the mathematical approach taken can be reduced to a minimum if you use this method as a stand-alone procedure, because all attempts made to distil out some sort of an "environment analysis" were not greeted with much success. I have not "opened the throttles" in terms of computation but combined different fractions of the sediment as to the density groups (light and heavy minerals) and morphology (spherical issues). Thereby you get a much better insight into the environment of deposition which I assume is one of your targets.

Best regards

H.G.Dill

For normal distribution yo can use Arithmetic mean mod skewness ect.. otherwise use Logarithmic (original) Folk and Ward (1957) method. Totally depend on your data set and Particle size range of your data. 

Nalin, you are touching on an issue as old as it is controversial. First of all, it is necessary to decide for what purpose you need the statistical data and, in this context, a major determinant is whether you are operating in a hydraulic system (i.e. sediment erosion, transport and deposition) or whether you simply wish to classify sediments in one way or another. As we are dealing with the former system at our institute, we analyse sediments statistically in the standard logarithmic transformation using the phi-scale, i.e. the negative binary logarithm of the mm-scale). We calculate textural parameters both on the basis of perdentile statistics (viz. Folk & Ward 1957) and moment statistics, keeping in mind that these statistics strictly apply to unimodal grain-size distributions. In the case of bi- or multimodal distributions one should decompose these into their individual hydraulic populations and then apply the statistics to each population separately.

We consider the binary logarithm more practical than the decadic logarithm for a simple scientifically well founded reason. Thus, in the laminar fall regime (Stokes' Law), the settling velocity of a particle is proportional to the square of its geometric grain size and in the turbulent fall regime it is proportional to the square root of the geometric grain size. As both are quadratic functions, the binary logarithm is more appropriate.

Because we are operating in a hydraulic system, we do not generate grain-size distributions by sieving but rather by settling velocity analysis. In the latter method both particle shape and density are accounted for, whereas in the former they are not. The settling velocities are subesequently transformed into equivalent settling diameters in correspondence to the water temperature at which the settling velocities were determined. The results of the two methods  (sieving vs settling) increasingly diverge from each other with increasing grain size, variable particle shapes and densities further increasing the discrepancy. In general, grain-size spectra determined by sieving are recorded as being coarser and less well sorted than their settling counterparts.

I'm afraid my discourse does not solve your problem directly, but it may entice you to think carefully about the actual purpose of your work and, on that basis, what statistical approach is the more appropriate one. Attached is a study which gives you a good insight into these issues.

Best regards,

Burg Flemming

Thanks all for your wonderful feed back

As has been pointed out by others already, 'moments' are a tricky tool to use; and controversial too!

I strongly advise you to read an editorial by Robert Ehrlich in Journal of Sedimentary Research (v. 53 p, 1; March, 1983) entitled : Size analysis wears no clothes, or have moments come and gone?

The point is size analysis and statistical measures of sedimentary rocks by themselves have limited value when applied to ancient sediments. This tool used in conjunction with other field, petrological and textural data can yield perfect results enabling definition of the depositional process and environments.

However, on a stand alone basis, this tool has ZERO meaning.

Having said that, given the recent advances in hydrodynamics of sediment transportation, I would recommend geometric computations as being more closer to models than the arithmetic ones. However, the sample size also will be a determinant in this, subject to the first point.  

All the best in your efforts.

Dear Vivek

I only just read your comment, otherwise I would have responded much earlier. Let me first make a comment on Robert Ehrlich's editorial. In my opinion he has done a great diservice to sedimentology in general because his message is: don't waste your time on grain-size analysis. Nothing could be more wrong and, for a start, I refer to the study I attached on 8 March 2016 (cf. further up), where I provided a very plausible interpretation of the sedimentary situation in a South African coastal lagoon on the basis of grain-size analysis. Another three publications in this context are attached to this reply.

In extension, I agree with you that the textural (statistical) parameters of one or two samples have little, if any, meaning and that only the textural differences between samples from a larger sample suite can reveal spatial trends that require intelligent interpretations. I claim to have achieved this and that my interpretations have stood the test of time. Coming back to Robert Ehrlich, I would say that, in his destructive statement, it was he who wore no clothes.

Burg Flemming

Dear Corona influenced people, as Burg Flemming and others have mentioned, the literature is full with explanations to this ancient question...

However, do not forget that complex scientific questions will always demand hard working and complex method.

I can add my (unfortunately) forgotten share

Daniel

Hi Dani!

Good to hear from you! Yes, that paper of yours is essential reading for anyone seriously concerned with grain size issues.

Burg

Dear Prof Flemming & Hartmann,

Really appreciate your inputs and views. Whether or not the Ehrlich critique served any purpose is something that can be debated upon, but that (in my view) is not the point!

I am in agreement with your observations with a caveat (if you will permit me).

Please note my full comment on which you have responded.

The statement was clearly :

'on a stand-alone basis' ...grain size has zero utility. This was based on my reviews of some manuscripts that ONLY had moment measures to justify their conclusions and ended up with some fantastic & unbelievable results!!!

I go further and state that "This tool used in conjunction with other field, petrological and textural data can yield perfect results enabling definition of the depositional process and environments."

Trust this clarifies that I am not trying to debunk grain-size analysis. It is a useful tool, but NOT A STAND-ALONE DIAGNOSTIC ONE!.

Take care and stay safe...

Hi Vivek!

My apologies, I certainly did not in any way mean to suggest that you supported the view of Robert Ehrlich. His editorial really upset me and I intended to write a scathing comment on it. Unfortunately, I was at that time busy moving from one continent to another and my response fell victim to that. Be reassured, I fully agree with the emphasis in your response above and have said as much in different words on several occasions.

Best regards,

Burg

I suggest you start by looking at the underlying distribution of your particle. Then ask yourself if a parametric distribution fit them well (see Numerical Recipes for distribution test). If a specific distribution fits well your data, compute its moments. If none does, consider using nonparametric statistics. You can never go wrong with non-parametric statistics as you do not assume an underlying distribution. You can compute characteristic nonparametric quantities that are equivalent to specific moments for specific distribution (e.g. the distance between the 16th and 84th percentile is equivalent to +/-1 stdev of a normal distribution). Most important is that you do not follow the literature blindly but ask yourself what is it that I am interested in describing about my dataset. Good luck!