to change the albedo of the dark halo, but not enough to completely obscure it (Figure 13). Incipient light-haloed craters were defined as dark-haloed craters that are just beginning to excavate the underlying light layer, as indicated by the presence of some light grains beyond the crater rim. Again, classifications were completed prior to any other analyses in order to minimize bias. As previously noted, the physical constraints of these experiments prevented us from ever forming a completely obscured dark halo. We were unable to make the overlying layers (Figure 8) thin enough for the largest craters formed to be able to excavate enough underlying light material to completely obscure the dark halo that was produced by the dark layer. However, the light-haloed craters can still be useful in providing a lower bound for the value of d_h.
       The morphometric characteristics (Figure 6) for each experimental crater were measured and the ratio of top layer thickness to crater depth (t/d_r) was calculated. The results are listed in Table 2. Again, as expected, the value of t/d_r is found to be greater for incipient craters than for light-haloed craters, which excavate more of the underlying light material. It can be seen, from Table 2, that the one incipient light-haloed crater has a t/d_r value of 0.44, which is considerably greater than the results from phase 1 or from Stöffler et al. [1975] (d_e/d_r = 0.33). Most probably, this high t/d_r value reflects a difficulty in distinguishing between light grains that originate from the top layer and those that come from the bottom layer. Clearly, the t/d_r value from the incipient crater in phase 2 is not measuring excavation depth reliably and, therefore, the results of phase 1 (d_e/d_r = 0.33) should be used for any further calculations required in phase 2.
       The light-haloed craters from phase 2 represent the partial obscuration of a dark halo. They excavate a quantity of underlying light material that is less than the amount required to obscure a dark halo completely. For these craters, the difference between the depth of excavation and the thickness of the overlying layers does not correspond to the exact value of d_h (Figure 8), but rather provides a lower bound to this value. The relationship can be expressed as d_h > d_e - t or, normalized to the rim-to-floor depth of experimental craters, as

dh/dr > de/dr - t/dr

(9)

For light-haloed craters, it can be seen from Table 2 that t/d_r ranges from 0.20 to 0.24, with a mean value of 0.21. Recalling that d_e/d_r = 0.33 from incipient craters in phase 1, and substituting these values into equation (9) we find that

dh > 0.12 dr

(10)

or

dh > 0.36 de

(11)

The value of d_h is significant, corresponding to at least 36% of the value of d_e. On the basis of phase 1 results, we also expected this value to increase at greater velocities. As anticipated, the value of d_h is found to be greater than the value of d_m. This results from the observation that a small quantity of dark material mixed into a light matrix produces a greater albedo effect than a similar quantity of light material that is mixed into a dark matrix [Hapke, 1993]. The consequence of this finding is that it is much easier to produce a dark halo than to obscure one, therefore, very large craters may be required to excavate enough crustal highland material to obscure dark halos in a cryptomafic area.
       The results from phase 2 show that, if craters large enough to be reaching the bottom of a cryptomafic deposit are present in a cryptomafic area, any thickness estimates obtained from these craters must take d_h into account or they will be considerably exaggerated. Equations that incorporate d_h to yield a better estimate (t_h) for the depth to the base of the cryptomafic deposit are derived. From Figure 3, it can be seen that, if the value of d_h is a minimum (equations 10 and 11), then calculations of t_h, based on the experimental light-haloed craters of phase 2, should produce maximum values. Considering this, and recalling that the average t/d_r value for the light-haloed craters is 0.21, we can say that

th < 0.21dr

(12)

To express this relationship in terms of the rim-crest diameter of lunar craters, equations (1) and (2), together with the relation d_e/d_r = 0.33 from Stöffler et al. [1975], are rearranged to provide

th < 0.053 Dr

(13)

for simple craters and

th < 0.095 Dr0.85

(14)

for complex craters. Again, these equations are expected to be accurate within an error of ±15%. Equations (13) and (14) should only be used to estimate the depth (t_h) to the base of a cryptomafic deposit when it is known that the largest dark-haloed craters are reaching the bottom and excavating the underlying highland crust. When the largest dark-haloed craters are not reaching the base of the cryptomafic deposit, incorporating the d_h value is not required since the highland substrate is not being excavated. In such cases, the depth of excavation provides the best minimum estimate for the depth to the base of the cryptomafic deposit and so equations (1) and (2) should be used.


