# Sedimentology (Particle size distribution parameters)

The Inclusive graphic standard deviation (sorting) value of this claystone sample is negative (-1.29). Is this right to be considered as very well sorting ? However, the bivariate plots of depositional environment do not include negative values on the axis of the standard deviation.

Note: The granulometric data was obtained by laser diffraction technique. The formula of the inclusive graphic standard deviation after Folk 1974: $\sigma_1 = \frac{\phi_{84} - \phi_{16}}{4} + \frac{\phi_{95} - \phi_{5}}{6.6}$

Folk and Ward (1957) were the ones who created a measure of sorting using graphical moments of particle size distribution based upon φ values obtained graphically from the cumulative frequency curve at specific percentile levels.

I wasn't aware that negative values were possible based on the equation, but I am not up on my sedimentology..

Assuming your value is correct, it would signify extremely well sorted material: the Inclusive Graphic Standard Deviation (Folk and Ward, 1957) has a phi range of <0.3 (extremely well sorted) to >3.0 (extremely poorly sorted).

Folk, Robert L., and William C. Ward. "Brazos River bar: a study in the significance of grain size parameters." Journal of Sedimentary Research 27.1 (1957).

• The sorting formula is calculated correctly. The obtained negative value is due to that the clay size is the predominant fraction, so the slope of the curve is inverted graphically, rather than in the case of sandstone data. The question: Could it possible to exchange the formula mathematically to be as: (φ16 - φ84/4 + φ5- φ95/6.6) ? Because, the scale of the bivariate plots, for interpreting the paleodepositional environment is not negative the bivariate plots of depositional environment, is not negative (on the axis of the standard deviation) !! Sep 10, 2016 at 15:50

Try to check the data, you have to arrange it from the highest value to the lowest value, and then use the phi formula to every data, that give the result from the lowest phi to the highest phi. So phi5 must be the lowest phi value and phi95 must be the highest phi value. Because the IGSD formula should be give result positive value.

The data here are shown in terms of percent finer, which might be why the standard deviation is negative. Both the USACE Coastal Engineering Manual and Dean and Dalrymple show examples of standard deviation calculations using percent coarser statistics.