Marek,
I very much enjoyed your post. Thanks!
Does the uplifting of the Sierras mean that if I go climb Mt. Whitney again, I'll be higher than I was when I climbed it 20 years ago? ;-)
Oh, and as far as polar alignment goes...many of us crazy imagers don't care about level. Having your mount's base be level can make it somewhat easier to drift align, since in that case adjustments in altitude don't also affect azimuth and vice-versa. But with computer-aided alignment (which I use and love), it matters not one whit. As long as the RA axis gets aligned with the earth's rotation, it don't matter how you get there ;-)
Go Giants! (they did win last night)
Paul
-----Original Message-----
From: sf-bay-tac-bounces@No-Spam [mailto:sf-bay-tac-bounces@No-Spam]On
Behalf Of Marek Cichanski
Sent: Wednesday, June 30, 2004 8:08 PM
To: TAC
Subject: [TAC] Pushing the limits of OT: Gravity anomalies, isostasy,and
polar alignment
Hoo boy, I'm going to push the limits of OT on this one...
But, I'm going to go for it, with the following two excuses:
1) Take a look at the moon - like we've got anything better to do than talk
about the earth's gravity. (Okay, actually the narrowband imagers DO have
something better to do...)
2) I'm going to try to hide behind my 'staff geologist' status here,
although I don't know how much good it's going to do me.
After my last OT post, about inclinometers, someone posted a question about
the gravitational attraction of a large nearby mass, such as Lassen Peak
(if one was set up at Bumpass Hell, say).
As you would expect, the gravitational deflection of one's local 'down'
direction would be real, but almost certainly not enough to affect the
setup of astronomical gear, at least not for our purposes, but it does lead
to some interesting asides...since you asked...
Exactly this sort of thing cropped up in the mid-19th century, and it led
to a major advance in our understanding of the earth's interior.
The story begins in the days of the British Raj, when Surveyor General
George Everest was in charge of the Trigonometrical Survey of India. A
great survey was undertaken, in order to map the 'jewel in the crown', and
to make it possible to establish rail lines, political boundaries, town
plans, etc... The surveyors basically used two methods for determining the
locations of their stations. One method was triangulation, where precise
bearings and distances from known points can allow one to located another
place very precisely. A 'triangulation net' was slowly established, based
on a series of agreed-upon starting points. I'm guessing that the starting
points (sometimes called a 'baseline') were at least in part located via
the second method - astronomy. Precise observations of Polaris can, of
course, be used to determine one's latitude, and transit times of various
stars can be used to determine longitude. (Longitude, of course, requires
precise timekeeping, but John Harrison and son had taken care of that a few
decades earlier.) A knowledge of the curvature of the earth is required,
but that was pretty well established by the mid 19th century, too. The
earth was known to be a spheroid - flattened at the poles - due to its
rotation.
Thing was, as the survey went on, the results from triangulation didn't
agree with the astronomical results. For example, two of the stations in
question, Kaliana and Kalianpur, had the following difference in latitude:
As determined by triangulation: 5deg 23 min 42.29sec
As determined astronomically: 5deg 23 min 37.06sec
This was way too big to be the result of sloppy surveying, or arithmetical
errors. Something weird was going on here.
A British archdeacon, J.H. Pratt, speculated on the cause of this. He
proposed that the mass of the Himalaya was pulling the surveyors' plumb
bobs northward, causing the survey errors. The farther north the station,
the closer to the Himalaya, and thus the worse the error.
Well, this was easy to check, because one could make a rough but reasonable
calculation for the volume of the Himalaya and Tibet, and by assuming that
they were made of normal sorts of rocks, calcuate their gravitational
attraction.
This is where things really started to get weird. The Himalaya should
produce a deflection, all right, but it should have been BIGGER than the
one observed. Somehow, the mountains weren't pulling as hard on the plumb
bobs as Newton's laws would predict. Hmmm...what's up with that?
Pratt suggested that perhaps the mountains were made of rocks that were
less dense than normal rocks. This might explain the discrepancy. Pratt's
hypothesis, although absurd-sounding today, had that most precious and
inestimable of all scientific virtues - it was TESTABLE. The test? Simple -
just go up into the mountains and see what kind of rock they're made of. Is
it light and fluffy? Maybe Nerf rock? Maybe that's where set dressers get
all those styrofoam boulders than always manage to miss the landing party
from the Starship Enterprise? Survey says...WRONG. The Himalaya were made
of normal rocks. Limestone, granite, schist, common crustal stuff.