        Phase 3
       On the basis of our experience from phase 1 of the experiments, it was possible to confine the results of phase 3 to the two types of craters that are most useful to our study: minimum dark-haloed craters, and incipient dark-haloed craters. As for phase 1, minimum dark-haloed craters were defined by the presence of tenuous, but relatively symmetrical, halos of dark material (Figure 14), and incipient dark-haloed craters were defined by a lack of dark halos, but the presence of some dark grains beyond the crater rim. As before, classification of craters was conducted prior to any additional analysis in order to minimize bias.
       The morphometric parameters (Figure 6) for each experimental crater were measured, and the results compiled in Table 3. The ratio of top layer thickness to crater depth (t/d_r) was calculated for each crater and then plotted as a function of the crater type and the percentage of dark material in the top layer mix (Figure 15). Again, some systematic difference in the value of t/d_r between minimum and incipient dark-haloed craters can be observed, with minimum dark-haloed craters generally having lower t/d_r values than incipient dark-haloed craters. Surprisingly, no consistent variations in t/d_r are observed for the different top layer mixtures, suggesting that the albedo of the pre-impact surface may not be a factor in the formation and detection of dark-haloed craters.
       Again, incipient dark-haloed craters represent the beginning of excavation of the dark layer, and therefore, the top layer thickness corresponds to the depth of excavation. From Table 3 and Figure 15, it can be seen that, for the incipient craters, t/d_r ranges from 0.27 to 0.32, with a mean value of 0.30. Recalling that the average t/d_r value for incipient craters was found to be 0.33 from phase 1 experiments, it can be seen that the phase 3 experiments tend to give lower t/d_r values. These lower values indicate that excavation of dark grains from the middle dark layer is more difficult to identify when the top layer itself contains dark grains. The beginning of excavation of the middle dark layer is, therefore, not being recognized as readily as in phase 1 of the experiments, where no confusion between layers is possible. Therefore, the t/d_r values from incipient craters in phase 3 are not considered to be giving a reliable measure of excavation depth and the results of phase 1 (d_e/d_r = 0.33) should be used for any further calculations.
       The minimum dark-haloed craters from phase 3 of these experiments represent the minimum amount of dark material that must be emplaced, on top of a mixed surface layer, before a dark halo becomes visible. The difference between the depth of excavation and the thickness of the overlying layer for these craters, provides another assessment of the value of d_m, one where the top layer more accurately reflects the conditions on the Moon. From Table 3 and Figure 15, the value of t/d_r is found to range from 0.24 to 0.28 for minimum craters, and the average is found to be 0.26. Considering that the range of t/d_r values from phase 1 of these experiments was found to be 0.22 to 0.30, with an average of 0.26, it can be said that the results from phase 1 and phase 3 are almost identical. This is consistent with our earlier finding that variations in the percentage of dark material in the top layer produced no systematic differences in the formation of dark haloes. We therefore conclude that either the albedo of the pre-impact surface is not a factor in the formation and detection of dark-haloed craters, or that the scale of these experiments is too small to allow for the detection of significant variations in the variables due to albedo.



Discussion

        Experimental Errors
       In the course of these experiments and their analysis, several factors may have led to the introduction of errors into these results. A change in sand type (starting with shot #3941) was required when the black-dyed sand was depleted and it was necessary to switch to a new, dark sand. This new dark sand was considerably different from the dyed black sand. It consists of undyed quartz grains that are naturally dark grey in color and so are not as opaque as the dyed sand grains. This new sand, however, appears to produce minimum and dark-haloed craters under similar conditions as other craters in phase 1 of the experiments, and with similar results (Table 1). This is interpreted to indicate that the two dark sand types are compatible. The spectrometer was no longer available at the stage of these experiments when the new dark sand was introduced, thus its spectrum could not be obtained. However, we suspect that the spectrum of this more translucent sand would not be as dark as that of the dyed-sand spectrum, but that it would still be different enough from the light sand to allow the classifications of the crater types to be unaffected. This interpretation is supported by our findings that albedo appears to play a minor role in dark halo formation and detection. Therefore, we conclude that any errors that might have been introduced by the changes of sand types used in these experiments should be very minor.
        Another source of potential error could result from a difference in grain size between the light and dark sand. A significant grain size difference could produce an alteration in the cratering behavior of the different layers, introducing effects that are unrelated to the dark halo forming process. To assess the possibility of such problems, the size fractions of all of the different sand types were measured and their average and median grain sizes were determined. Average grain size for the light sand was found to be 0.155 mm, with a median of 0.15 mm. The black-dyed sand was found to have an average grain size of 0.192 mm, with the median at 0.18 mm. This slight increase in grain size, with respect to the light sand, is caused by clumping of the sand grains due to the dying process. However, the grain sizes of light and dyed sand types are similar enough that we suspect no significant layer effects should be observed in the experimental results when these sands are used. The undyed dark sand was found to have an average grain size of 0.22 mm and a median of 0.3 mm. Here the larger size is simply due to a coarser sand, and it can be seen from the high median value that the grain size distribution for this sand type is considerable different from the others. Fortunately, no difference in crater morphology was observed between the types of craters that were produced with the dyed vs. the undyed dark sand. Thus, we suspect that the courser, undyed dark sand produces no significant cratering phenomena that would affect our results, and so experimental errors from differences in grain sizes should be negligible.
       The largest source of error is expected to occur during the measurement of the morphometric parameters of the experimental craters. We estimate that the accuracy of our measuring instrument is ±0.02 cm. We also consider that these measurements may be in error by as much as the thickness of one sand grain. The average grain size for all of the sand types combined is found to be 0.18 mm, so this error is estimated to be another ±0.02 cm. The combined measurement error is, therefore, ±0.04 cm for each morphometric parameter shown in Figure 6 and Tables 1, 2, and 3. The error for the ratios in Tables 1, 2, and 3, can be calculated from the measurement error and is found to be ±0.02. Thus, the t/d_r calculations are accurate to ±0.02. This value can be compared to a statistically derived estimate of experimental error, based on the resulting t/d_r data, which is found to range from 0.004 to 0.007. This is considerably lower than the measurement error, thus confirming that measurement is the most significant error component in the data analysis.


