Most of the surface material in the regolith is finer than 6~ (including the regolith of fresh craters) (infrared emissivity and Surveyor studies). The density of the near surface regolith is about 1.5 gm/cc (radar cross sections and Surveyor surveys) o.
SPECTRAL REFLECTANCE MAPPING
Therefore, a telescopic observational study was conducted to map and classify the spectral reflectance of a portion of the lunar surface. No major changes with phase angle were found in the positions of the other maxima listed in Table 1.
TYPE Sr
TYPES
TYPE Sb
TYPE Tr
TYPE T
TYPE Tb
TYPE P
THE SEQUENCE OF FORMATION OF REGIONAL MARE UNITS
The distribution of more lithologies swept in this study is in the northeastern quadrant of the Moon. A direct comparison of the spectral types and relative ages of a large number of lunar regions is shown in Figure 11. A fourth period, apparently without major events of mare formation, extended from the end of the deposition of the maria of the third stage to the present.
Materials north of the ridge, however, were deposited during the third phase of mare formation. Incorporation of marae material into Oceanus Procellarum occurred during the second and third phases of marae formation o Two smaller S-type reflectivity units were deposited during the second phase o These units are north of Aristarchus and southwest of Landsberg near the Apollo 12 landing site. Most of the Oceanus Proce !Ia rum was flooded with T-type mare materia I in the third state of mare formation.
The following important conclusions implied by this research can be summarized as follows: a) The formation of the lunar mario can be divided into three main periods, each period related to the deposition of material from one. The error oars indicate uncertainties in measurements of the diameter of craters that have eroded up to 4° in a time equal to the age of the surface.
APPENDIX I
With the return of lunar samples, such remote sensing techniques have become extremely important tools to extend knowledge of the composition of single landing sites to other parts of the Moon. The second approach is to map the oral variations of the reflectance spectra to study the relationships between mappable spectral units and variations in albedo, morphology and age. Normalized lunar relative reflectance curves obtained by McCord (1968) indicate that a minimum of three narrow-bond reflectance measurements between 0.4 microns and 0.7 microns are required to resolve each of the spectra I types.
Lateral changes in the lunar reflectance spectrum were measured by scanning strips 130 ores long and 18 ores wide twice in each of the three filters. The width of the strip is controlled by the field of view of the instrument. o This radiation can be represented by the function B(x1A.), which is the average brightness over the strip in the intervals x-x+dx and x.-x_ +dx_, where x is the coordinate along the strip and A. The transmittance of the Earth's atmosphere can be written as the sum two functions.
S orne periods of V (A., t) are longer than the integration times of the measurement 1 and are therefore an important source of noise. W(x) has the shape of a symmetrical trapezium and depends on the instrument aperture diameter and the scanning speed; F. A) is the transmission of the ith.
WAVELENGTH (MICRONS)
The numerical technique used in this operation adds high-frequency noise, which is later removed by low-pass filtering (Figure 14) o The fi Iter used has an upper cutoff slightly lower than the Nyquist frequency of the original sample. This form minimizes the effects of the albedo and insolation function Along the parts of a scan where C.(x) is constant D:, j becomes. BOUNDARY RECOGNITION AND CLASSIFICATION OF SPECTRAL TYPES Due to the presence of noise in D: ., primarily due to variations.
The positions of the boundaries can be obtained using a model boundary and companng. The next step in processing the data is to obtain the distribution of the spectral types. This figure also shows that the variation between spectral types mainly occurs in the form of a rotation of the spectrum of approximately 0.52 microns.
The consistency and accuracy of the mapping technique can be tested in a variety of ways. The linear response of the photoelectric system over a wide range of luminance is demonstrated at boundaries such as that between Mare Crisium and the highlands to the west.
LEGEND
Sr DTb Er.l
Solid lines represent reflectance spectra obtained by McCord (1968); the phase angles of those observations are given in parentheses. The similarity of spectral types east and west of this boundary was documented by McCord (1968). The validity of the method is further demonstrated by the correlation of spectral type and boundary position between independent scan lines.
By comparison with the position of such marked albedo boundaries, the errors in the measured positions of color boundaries are generally estimated to be less than half the aperture diameter (about 15 km). Much higher resolutions (<3 km) can be obtained by using smaller apertures and slower scan speeds. The dominant sources of noise are statistical pulse count errors (1/N 1/2 about 1%) and variations in atmospheric transmission (nominal about 2%) that have periods of less than a few minutes.
