There are 3 types of volcano.


EXECUTIVE SUMMARY:
- Similar to a prev study, we look at the distribution of UFO sightings
  from the major ~50 volcanoes across the USA.
- Surprisingly the volcanoes break down into 3 groups.  (a) Those have
  have "no effect". (b) Those that attract UFO sightings with a power
  law around r^(-.25). (c) Those that repel UFO sightings with a
  power law around sqrt(r).
- We've seen the sqrt(r) law before with respect to US AFB.  It can be
  interpreted to mean someone is wary of something flying under
  continuous acceleration (transit time proportional to sqrt(r)) like
  a missile. Or another UFO.
- The power law r^(-.25) is a bit of a puzzle. It doesn't exactly jive
  with some volcanoes being "home bases" for UFO activity.  That
  would be r^(-2). It may suggest UFO's have a flying pattern that
  weights longer distances approximately r^1.75.  Why that pattern is
  not obvious. But if you have access to machinery that can
  super-cruise all day long you probably don't use much it to cruise
  your own street.



The folklore would have it UFO's are at least weakly associated with
volcanoes. Supposedly they have been seen going into and coming out of
craters of even active volcanoes.

So let's check this and look at the distribution of UFO sightings jives
with the location of major volcanoes across the US.

As usual we'll use the sightings data from NUFORC. 

The volcanoes we'll consider are the ~50 major named US craters listed
in Wikipedia.

We'll use a variation of the program we already looked at to examine
the distribution of UFO's across the US in respect of Air and Army
bases. We recall from that prev post the way the density drops off
from what we would interpret as a "threat" to the somewhat stealthy
operation of an aircraft indicates what kind of threat those aircraft
consider a base to present. If they fall off proportionally to 1/r it
seems they are concerned about interception from e.g. aircraft flying
at constant speed from that base.  If they fall off at 1/r^2 then they
are concerned with routine area patrols. If there is no drop off in
density then they are either not concerned with the base or perhaps
are only worried about something that travels at the speed of light --
i.e. being sighted visually or via radar.

In the case of military bases we treated all bases the same and just
wanted that rate of drop-off from any sighting to any base.  (But we
did treat air bases and army bases separately to see which were
consider the "bigger threat" to Our Friends).

In the case of volcanoes it seems prudent to treat each crater
separately. They all present their own unique properties -- whether
inactive/active/how active/whether sometimes spewing smoke, lava,
rocks, etc.

It seems unlikely we will find anything much but be prepared for a shock.

Running each volcano 1 by 1 we find only about 1/2 have no
relationship with UFO density. The rest appear to alter the wide-area
distribution of UFO sightings.

And -- further surprise -- volcanoes spit UFO's into at least 2
groups. The presence of some volcanoes reduces the density of
sightings the closer they get to the crater; and some "attract" UFO's
and increase the density of sightings the closer they get.

Further surprise -- there seem to be only 2 different "laws"
involved.  About 1/2 the relevant volcanoes seem to show a
relationship of sqrt(r) with respect to sightings; the rest show a
relationship of about 1/r^.25.

We've seen the sqrt(r) relationship before. What originating at a
point increases around sqrt(r) from that location? At least one thing.
A continuously-accelerating aircraft or missile (s = 1/2 a t^2 => t =
sqrt(2s/a)). In the case of air bases in that prev post we presumed
some UFO types were flying defensively and are concerned with being
hit by A2G missiles from US (specifically) air bases.

In the case of the relevant volcanoes -- what could fly from a volcano
and continuously accelerate? Rocks? Gases? Lava? None of
these. Missiles?  I don't think the AF has build many anti-aircraft
missile batteries in craters around the nation.  

We are almost forced to conclude some UFO's are flying defensively
apparently concerned with interception by other UFO's.

Has anyone seen UFO's battling? Missiles flying out of volcanoes?

But let's look at the numerical results. For each volcano we calculate
the distance to each US sighting since 1950.  This procedure is not
statistically upset there was a change of methodology at NUFORC around
2006 (the advent of the web report form that saw reported sightings go
up 10x "overnight").