        Application to the Moon
       When applying these results to actual lunar craters, it is important to keep in mind that there are several factors that distinguish laboratory experiments from conditions on the Moon. Primarily, the velocity range and vertical impact angles of these experiments do not duplicate planetary conditions. Impact angles for planetary events can range from 90 to <5 degrees and the effect of such variations on our results is not clear. The velocities of planetary scale impacts are usually more than 10 km/s, a factor of 10 greater than the velocities used in these experiments. The results of Phase 1 suggest that a factor of 10 increase in the impactor velocity adds an uncertainty of approximately 10% to these results. However, equations (1) and (2), which are used to calculate the relations for t_m and t_h, are associated with an uncertainty of approximately ±15%. Thus, errors associated with velocity are expected to be minor in comparison. However, some non-linear velocity effects are also expected [Oberbeck, 1975], such as ballistic sedemtentation, which is discussed below.
       Another factor worth considering is the size of the sand grains. As was noted above, the average grain size of the experimental medium was 0.18 mm. It can be assumed that, for the most part, no further fracturing of the target material occurs at the energies used in these experiments, thus most ejected material should have a similar grain size distribution and size average as was measured for the pristine sand. Ejecta particles should, therefore, have an average grain size of 0.18.mum. If the experimental craters are scaled to lunar size, say 10 km in diameter, the ejecta material would scale to an average particle size on the order of 14 meters. While ejecta blocks of this size are observed (i.e., the Ries impact crater [Pohl et al., 1977]) it is not clear if they can be considered as representative of the ejecta deposit.
       In these experiments, the crater ejecta was emplaced on top of the pre-impact surface with little or no interaction with the surface material. On the Moon, however, the higher velocities associated with planetary scale impacts may produce ejecta deposits that are intimately mixed with the surface materials [Oberbeck, 1975]. In such cases, excavated mafic material can become contaminated by the presence of a highland component incorporated when materials from the surface layer are intimately mixed with ejecta during the emplacement process. This process is not modeled well by these experiments and there is a possibility that larger quantities of mafic material may be required to form a dark halo than are estimated by the experimentally determined value of d_m. Consequently, equations (7) and (8) should be considered to give a maximum estimate of t_m.
       It was also noted that the ejecta deposits produced by these experiments were on the order of one or two grains thick. On the Moon, ejecta is expected to be 10's to 100's meters thick [McGetchin et al., 1973; Schultz et al., 1981], and so will contain more than a few individual grains throughout its great thickness. It has been observed that the entire thickness of a lunar ejecta deposit is more or less homogenous, with ejecta materials being completely mixed throughout the deposit [Blewett et al., 1995]. Thus intimate mixing also occurs within the ejecta deposit itself, and mafic and highland components of the ejecta are expected to be mixed throughout the deposit. Again, this process is not being modeled by the experimentally produced ejecta deposits that are one or two grains thick. Since small quantities of dark material have a great effect on the albedo of the ejecta deposit [Hapke, 1993], larger quantities of highland material may be required to obscure a dark halo than are estimated by our experimentally determined value of d_h. Consequently, equations (13) and (14) should be considered to give a maximum estimate of t_h.
       Finally, the materials used in these experiments have very large albedo contrasts (Figure 12). On the Moon, the albedo contrast between highland and mafic materials is significantly lower. This factor could affect the values of d_m and d_h, since larger quantities of mafic material may be required to produce a dark halo, and smaller quantities of highland material may be required to obscure a dark halo, when the albedo contrasts are significantly lower. Furthermore, the observation that albedo of the pre-impact surface does not affect dark halo formation or detection may not be equally valid when the albedo contrast between materials is much lower.
       All of the factors mentioned above also have implications for the spectral detectability of dark-haloed craters. If remote sensing data, such as that from Clementine, are to be used in the detection of dark-haloed craters, then it is important to understand how the differences between experimental conditions and those on the Moon will affect dark halo identification. For our experimental materials, little spectral distinction exists (Figure 12) between the dark and light sand that was used for the different layers. Thus, no conclusions can be made about the spectral determinability of dark-haloed craters from this study. Considerable spectral differences exist between mafic materials that make up the lunar maria and anorthosites that predominantly make up the highlands. Thus, it is possible that the presence of a mafic component could be spectrally identified in an ejecta deposit when it is not visually observable. If this is the case, then the amount of dark material required to produce a dark halo and the amount of light material required to obscure a dark halo may be affected. Further work still needs to be done to resolve these issues.



