B. Based on the data, compaction/erosion cannot explain the differences in dip angles between dunes and sandstones Some have recognized that supposed eolian sandstones lack crossbed inclinations which are at the angle of repose; this is refreshing considering how many claims there are to the contrary. Authors have appealed to post-depositional compaction to explain the reduction of cross-bed inclinations (Corey et al. 2005; Glennie 1972, p. 1058; Hunter 1981, p. 323; McKee and Bigarella 1979a, p. 191, 218; Rittenhouse 1972; Walker and Harms 1972, p. 280). Walker and Harms calculated (p. 280) that if cross-bedded sand at the angle of repose (34°), had an initial porosity of 40% and was compacted down to 20% porosity, the angle would become about 27°, or an angle reduction of about 24%. Corey et al. found a similar value and claimed compaction and cement production could reduce angles from 32° to 24° in the Navajo Sandstone (24° was their average (compacted) angle measurement). Our calculations (Emery et al. 2011) showed that angle reduction probably happened, but only by a few degrees. The work in that abstract was preliminary and needs to be further developed. However, based on hundreds of thin sections that we examined from the Coconino, we found very little evidence for significant compaction. We looked for things like fractured grains, deformed ooids, and bent muscovite flakes, all of which were largely lacking from the Coconino and shows that an initial porosity of 40%, similar to eolian dunes, which is unreasonable. Missing higher angles have also been attributed to the erosion and non-preservation of the uppermost part of the foreset beds (where the angles are usually the steepest) being eroded away and not preserved (Collins 2022, McKee and Bigarella 1979a, p. 218; Poole 1962, p. D148; Walker and Harms 1972, p. 280). It is well-known that the steepest parts of eolian dunes are on the upper part of the foreset slope, just below the crest (Hunter 1977). When making comparisons of cross-bed angles in supposed eolian sandstones to modern eolian dunes, the focus has always been on high angles, missing high angles, or the average. However, this study has uncovered a major oversight in comparing sandstone cross-bed angles with modern dunes. The low-angle dips missing from the sandstones and abundantly present in modern dunes have been overlooked (examine Fig. 6). More than 25% of modern dune angles are less than 10%, compared to only 1.4% of sandstones. If the sandstones have been compacted, the low dip angles should still be there; but they are missing. Examining the two sets of data using quartiles and standard deviations (Fig. 7) shows that the cross-bed dip data of sandstones and modern eolian dunes that can be clearly distinguished. The sandstone cross-bed data set cannot be achieved by compacting the modern eolian dune set; it would not produce the low angles so abundant in the dune data set. Considering Fig. 7, note that the dune set is bimodal, compared to the more normal distribution of the sandstone dip angles; compacting the dune set would not give the same distribution as the sandstone set—there would be even more low angles (note that the sandstone set is already “compacted”). A similar problem occurs by claiming that the higher angles were just eroded away and that is why they are not preserved. Erosion of the tops of the dune sets would still preserve the lower parts of the dunes that contain the low angles. To help illustrate this problem, Fig. 10 was drafted. Consistent with what Corey et al. (2005) and Walker and Harms (1972) proposed, each of the initial 855 dune measurements was compacted 24% and then re-plotted. One can see that compacting the dune data does not produce the sandstone data. Not only do the higher dune angles of the compacted dunes not “catch up” to the percentages found in the sandstones (compare the blue and red shading on the right side of the plot), but now there are even more low angles in the dune data (on the left side of the plot). Note that the dune data nearly loses its bimodality and becomes, more or less, a normal curve that is skewed to the right. The methods of making this curve are more fully described in the figure caption. One may argue that the current dune data set of individual measurements are primarily from the coastal dunes in Brazil and the gypsum dunes of New Mexico, which may not be quite analogous to depositional environments of sandstones like the Coconino or Navajo. It is not that no measurements were made in other locations, it is simply the type of data that are available from these other locations. The plots of the Nebraska Sand Hills (Fig. 3), an inland sand sea, could similarly be compacted, and the results would be the same with an abundance of low angles. C. Is “steep” an optical illusion if cross-bed sets are thick? I have often asked groups of people standing with me around crossbedded sandstones to estimate the angle of the cross-beds for me. Inevitably, when cross-bed sets are thick higher angles are guessed and when cross-bed sets are small, lower angles are anticipated. All are usually surprised when I demonstrate the dip angle with a Brunton compass or, more recently an iPhone. I have made the same observation from the literature. Never have I read about the Tapeats Sandstone (with small cross-bed sets) having “angle of repose dips” or even “steep” dips. However, descriptions of sandstones with thicker cross-bed sets like those of the Coconino, or especially the Navajo, abound with descriptors like “angle of repose,” “steep,” or “steeply inclined” even though these sandstones have average angles that are very close to one another (Fig. 8). The only conclusion that I have been able to reach, is that observers are often fooled into thinking that thicker sets of cross-beds have steeper angles. As scientists, we should always fall back on data to back up our claims. Even Edwin McKee himself seems to have fallen to this illusion. In his 1940 paper, where he published the Tapeats Sandstone data used in this paper, he has an interesting discussion of how much steeper the Coconino cross-beds are than the Tapeats cross-beds (p. 823), where, as this paper has shown, the two sets of data cannot be statistically distinguished from one another (Fig. 9)! D. Are average cross-bed inclinations in eolian dunes less than cross-bedded sandstones? An unexpected result of this study is the conclusion that eolian crossbeds may have (on average) shallower cross-bed dips than crossbedded sandstones. An examination of Fig. 6 shows that dunes have an average of 15° compared to 20° for sandstones. Again, this is a surprising result because most people have focused on the steep dips for modern dunes and have ignored the abundance of shallow dips that are also present. WHITMORE Cross-bed inclinations 2023 ICC 608
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