Maybe you have read that the sediment that formed these sharpening stones mined for 800 years in the outskirts of Kyoto was spewed as dust from a volcano. I have not, nor do I have the means to prove for sure that the particles were spewed into the open during a Pilinian event as airborne dust, or as some have said they were dispensed as floating dust particles ejected from an underwater volanic vent. In anycase the fact that the heavier and larger particles settled first or closest to the source is logical and that the smaller finer particles settled last or farthest away. It has been stated that the layering of these sediments took a very long time to accomplish, somewhere in the 1mm per 1,000 year range.
I am a theorist, not a trained scientist in any specific field like geology, and my gut feeling or speculation tells me that the particles were released into the air in an event similar to the Pompeii Herculaneum Mount Vesuvius incident (an excellent explanation here), where millions, if not tens of millions of tons, an enormous amount of material was released into the atmosphere over relatively short period of time, maybe even just a few weeks or months, but not eons. And that during that period of, lets just say two weeks, the ash deposits were carried up into the atmosphere and away laterally by the prevailing winds from the source (the cone of the volcano), and that then these ash particles were deposited at various distances as falling ash in a direct ratio and wholly dependent opon their specific gravity. Layer upon layer alighted upon pools of realitively shallow water and settled in an orderly manner, sometimes traping or including radiolariums, some layers having chemical components that would react to form miniature gas bubbles, some not. Some layers were more variegated as in these examples,
I am speculating that at intervals determined by the activity of the volcano, massive waves of larger unrelated alternate material in particle form and size was thrown farther up or enough towards those pools that they settled upon each of the previous deposits and that this new material sealed or acted as a cap or shield to seal off each layer respectively thereby retaining the purity of the earlier sediment composition from contaminates. We know this particle type in its current form as kawa, a kind of skin found between the layers of awasedo sharpening stone in the mines of Kyoto.
The kawa on each stone is like its fingerprint with unique characteristics of color and chemical composition and the kawa from each mine in the Yamashirio area of Kyoto is like a variety of tree bark growing in a different location with a different genus. In my open air dispersal senerio those same winds goverened by the specific gravity and wind speed acted on the kawa particle material (much of it iron) in exactly the same was as it did with the purer silica material in its dispersal at different distances along the path leading away from the volcano; not randomly but in a understandable and logical manner. It is not difficult to believe that a strong prevailing wind could remain stable in a particular directions over a period of time long enough to deposite large amounts of material.
As the next 200 million years unfolded other events would have profound effects on the layers, but the original deposits in my model through airborne dispersal of the sharpening medium and the skin or waste particles could be workable.
The commonly held alternate dispersal and layering senerio is that all this activity occured as the result of an underwater event with the source being a volcanic vent, and further suggests that water currents not air distributed the particles along the path away from the source as they sunk to the bottom as heavier or lighter paritcles.
In either case I hope that this short description will open up some conversations on the subject. Alx