Summary

       We conducted experiments in order to study the formation of dark-haloed craters, which can be used to indicate the presence of cryptomafic deposits and determine their volumetric extents. In Chapter 1, the depths of excavation of dark-haloed craters were used to identify the top and base of cryptomafic deposits. However, this method provides only first-order estimates of thicknesses, since some thickness (d_m) of mafic material must be excavated before a dark halo can be observed, and some thickness (d_h) of underlying highland crustal material must be excavated before a dark halo is obscured. This series of experiments was begun to determine the values of d_m and d_h, and to derive equations which yield improved estimates of the depth to the top and base of cryptomafic units.
       Layered targets of resin-coated sand were constructed to simulate the configuration of cryptomafic deposits and then impacted to produce barely visible dark haloes. Experiments were conducted in three distinct phases. In the first phase, simple dark halo formation was studied. The depth of penetration into the dark layer required to produce a dark halo, was found to equal 20% of the depth of excavation. The thickness (t_m) of the layer overlying a cryptomafic deposit was found to be estimated by the equations t_m ~ 0.066 D_r for simple craters, and t_m ~ 0.12 D_r^0.85 for complex craters, within an error of ±15%. In the second phase, dark halo obscuration was studied. The lower bound for d_h, or penetration required into a bright substrate to obscure a dark halo, was found to equal 36% of the excavation depth. The depth (t_h) to the base of a cryptomafic deposit was found to be estimated by the equations t_h < 0.053 D_r for simple craters, and t_h < 0.095 D_r^0.85 for complex craters, within an error of ±15%. The third phase of these experiments attempted to study the effects of albedo variation within the surface layer. The results from this phase were found to be almost identical to phase 1 results, indicating that albedo of the pre-impact surface may not be a factor in dark halo formation or detection.
       Several sources of potential error were introduced during the course of these experiments. The largest source of error is believed to result from measurement uncertainties.
       It is important to consider the differences between experimental conditions and those on the Moon when applying the results of these experiments to lunar craters. The intimately mixed nature of lunar ejecta is not being modeled by these experiments. The albedo contrast between experimental materials is significantly greater than between the lunar mafic materials and highlands. When scaled to planetary sizes, sand particles may not adequately represent impact ejecta. These factors all tend to affect the experimental results. An ability to detect dark-haloed craters using spectral methods can also affect these experimental results, an important consideration if remote sensing data such as Clementine is to be used in dark halo identification. More work is required to address these issues.



References

Adams, J.B., and T.B. McCord, Vitrification darkening in the lunar highland and identification of Decartes material at the Apollo 16 site, Proc. 4th Lunar Sci. Conf., 163-177, 1973.

Antonenko, I., J.W. Head, J.F. Mustard, and B.R. Hawke, Criteria for the detection of lunar cryptomaria, Earth, Moon, Planets, 69, 141-172, 1995.

Bell, J.F., and B.R. Hawke, Lunar Dark-haloed impact craters: Origins and implications for early mare volcanism, J. Geophys. Res., 89, 6899-6910, 1984.

Blewett, D.T., B.R. Hawke, P.G. Lucey, G.J. Taylor, R. Jaumann, and P.D. Spudis, Remote sensing and geologic studies of the Schiller-Schickard region of the Moon, J. Geophys. Res., 100, 16,959-16,978, 1995.

De Hon, R.A., Thickness of the western mare basalts, Proc. Lunar Planet. Sci. Conf., 10th, 2935-2955, 1979.

Hapke, B., Theory of Reflectance and Emittance Spectroscopy, 455pp, Cambridge University Press, New York, NY, 1993.

