Karen was kind enough to reference my paper in JBIS on this subject during
the thread from which this seems to have developed, but I've had some more
thoughts since1990.  Dave has mentioned some concepts from which my
present thinking began to take shape.  

The basic problems for any radar detection of lunar lavatubes are
resolution, penetration, and signal to noise ratio.  (Did I mention
Money?)  We MAY have a way to get around all of those at acceptable cost,
but it definitely isn't your standard GPR setup.

My idea  evolved from elements of the 2 schemes Dave began mentioning
above, radar and impactors for geophones.

The radar equation describes the signal to noise ratio we'll get from a
radar, with some hard relationships to make work.  First is the 4th power
range coefficient in the denominator, a real pain.  Second is the fact
that the s/n ratio gets worse with the 2nd power of the frequency. Also,
penetration without massive attenuation pushes us to longer wavelengths.
Of course the rayleigh limit for resolution and the ionospheric limits for
radio frequency require useful wavelengths on the order of a meter, as
Frank Crary has ably pointed out.  I should note, however, Dr. Coombs
initial work does seem to indicate some lavatubes much bigger than 200
meters in diameter.  Indeed,  I remember indications of one tube 500
meters wide by about 7500 meters long and another 1100 meters across.
Nevertheless, frequency/aperture is still a problem for any regular GPR
looking for lavatubes from lunar orbit.  :>(

There is also a problem with geophones that I'm unhappily resigned to.
Once again it has to do with frequency and resolution, and in addition,
the state of cooled basalt.  According to Steve Gillet, who has posted to
s.s.p. in the past and worked with Oregon L-5's research Team in Bend,
Oregon,  when a flow of basalt cools, it cracks.  It cracks a lot!  Those
cracks will cause signal/noise problems for short wavelength searches with
sound that are far worse than they would be for EMR methods.  Reflection
of sound from a crack in vacuum would be total.  I believe now that any
wavelengths long enough to avoid attenuation by these cracks may well be
so long that we won't get the resolution needed for even 500 meter tubes.
:>(

However, the use of impactors (I called them "Thumpers") to deliver the
needed energy for geophones stayed with me.   I had wanted to put them in
a spacecraft doing figure eight orbits between Earth and the Moon,
dropping them off with a little shove that would put them on an accurate
lunar impact trajectory.  Then, someone mentioned to me that tracking
spacecraft by radar is done with a "Cooperative Target" most of the time.
I was feeling sorry for myself that lunar lavatubes didn't "Cooperate" as
well.  I had already been looking at doing the job of synthesizing the
radar dish down here, on Earth, using VLBI techniques in my earlier paper,
in order to get better resolution at lower cost.  Unfortunately, the
signal/noise ratio for surface work already required 124 seconds of
integration time for each 50X50 meter pixel, and penetration, even on a
dry Moon, would only make it worse.

So, what would happen if we delivered, to the area near a suspected
lavatube, a powerful EMR source of appropiate frequency, to make the
object of desire more "cooperative".  Good news!  It could have close
range penetrating power!  It's equivalent equation to the radar equation
should have only a 2nd power on the range coefficient, thus giving a much
better s/n ratio!  Bad News!  It would cost like sin to set such a power
source down on the lunar surface by soft landing!  I remembered the
"Thumpers".  Too bad their K.E. wasn't EMR.  It would be like a flashbulb
illuminating a sea bottom, observed from a telescope in an airplane at
night.  You could probably "see" reflective voids in the lunar crust for
several kilometers around the impact using the VLBI.

Then I was reminded of homopolar generators.  These are neat storage
devices for energy that turn K.E., from gyroscopes on steroids, into
monster electric currents.  If we could do, just once and very fast, the
same thing with the linear motion of a compressible  impacting "Thumper"
that homopolar generators do again and again with rotary motion, then we
might just have a good source of EMR for a lunar EMR "flashbulb".  At 2350
meters/sec. that's a lot of ergs available for conversion into a really
massive radar pulse!

Of course, the current pulse has to be converted into a properly modulated
radar pulse and then directed down into the lunar crust, and all in 1/2350
seconds if the "Thumper"'s linear compressive motion is about a meter
long.  Then the Thumper is splattered.  That conversion part I'm not
enough of a radar engineer to work out yet.  Still, I've been told in
passing by those who are experienced in that field that the idea sounds
"not-impossible".  So we may have the elements of a useful search system
for underground lunar phenomena, including lunar lavatubes most
prominently.

These would be:

1.)  A VLBI about as large as you can get on Earth.  NRAO has made a good
start on this with their currently operating VLBI.  We must equip it with
receivers in the appropriate frequencies.

2.) A supply of EMR "flashbulbs" in a useful storage orbit that has low
d/v for impact with a large part of the lunar near side.

3.) Information from Clementine and other lunar probes about where we
could best place these EMR "flashbulbs" for the best chance of
illuminating our desired lavatube features.

As Jeff Greason has noted elsewhere, Oregon L-5 is still struggling with
shoehorning a proper lavatube search of the massive Clementine data set
into whatever private funding we might get.

I hope that someone out there might contribute  their knowledge of power
engineering and radar into an analysis of the "flashbulb" and it's
particular problems.  

Thanks for any Comments,

Tom Billings

--
Tom Billings,  Institute for Teleoperated Space Development
"Minds Wielding Tools, Preparing Our Way Into Space"
http://www.teleport.com/~itsd1/index.html