This is where the Astronomer Royal, George Airy came in. Perhaps you've
heard of him... Airy conceived a much subtler idea, which further
investigation has tended to support. Like Pratt, Airy imagined that the
crust of the earth is made of lighter rocks than the earth's mantle. Even
though both are almost entirely solid (no, the interior of the earth ISN'T
magma - it's rock), solids can flow on geologic timescales. Viewed over the
timescales needed to, say, uplift or erode a mountain range, the crust
floats on the denser mantle much like ice floating on water. This concept
of flotation is called 'isostasy'.
Imagine a strip-like section of the earth's crust, say a north-south strip
from India up through Tibet. Imagine dividing this strip into a number of
individual 'columns'. At some depth, the weight of each column must be the
same, else one column would be observed to be sinking or rising relative to
another. Below some depth, each column is said to be 'isostatically
compensated', or to be in 'isostatic equilibrium', or at least we
assume/hope so - more on that anon...
Pratt imagined that some columns have lower-density crust than others, but
that the base of the crust is at an equal depth everywhere. That hypothesis
didn't work, however. This is where Airy's genius comes to the fore... he
imagined that the crust is pretty much the same everywhere, at least within
the continents, but the THICKNESS of the crust varies! Thus, a mountain
range must have a deep, low-density, crustal 'root', much like an iceberg
or a large ship. It is this root that keeps the mountains standing high. A
mountain range that's supported by a crustal root is in isostatic
equilibrium.
Cool, huh?
For the last century or so, geophysicists have traveled around the world
with gravimeters, which can measure the force of gravity to less than a
'milligal' (I'm pretty sure that 1 gal = average force of gravity on some
standard mass at earth's surface.) We have 'gravity anomaly' maps for
pretty much the whole world, although not all of them are equally detailed.
They've added support to the idea that many mountain ranges are in
isostatic equilibrium. They've shown that the ocean crust is more dense
(and thinner) than the continental crust. They've helped to locate
orebodies. They've helped to understand how oceanic subduction zones work.
Knowing the world's gravity field was also rather important in making sure
that ICBMs would reach their targets accurately. Perhaps most
interestingly, there are places where isostatic equilibrium CAN'T explain
things. Some mountain ranges don't have much of a crustal root, and must
have some other means of support. For example, the Sierra Nevada ought to
have a crustal root, based on its topography and gravity. But seismic
refraction studies (which can determine the thickness of the crust) show
that the crustal root ain't there. Whazzup? One hypothesis for this is
'delamination'. It's possible that the until-recently-subducting slab under
the Sierra may have recently broken off and started to sink into the mantle
on its own, with the result that the Sierra has been popping upward like a
helicopter that's unexpectedly lost its sling load. Wild, eh? Much of
Scandinavia is 'rebounding' upward as well, due to the geologically recent
melting of the Pleistocene ice sheet. (This can be seen by things like
beach ridges that have been uplifted, etc... Same thing happens around
Hudson Bay. boinnnggg....)
Gravity has been measured on other planets, too. Read the Apollo Lunar
Surface Journal, and you'll see that some of the later missions spent a lot
of time reading a gravimeter on the lunar rover. The whole 'aerobraking'
thing with Magellan was intended to allow a detailed gravity survey of
Venus to be done, by tracking the doppler shift of the spacecraft's carrier
wave.There's a Tibet-sized plateau called Ishtar that ain't in isosatic
equilibrium. There's a mission in orbit around the earth right now called
GRACE, which is measuring the earth's gravity field to a high degree of
precision.
Now, what would any of this have to do with polar alignment at Lassen?
Well, you might think that the mountain's gravitational pull would make
your inclinometer read 'level' when it's not really level. But here's the
thing... it IS level! 'Level' is simply a matter of being parallel to the
local equipotential gravity field. In fact, sea level itself is affected by
the gravity of the mountain ranges, and thus they have an effect on their
own 'height above sea level'. Sea level a.k.a. the 'geoid', is a surface of
a certain constant gravitational pull, basically. It's often described as
being the position of the sea if one could cut an extremely narrow, deep,
vertical trench from the sea through the mountain range. The mountains
would pull the sea up a bit, and it's THIS sea level that we use to
measure the 'height' of a mountain. Your inclinometer is indeed level, but
that may or may not agree with your 'astronomical latitude'. There are many
versions of latitude, and I'll leave the visualizations of these different
types of latitude an an exercise to the student.
Okay, I've killed enough time...the Giants game has filled enough of the
Tivo buffer so that I can probably fast-forward through all of the ads...
let's hope they beat the Dodgers tonight. Hope y'all enjoyed the geophysics
lesson!
Marek
Received on Thu Jul 1 07:50:22 2004