are accounted for, the values of which are saved. Poor resolution and overlapping points on some of the plots led to slight differences in the number of points I measured and those reported by the authors. A large amount of eolian data were presented in table form as a number of values (n) and a mean (x̅). In these cases, a weighted mean was calculated for the data. An example set of data are shown in Table 1. The numbers of measurements (n) for Ipanema are 56, 39, and 23, with respective average dips of 12.4, 12.1, and 10.0 degrees, for a total of 118 measurements. The calculation for a weighted mean would be the following: (where wi = the number of measurements and xi = average dip of the measurements). Substituting the actual values in we get a weighted mean of 11.8°: A calculation like this was done for 4,930 of the dune measurements. These data were useful for calculating means of dunes, but not as useful as individual dune measurements, which showed the spread of the data. Microsoft Excel and Golden Software’s Grapher were used to analyze and graph the data. III. RESULTS Table 2 is a summary of the measurements from both modern and ancient cross-bedded deposits using the collection methods described above. Table 3 shows a summary of the overall results. A. Sandstones and eolian dunes have similar central tendencies of cross-bed inclinations Analysis of the data showed that dip inclinations in modern dunes have similar central tendencies to those found in ancient sandstones (Fig. 6, Table 3). Since the data were collected and calculated in two different ways for modern dunes, two plots are shown in Fig. 6, and two rows of results are shown in Table 3, comparing the two methods. Table 3 summarizes the means and medians of cross-bed inclinations for the weighted means of dunes (19.8°, 19.8°), actual measurements of dunes (17.8°, 15.0°) and sandstones (19.8°, 19.9°). Note that the central tendencies of all these measurements are within a few degrees of each other, independent of whether the deposit is modern or ancient. The “dunes” category in Fig. 6 is most similar to the measurement method used for “sandstones.” B. Sandstones and eolian dunes have different standard deviations for their dip distributions Fig. 7 shows a comparison of the dip angles of 855 modern eolian dunes with 5,242 sandstone foresets. The data were converted into percentages so the two sets of data could be compared. The plot shows eolian dunes have a much wider “spread” than the sandstone data. This can be expressed as standard deviation (10.1 for eolian dunes and 5.7 for sandstones) and visualized as quartiles (the lower part of Fig. 7). Eolian dunes have nearly twice the standard deviation as sandstones which is expressed by the wider spread of the data when compared to the sandstones. The plot of eolian dunes is bimodal, peaking at about 10 and 33 degrees; the sandstone plot is unimodal, peaking at about 20 degrees. The plots show these are two different sets of data. Fig. 5. A. An example of a polar data plot from Bigarella and Salamuni (1961, p. 1094). The circles represent 5, 20, and 35° dips. B. To use polar plot data, WebPlotDigitizer was used to get an accurate azimuth and dip angle. This web application allows superposition and calibration of a plot like “A” in the software. Points can be clicked on and then tabulated in a spreadsheet as they are selected. WHITMORE Cross-bed inclinations 2023 ICC 591
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