Then we do a log(x)/log(y) regression between distance and number of
sightings at that distance to end up with a law count = A*distance^r.

The table:

Lat Lng       Name          Power law              Sign test     R2
                               A           r       on "r"

DEFENSIVE FLYING
52.83 -169.95 Cleveland     155.298 * x^0.456656   0.920954  0.04918286
54.13 -165.99 Akutan        181.925 * x^0.425113   0.920159  0.04881822
54.77 -163.72 Isanotski     200.608 * x^0.405183   0.919638  0.04858148
55.08 -162.81 Frosty.Peak   209.083 * x^0.396614   0.919467  0.04850400
56.88 -158.17 Aniakchak     264.627 * x^0.34649    0.919450  0.04849608
57.13 -156.99 Chiginagak    281.623 * x^0.333065   0.919470  0.04850532
58.35 -155.09 Griggs        321.298 * x^0.303567   0.921218  0.04930454
59.36 -153.43 Augustine     367.288 * x^0.273141   0.923435  0.05034696
60.03 -153.09 Iliamna       391.274 * x^0.258232   0.925320  0.05125978
19.69 -155.87 Hualalai      402.01 * x^0.249174    0.904943  0.04252556
BASES
43.1 -117.4 Jordan.Craters  2151.26 * x^-0.196994  0.905935  0.04290014
36.45 -104.09 Capulin       2232.04 * x^-0.234003  0.923204  0.05023691
33.7 -106 Carrizozo         2285.75 * x^-0.235633  0.929382  0.05331452
43.1 -118.7 Diamond.Craters 2327.69 * x^-0.218853  0.926916  0.05205218
44.28 -121.83 Belknap       2467.22 * x^-0.231597  0.957783  0.07259529
44.67 -121.8 Jefferson      2469.04 * x^-0.231915  0.960114  0.07475559
43.5 -120.9 Devils.Garden   2521.51 * x^-0.239189  0.950085  0.06625591
43.37 -121.07 Fort.Rock     2527.03 * x^-0.239513  0.949933  0.06614157
42.94 -122.11 Crater.Lake   2590.54 * x^-0.244646  0.949734  0.06599181
45.4 -121.7 Hood            2599.5 * x^-0.246812   0.965021  0.07976403
46.21 -121.49 Adams         2708.55 * x^-0.258871  0.970238  0.08595201
48.11 -121.11 Glacier.Peak  2873.43 * x^-0.274898  0.972023  0.08832786
48.79 -121.82 Baker         3007.83 * x^-0.285426  0.968948  0.08432451


While the R2 values show the relationships are very noise -- typically
only explaining 5-10% of the UFO counts by their distance from the
relevant crater -- they are quite certain. The T-test on the sign of
"r" (which is the \beta in the underlying OLS) typically shows 95%
certainty. There is only around 5% chance in each case the 1000s of
sightings line up with the distance law from the relevant crater just
by luck. Of course since we're listing ~25 such laws in the table
above it is likely 1 or 2 *are* just luck because there's that 5%
chance we might be wrong. But that shows us that the vast majority of
the rate formulas above are about right.

So it seems volcanoes across the US fall into 3 categories.  Those that
are ignored by UFOs.  Those that associate with UFO density falling
off closer to the volcano.  Those that associate with UFO density
increasing closer to the volcano.

The approx sqrt(r) cases seem to be explained by defensive flying.
Some UFO's are wary of being intercepted or "hit" maybe by something
flying under continuous power and acceleration from that location.

This would not be the first time we've seen a hint of different UFO
"camps". The influence of some UFO types on various measurable
mundane phenomena sometimes shows up a divide. As our binary friend
Ugh would put it -- "some UFO good; some UFO bad; Ugh!".

The approx 1/r^.25 are a bit of a mystery. As r decreases the
sighting count is increasing. It's as if certain volcanoes are "home".
But the power law is wrong. If UFO's were coming out of volcanoes
you'd expect the sighting density to fall of at 1/r^2 not 1/r^(1/4).
Unless each UFO tended to regularly fly a distance r about r^1.75
times.  For some reason.

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