Hawke, B.R., and J.F. Bell, Remote sensing studies of lunar dark-halo impact craters: Preliminary results and implications for early volcanism, Proc. Lunar Planet. Sci. Conf., 12th, 665-678, 1981.

Head, J.W., Lunar mare deposits: Areas, volumes, sequence, and implication for melting in source areas, in Origins of Mare Basalts and their Implications for Lunar Evolution, Lunar Science Institute, Houston, TX, 66-69, 1975.

Head, J.W., Lava flooding of ancient planetary crusts: Geometry, thickness, and volumes of flooded lunar impact basins, The Moon and the Planets, 26, 61-88, 1982.

Head, J.W., and L. Wilson, Lunar mare volcanism: Stratigraphy, eruption conditions, and the evolution of secondary crusts, Geochim. et Cosmochim. Acta, 56, 2144-2175, 1992.

Head, J.W., S.M. Murchie, J.F. Mustard, C.M. Pieters, G. Neukum, A.S. McEwen, R.F. Greeley, E. Nagel, and M.J.S. Belton, Lunar impact basins: New data for the western limb and far side (Orientale and South Pole-Aitken basins) from the first Galileo flyby, J. Geophys. Res., 98, 17,149-17,181, 1993.

McGetchin, T.R., M. Settle, and J.W. Head, Radial thickness variation in impact crater ejecta: implications for lunar basin deposits, Earth Planet. Sci. Letters, 20, 226-236, 1973.

Oberbeck, V.R., The role of ballistic erosion and sedimentation in lunar stratigraphy, Rev. Geophys. Space Phys., 13, 337-362, 1975.

Pohl, J., D. Stöffler, H. Gall, K. Ernstson, The Ries impact crater, in Impact and Explosion Cratering , D.J. Roddy, R.O. Peppin, R.B. Merrill (eds.), Pergamon Press, New York, NY, 343-404, 1977.

Schultz, P.H., and P.D. Spudis, Evidence for ancient mare volcanism, Proc. Lunar Planet. Sci. Conf., 10th, 2899-2918, 1979.

Schultz, P.H., and P.D. Spudis, Beginning and end of lunar mare volcanism, Nature, 302, 233-236, 1983.

Schultz, P.H., D. Orphal, B. Miller, W.F. Borden, and S.A. Larson, Multi-ring basin formation: Possible clues from impact cratering calculations, in Multi-ring Basins, Proc. Lunar Planet. Sci., 12A, P.H. Schultz and R.B. Merrill (eds.), 181-195, 1981.

Solomon, S.C., and J.W. Head, Vertical movement in mare basins: Relation to mare emplacement, basin tectonics, and lunar thermal history, J. Geophys. Res., 84, 1667-1682, 1979.

Solomon, S.C., and J.W. Head, Lunar mascon basins: Lava filling, tectonics, and evolution of the lithosphere, Rev. Geophys. and Space Phys., 18, 107-141, 1980.

Solomon, S.C., R.J. Ahrens, P.M. Cassen, A.T. Hsui, J.W. Minear, R.T. Reynolds, N.H. Sleep, D.E. Strangway, and D.L. Turcotte, Thermal histories of the terrestrial planets, Basaltic Volcanism on the Terrestrial Planets, Chap. 9, Pergamon, NY, 1129-1234, 1981.

Stöffler, D., D.E. Gault, J. Wedekind, and G. Polkowski, Experimental hypervelocity impact into quartz sand: Distribution and shock metamorphism of ejecta, J. Geophys. Res., 80, 4062-4077, 1975.



Tables

Table 1. List of data from phase 1 of these experiments. Four types of craters were identified: dark-haloed craters (DHC), minimum dark-haloed craters (Min), incipient dark-haloed craters (Incip), non-haloed craters (Non). Type examples are presented in Figure 9. Three different projectile compositions were used, including aluminum (Al), glass, and nylon. Shot numbers were used to distinguish the different impacts and resulting craters. Velocities were determined with a laser-occultation system. Spectra were obtained for 10 of the craters; their type identifiers are the same as for crater types. Examples of spectra sets are presented in Figure 12. The morphometric parameters D_r, t, d, h_r, and d_r are defined in Figure 6. These were measured from the cross-sections of the sawed targets. The ratio t/d_r was calculated from the measured values.