The technique presented here is sufficient to (1) map variations in the moon's normalized reflectance with amplitudes greater than approx. 1%, (2) locate the boundaries between larger spectral units with an accuracy of approx. 15 km, and (3) identify the spectral types of the mapped units and determine whether these types form a continuous progression or fall into different categories o.
DISTANCE ALONG SCAN (ARC SECONDS)
APPENDIX II
A model of the erosion of the lunar surface due to the impact of small projectiles has been developed, which provides an analytical representation of the change in the shape of the crater as a function of time. In recent years, knowledge of the distribution of lunar craters has been extended to include craters smaller than 10 em in diameter with the Ranger 1 Orbiter and Surveyor imaging systems. The general shape of the observed diameter-frequency relationship for craters in the lunar sea is shown in Fig. 21.
The discrepancy between the observed and predicted exponents is likely due to the sensitive dependence of the secondary distribution of a single impact on the proximity to that impact. Any prediction of the secondary population above the lunar surface must take this effect into account. The downward displacement, W, of the center of mass of the entire exhaust pattern is then.
For craters about a meter or more in diameter, experimental evidence indicates that most of the ejecta falls within a few crater radii (D.Eo Gau It, personal communication, 1969). Dependence of the constant in equation (6) on the shape of the ejection profile or eroded craters.
PROFI E: F<r> e
A simple differential equation for the steady -modification of the surface by random impacts of small bodies can be derived using Next, consider a two-dimensional topography in which the height, h 1 is a function of only one variable, x. 2 can be derived from equation (11)o From conservation of mass the following simple differential equation for the height is obtained.
With this series it is easier to observe the dependence of the time constant on the spatial frequency in the solution. This is a logical choice of initial form because the first root is the longest in the solution. Assuming that the surface is covered when the total area of the crater is twice the area, then.
11 lifetime 11 of a crater, 'T" 1 is defined as the time after which the maximum slope in the crater is less than an arbitrary small slope, Sf. Below 10° to 15° the surface becomes mottled and the crater shape it is irregular as erosion from larger craters becomes effective.
CRATER SLOPE (DEGREES)
As the slope approaches -4.0, mode I breaks down because the erosion rate depends on the lower limit of the eroding craters rather than on an upper limit (R). The observed distribution is probably best suited for this. It is important to examine the stability and sensitivity of the model to various assumptions inherent in its development. Such low-slope spreading was probably involved in the formation of the lunar highlands (Gault 1 1969).
The model is still valid if 'f' is thought of as the integrated flux that has fallen to the surface since the formation of the crater. In the case of the radially symmetric crater, the morphology approaches the shape of the Bessel function. The technique used here to obtain the relative age is based on a determination of the total accumulation of craters on an initially flat and featureless surface.
Another technique used to measure relative age is based on a determination of regolith thickness (Oberbeck and Ouaide, 1968; Shoemaker, 1970). In principle, it is possible to obtain the surface age by measuring any of the
The age of the surface is just the time required to erode a crater of a given radius to the slope that terminates the slope-frequency distribution of craters of that radius. The most consistent definition is that a crater is unshadowed when features (indentation marks1 fractures1 crater scars) are visible in the nearly shadowed portion of the wall. The size of the crater eroded below 4 o in the age of the surface was determined for each site from two different photographs taken at different solar illumination angles.
The shaded areas represent areas of acceptable fit of the theoretical functions to the data. Comparison of the observed and predicted ratio of unshaded to shaded craters as a function of crater d:a:-.1eter. Based on these criteria, there is some reason to believe that these sites are of the same age.
Many of the craters in this frame appear to have a flat bottom, and part of the crater walls are shaded. The technique presented here can be used to determine the DL, the largest crater that can be continuously eroded below the detection limit in surface age with an accuracy of about 10%.
APPENDIX IV
This appendix contains a list of data used to calculate the relative ages of many areas on the Moon's surface. DL is the calculated diameter in meters of a crater that would be eroded to a slope of 4° in a time equal to the age of the surface. Adams, J.B., 11 Lunar and Martian surfaces: petrological significance of near-infrared absorption bands, 11 Science, 159,.
Whitaker, "Observations of the Lunar Regolith and Earth from the Television Camera on Surveyor 7.11 J.
