Akadama is a volcanic soil - it is comprised of partially to completely altered tephra deposits of volcanic ash and pumice. It's parent material was from arc volcanics, probably andesitic in composition like those in the Cascades. Remnant pumice grains are apparent in several bags I've bought, but generally the pumice and ash are nearly completely altered.
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The pictures you may have seen of the akadama mined in Japan have layers - a dark organic-rich layer on top, then the red akadama layer, then the yellow kanuma layer. The boundaries between these layers are called soil horizons.
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These kind of volcanic soils are called Andosols. An- is japanese for "dark" and -sol means soil. It refers to the dark, humic rich upper layer of the soil. This layer is part of the definition of an andosol - it must occur within the upper 15cm of the ground surface. So you should think of akadama as a soil, not a volcanic tephra deposit. It used to be many years ago, but that is mostly all gone now and replaced by clay minerals.
The alteration is interesting - with a lot of water, the ash breaks down to form allophane and imogolite, smectitic clay minerals that commonly occur together in an andosol. In fact, their occurrence is nearly diagnostic - andosols are pretty much the only kind of soil in which they are found. There is an interesting pH control on the allophane-imogolite association, however. As pH changes, aluminum can combine with humic acid that leaches from the surface forming Al-humus complexes that can substitute for the allophane-imogolite clay minerals. At a certain pH, one becomes dominant over the other. So in a typical andosol, horizons form as a response to changing pH in the subsurface. This is what I suspect the akadama-kanuma horizon is. Akadama is dominated by allophane-imogolte clay minerals with subsidiary Al-humus complexes whereas kanuma is dominated by Al-humus complexes with subsidiary clay minerals.
So to replicate the conditions in Japan, you need 1)volcanoes, 2)a lot of rainfall, 3) a lot of organics, and 4)time. About 50% of the andosols in the planet are in the tropics because of 2 and 3. But they can also occur in temperate areas where there is a lot of rainfall - areas like the Pacific NW. They're all over the place there.
Scott