Type	Projectile	Shot #	Velocity (km/s)	Spectra Traverse	Dr (cm)	t (cm)	d (cm)	hr (cm)	dr (cm)	t/dr
DHC	Glass	3876	0.996	-	10.93	0.44	1.57	0.12	1.69	0.26
DHC	Glass	3877	1.020	DHC	11.37	0.44	1.83	0.26	2.08	0.21
DHC	Glass	3872	1.133	-	12.42	0.40	1.47	0.24	1.71	0.23
DHC	Glass	3884	1.457	DHC	12.30	0.36	2.14	0.28	2.42	0.15
DHC	Glass	3885	1.482	DHC	12.98	0.50	2.46	0.30	2.76	0.18
DHC	Glass	3882	1.483	DHC	13.35	0.66	2.00	0.28	2.28	0.29
DHC	Glass	3883	1.485	DHC	13.24	0.56	1.98	0.26	2.24	0.25
DHC	Glass	3942	1.486	-	13.08	0.66	2.50	0.22	2.72	0.24
DHC	Glass	3941	1.507	-	12.58	0.60	2.26	0.22	2.48	0.24
DHC	Glass	3898	2.039	-	14.59	0.77	2.46	0.22	2.66	0.29
Min	Al	3900	1.454	-	12.34	0.66	2.02	0.16	2.18	0.30
Min	Al	3906	1.482	-	13.87	0.70	2.10	0.22	2.32	0.29
Min	Al	3905	2.127	-	15.44	0.83	2.56	0.30	2.86	0.29
Min	Glass	3902	1.029	-	11.43	0.66	2.16	0.26	2.42	0.27
Min	Glass	3875	1.053	Min	11.83	0.54	1.86	0.26	2.12	0.25
Min	Glass	3908	1.061	-	11.17	0.58	1.77	0.18	1.94	0.30
Min	Glass	3943	1.494	-	12.92	0.68	2.44	0.30	2.74	0.25
Min	Glass	3891	2.054	Min	14.76	0.71	3.02	0.22	3.24	0.22
Min	Glass	3901	2.106	-	14.60	0.75	2.46	0.20	2.66	0.28
Incip	Al	3907	1.503	-	13.69	0.81	1.92	0.18	2.10	0.39
Incip	Glass	3874	1.040	-	11.87	0.81	2.14	0.20	2.34	0.35
Incip	Glass	3880	1.472	Incip	12.94	0.81	2.18	0.20	2.38	0.34
Incip	Glass	3886	1.485	Incip	13.93	0.73	2.04	0.20	2.24	0.33
Incip	Glass	3888	1.998	Incip	14.49	0.85	2.58	0.18	2.76	0.31
Incip	Glass	3903	2.079	-	14.21	0.81	2.48	0.24	2.72	0.30
Incip	Nylon	3904	1.400	-	9.90	0.52	1.75	0.24	1.98	0.26
Incip	Nylon	3899	1.546	-	9.45	0.75	2.02	0.20	2.22	0.34
Non	Glass	3873	1.047	-	12.62	1.37	1.27	0.28	1.55	0.88
Non	Glass	3897	2.044	-	14.82	1.07	2.10	0.28	2.38	0.45

Table 2. List of data from phase 2 of these experiments. Two types of craters were identified: light-haloed craters (LHC), and incipient light-haloed craters (Incip). An example of a light-haloed crater is shown in Figure 13. Only glass projectiles were used in this phase of experiments and no spectra were obtained. See Table 1 for descriptions of other variables.

Type	Projectile	Shot #	Velocity (km/s)	Dr (cm)	t (cm)	d (cm)	hr (cm)	dr (cm)	t/dr
Incip	Glass	3944	1.518	14.64	1.67	0.83	0.24	1.90	0.44
LHC	Glass	3948	1.492	15.24	1.71	0.38	0.18	1.88	0.20
LHC	Glass	3945	1.528	15.04	1.57	0.42	0.18	1.75	0.24
LHC	Glass	3946	2.035	15.68	2.24	0.50	0.24	2.48	0.20
LHC	Glass	3947	2.183	16.79	2.20	0.47	0.12	2.32	0.20

Table 3. List of data from phase 3 of these experiments. Two types of craters were identified: minimum dark-haloed craters (Min), and incipient dark-haloed craters (Incip). An example of a minimum dark-haloed crater is shown in Figure 14. Only glass projectiles were used in this phase of experiments and no spectra were obtained. The percentage of dark material in the top layer was varied for this phase. Mixtures with 10%, 20%, and 33% dark material in the top layer were tried. See Table 1 for descriptions of other variables.

