fine porous rock like a natural HEPA filter is kind of hard to find around here. It would have to probably be shipped thousands of miles from where quarried to build a useful filter.

However, we have an abundance of sand. The space between sand grains while small, isn't small enough for things like smoke sized particles.

The electrostatic separation was inspired by devices on the ceiling of a night club, over the bar and surrounding the dance floor. They had the trade name SmokEeter, and the electrostatic charge sucked smoke in one end, actually provided some air flow from the ion movement, and blew much cleaner air out the other end.

At closing time, they would shut down the units right over the bar first, discharge the high voltage, and then the positive collector / anode plates could be easily unseated once the cover was removed. They'd just put the anodes in the dishwasher to clean away all the tobacco smoke residue and related gunk, then put the clean ones in.

the other units would continue to operate to keep removing smoke from the air - now that all the drunk cowboys and cowgirls were no longer smoking like chimneys, there was no more input of fresh smoke, so the air kept clearing while the first group of units were cleaned.

Once other bar cleanup was taken care of, at some point they'd shut down some more units, remove the plates, clean and re-install.

And finally once the interior air was somewhat cleared out, they'd shut down the remainder and clean them.

Last step, they'd start them all back up for about the last 30 minutes as all the final bookkeeping and related things were done, and then shut off around dawn as they went home and locked up to be ready for yet another night.

Without them, the smoke would be so thick you could cut it with a butcher knife, your eyes would be watering, and visibility would be well below IFR Category 1 landing conditions.

It probably saved a lot of people from second hand smoke induced cancers compared to the poor ventilation of such places in the 1920s to the 1960s.

Japan has numerous volcanos all over the country. Many of them dormant, but much of the understructure has natural pockets of pumice. These pockets are mined and cut to make square or round brick/block like filters. It's quite light in weight and is porous. 

Pumice - Wikipedia

FWIW

I don’t think of Japan as volcano country. It’s almost never discussed in our media.

Pumice in the US is apparently not found in contiguous pieces big enough to cut into useful shapes like filters.

I have seen it mostly sold here as toilet scrubbing sticks to remove lime scale, and similar applications.

But the bubble size in the pumice I have seen are way too coarse to be useful for filtering.

Now activated charcoal, on the other hand, may have a surface area of several acres in a couple of tablespoons of material. So it is great for absorbing all sorts of sub-microscopic material and is used in a variety of industrial processes, such as to yank heavy metals from water

This, however, isn't really a filter per se - it exploits the electrostatic attraction forces at very small scales to grab stuff out of the water (or air) and hang on to it.

A synthetic material is often used in water filtration systems - it's activated charcoal manufactured in a block that requires the fluid to be filtered to pass through its microscopic pores.

This does make an effective filter, but you need a series of progressively finer and finer pre-filters upstream to get rid of fine sand, silt, and finally bacteria, and often unwanted chemicals that can bind to the carbon matrix and let the pure water go on to the reverse osmosis membrane which finally only passes water molecules and excludes salt and other dissolved minerals.

What about shale like that found all over Florida if you dig deep enough?

FWIW

Shale is kind of closed cell porosity until you break it up to release the trapped material. That's how they are getting oil out of it in the Bakken and a few other places. Drill horizontally into the seam, then apply ungodly amounts of hydraulic pressure to frack it and inject sand to act as proppant and hold open the cracks once the fluid pressure is relieved.

Probably not enough porosity to pass a reasonable amount of air through at any reasonable sized filter area. You'd probably need to make a couple of entire walls out of the stuff to get enough area to force enough air through at reasonable pressure to adequately ventilate a shelter.

Like a filter 8 feet high and 16 feet wide, maybe a half inch to a quarter inch thick, and maybe 3 or 4 PSI differential to force the air through, which means a lot of mechanical support, like a bazillion smaller panes supported by, say, steel beams, so the pressure doesn't just make it implode.

now I've got to do some more research on shale porosity when it's quarried unaltered from the ground.

I know that it metamorphoses under heat and pressure into slate, which is quite non-porous. They used it for some castle roofs all over Europe for many thousands of years. And it is used as pool table sub-surfaces, beneath the felt, because it's heavy and flakes off nice and smooth.

The outer walls and roof of my home are made of slate. The slate walls are about 1.5" in thickness and work great to keep the heat out or heat in. 

In the summer months, the outer walls are hot but the inner walls are still cool. Likewise, when we heat the inner house, the heat doesn't dissipate to the outer surface of the slate.

FWIW

I have a small water filter and it uses carbon. But it also leaves small particles in the water right after it’s changed out for a new one.

How does Japan have such a big supply of slate?

In short response: Nozawa Corporation

The longer reply is: