Is there an inexpensive (about $100) instrument that will detect and
measure the presence of "infrasound." Infrasound in this use is a
vibration that can be felt but not "heard" by humans because it is below
the necessary perceptual threshold.

The device would need to read constant or random vibration from about
1 HZ to 20 HZ. Output to a computer (PC) would be excellent.

For example, there are relatively inexpensive "radio frequency
counters" that are hand held, with rechargeable batteries, and they
measure and display near field electromagnetic emissions' frequencies
and strength. Some will even allow the data to be stored on a connected
computer. -- Is there something similar for infrasound?

Infrasound (ultrasound) scanners are usually equiped with several
probes of different frequency. I have not yet encountered a machine
which will scan in the ranges you are looking for without multiple
probes. The usual price of a probe is around $3000-$6000. Consider now
that multiple probes will be needed to achive the scan range you are
looking for. This is due to the higer frequency probes having
producing a more detailed scan at the expense of scan depth. The lower
freqency will alow a greater scan depth at the cost of detail.

Small portable machines do exist, they are however expensive and
mainly for use in hospitals. They also reqire a selection of probes.

So in short: The machines you are looking for do exist however not at the cost.

Regards

I don't have the numbers in front of me, but with density, there's a
rise in the frequency, so a microphone that tolerates water would hear
a higher pitch. Mikes that can hear 20Hz aren't uncommon. Denser than
water (mercury, etc.)is outside my area of expertise, and I might have
it backwards -- lower frequency, not higher. Anyway, jerry rig for $50
might be do-able.