Type	Projectile	Shot #	Velocity (km/s)	% Dark	Dr (cm)	t (cm)	d (cm)	hr (cm)	dr (cm)	t/dr
Min	Glass	3953	1.460	10	11.29	2.38	0.71	0.20	2.58	0.28
Min	Glass	3949	1.468	10	11.37	2.38	0.62	0.16	2.54	0.24
Min	Glass	3955	1.506	20	12.05	2.26	0.66	0.20	2.46	0.27
Min	Glass	3962	1.485	33	11.77	1.98	0.64	0.26	2.24	0.28
Min	Glass	3959	1.500	33	12.14	2.28	0.68	0.18	2.46	0.27
Min	Glass	3963	1.505	33	11.73	2.18	0.60	0.18	2.36	0.25
Incip	Glass	3952	1.499	10	11.99	2.50	0.85	0.20	2.70	0.32
Incip	Glass	3954	1.454	20	11.59	2.26	0.73	0.20	2.46	0.30
Incip	Glass	3950	1.504	20	12.24	2.56	0.73	0.20	2.76	0.27
Incip	Glass	3961	1.450	33	12.42	1.92	0.70	0.30	2.22	0.31
Incip	Glass	3951	1.487	33	11.87	2.32	0.77	0.28	2.60	0.30
Incip	Glass	3960	1.545	33	11.87	2.20	0.68	0.20	2.40	0.28

Figures


Figure 1. High sun-angle image from the Clementine data set, showing an example of a dark-haloed impact crater, indicated here by the white arrow. This crater (Drebbel N) is 9 km in diameter and is located near the crater Schickard on the western limb of the Moon.




Figure 2. Schematic diagram illustrating the formation of a cryptomafic deposit by the emplacement of a basin ejecta deposit on top of a pre-existing mafic unit. Later impacts penetrate into the hidden mafic layer, excavating mafic material that matures to form dark-haloed craters. The excavation depth of the smallest dark-haloed craters (Min DHC's) defines the top of the cryptomafic deposit, while the excavation depth of the largest dark-haloed craters (Max DHC's) defines the bottom of the cryptomafic deposit. The size of the smallest dark-haloed craters varies as a function of distance from the basin ejecta source; minimum craters closer to the ejecta source are larger since they must penetrate through thicker, proximal deposits. Very small craters will not form dark-haloed craters, because they do not excavate the mafic layer. Very large craters will also not form dark-haloed craters, because they excavate enough highland crustal material to obscure the dark halo signature. From Chapter 1.




Figure 3. Block diagram illustrating the limitations of using depth of excavation (d_e) for measuring depths of stratigraphic layers. The diagram shows a schematic representation of the smallest possible dark-haloed crater that can form (Min DHC), where the dark halo is just barely begun to be visible, and the largest possible dark-haloed crater that can form (Max DHC), where the dark halo is still barely visible despite the presence of obscuring highland material. For the minimum dark-haloed crater, d_e overestimates the thickness of the overlying layer (t_m) by a value d_m, which represents the penetration into mafic material that is required to produce a barely visible dark halo. The relationship between d_m, t_m and d_e is shown to be d_m = d_e - t_m. For the maximum dark-haloed crater, d_e overestimates the combined thickness of the overlying layers (t_h) by a value d_h, which represents the penetration into highland crustal material that can occur before sufficient highland material is excavated to obscure the dark halo. The relationship between d_h, t_h and d_e is shown to be d_h = d_e - t_h. From Chapter 1.




Figure 4. Photograph of a prepared target surface. A round target container, 25 cm in diameter and filled with layered sand, is shown surrounded by a platform apparatus. The top of the platform lies flush with the sand surface inside the container, thereby extending the experimental surface area. The platform top has been sprayed with adhesive glue and sprinkled with light-colored sand, in order to simulate a sand surface. Additional sand has been sprinkled over the platform surface, allowing for interaction between free-moving sand grains. Several small, plastic vials and two plastic vial lids (closest to target center) are shown placed at intervals of 2.54 cm. These act as catchers during the experiment, collecting samples of the ejected material for later study.




Figure 5. Photograph of the cross-section of a hardened target, shot #3882. The three layers of the target are clearly visible here. Morphometric parameters of the craters, illustrated schematically in Figure 6, were measured from the cross-sections.




Figure 6. Schematic diagram illustrating the characteristic features of experimental craters. The rim-to-rim diameter (D_r), rim-to-floor depth (d_r), floor-to-pre-impact surface depth (d), rim height (h_r), and thickness (t) of the top layer(s) was measured for each experimental crater. The results are shown in Tables 1, 2, and 3.




Figure 7. Block diagram of the setup for phase 1 experiments, illustrating the relationship between the thickness of the overlying light layer (t), the depth of excavation (d_e), and the depth of dark layer penetration (d_m) that is required to produce a barely visible dark-haloed crater.




Figure 8. Block diagram of the setup for phase 2 experiments, illustrating the relationship between the combined thickness of the overlying layers (t), the depth of excavation (d_e), and the depth of penetration (d_h) that is required into the lower light layer before a dark halo is obscured.




Figure 9. Overhead views of the four distinct crater types identified in phase 1 of these experiments. Crater types were determined by the visual inspection of targets and high-angle illumination photographs. a) Dark-haloed crater (shot #3883, glass projectile, 1.5 km/s) shown in high-angle illumination. Such craters are defined by the presence of substantial and well-developed haloes of dark material. b) Minimum dark-haloed crater (shot #3900, aluminum projectile, 1.5 km/s) shown in high-angle illumination. Minimum dark-haloed craters are defined by the presence of tenuous, but relatively symmetrical, halos of dark material. c) Incipient dark-haloed crater (shot #3888, glass projectile, 2.0 km/s) shown in high-angle illumination. These craters are identified by the presence of dark grains beyond the experimental crater rim, demonstrating that excavation of dark material has begun. Also shown in this image are the locations, indicated by letters and numbers, where spot spectra were taken for this experimental crater. See Figure 12c for the corresponding spectra. d) Non-haloed crater (shot #3897, glass projectile, 2.0 km/s) shown in low-angle illumination to illustrate the position of the crater rim. The lack of dark grains beyond the crater rim identifies these craters, showing that no excavation of dark material has occurred.




Figure 10. Plot of the top light layer thickness divided by crater depth (t/d_r) for phase 1 craters, shown as a function of crater type and projectile composition. The value of t/d_r is seen to vary as a function of crater type, with minimum values occurring for dark-haloed craters (DHC), where excavation of dark material is greatest, and maximum values occurring for non-haloed craters, where excavation of dark material does not take place. Projectile density also appears to be responsible for slight trends in t/d_r, where denser aluminum projectiles produce higher t/d_r values and less dense nylon projectiles produce lower values with respect to glass. Note that the highest t/d_r value, for a non-haloed crater (Table 1), is not plotted in this figure, which is scaled to illustrate the variations in t/d_r for the other crater types.




Figure 11. Plot of top layer thickness/crater depth (t/d_r) verses impact velocity for phase 1 minimum and incipient craters, glass projectiles only. Slight trends in t/d_r, which are related to the impact velocity, can be observed when the crater types are considered separately. However, these trends are poorly constrained.




Figure 12. Spectra traverses of the three distinct crater types, as identified in phase 1 of these experiments. The letters C and R represent spot spectra taken at the center and rim of the crater, respectively. Numbers represent spot spectra taken at 2.54-cm intervals from the crater rim. a) Typical spectra traverse for a dark-haloed crater (shot #3877, glass projectile, 1.0 km/s). These craters are defined by the similarity between the center (C) and rim (R) spectra, and by the systematic brightening of spectra as a function of distance form the crater rim. b) Spectra traverse for a minimum dark-haloed crater (shot #3875, glass projectile, 1.0 km/s). Minimum craters are defined by a significant difference between the center (C) and rim (R) spectra, and by the systematic brightening of spectra as a function of distance form the crater rim. c) Spectra traverse for an incipient dark-haloed crater (shot #3888, glass projectile, 2.0 km/s). Such craters are defined by a large difference between the center (C) and rim (R) spectra, and by the lack of systematic brightening of spectra as a function of distance form the crater rim. Note how in this figure, the spectrum from the rim has already reached maximum brightness and is more or less indistinguishable from subsequent spectra taken beyond the crater rim (numbered spectra). The spot locations for some of the spectra of this figure are shown in Figure 9c).




Figure 13. Overhead view of a light-haloed crater (shot #3946, glass projectile, 2.0 km/s) from phase 2 of these experiments, shown in high-angle illumination. We define light-haloed type craters as those that excavate sufficient material from the lower light layer to affect the dark halo, but not to obscure it completely . These craters were identified by visual inspection of targets and high-angle illumination photographs.




Figure 14. Overhead view of a minimum dark-haloed crater (shot #3959, glass projectile, 1.5 km/s, 33% dark in top layer) from phase 3 of these experiments, shown in high-angle illumination. In phase 3, a known percentage of dark material was mixed into the top light layer, thus improving the analogy to an obscuring unit on the Moon. We define minimum dark-haloed craters by the same criteria as for phase 1, namely by the presence of tenuous, but relatively symmetrical, halos of dark material, that are distinguishable from the pre-impact surface. These craters were identified by the visual inspection of targets and photographs taken at high illumination angles.




Figure 15. Plot of the top light layer thickness divided by crater depth (t/d_r) for phase 3 craters, shown as a function of crater type and content of dark material in top layer. The value of t/d_r is seen to vary as a function of crater type, with lower values occurring for minimum dark-haloed craters and higher values occurring for incipient dark-haloed craters. We can identify no consistent variations in t/d_r with respect to the different top layer mixtures, indicating that albedo of the overlying layer may not be a significant factor in dark halo formation and identification.

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