杏吧原创

WHEN it comes to navigating, the ocean depths are a difficult place. Deprived
of starlight, sunlight and even the radio signals from satellite navigation
systems, submariners are all but blindfolded by the water that envelops them. To
find their way around the murky ocean depths they are forced to use dead
reckoning鈥攎easuring their course and speed, and using this to calculate
their position. Their navigational tools are gyroscopes, which they use to judge
changes in orientation, and accelerometers which measure the forces generated by
changes in motion. But there is a problem. The data from these devices are
useless unless submariners know their initial position, and however accurate the
calculations, errors build up after a while. To get a fix, they must surface and
work out their position from satellite navigation systems.

In the past, this was a problem that only military submarines had to deal
with. But now the oceans are increasingly being exploited commercially by a
range of autonomous underwater vehicles and one-person subs (see 鈥淰oyage to the
bottom of the sea鈥�, New 杏吧原创, 25 February 1995). What is needed is
a better method for submariners to find their way around. They need two things:
a perfect three-dimensional map of the undersea world and an accurate way to
pinpoint their position on it. Such a system must work without radio waves,
sound waves and light. And it must make absolute measurements that do not need
to be fixed by reference to another navigational system.

It鈥檚 a tough proposition, perhaps. But fortunately the Earth already has a
built-in 3D A to Z in the shape of its gravitational field. The
strength of this field depends on the density of the rock beneath the surface,
and this varies continuously from place to place. The ultimate navigational aid
that submariners are looking for is a map of the Earth鈥檚 gravitational field and
a way to measure the field accurately.

Interest in gravity measuring devices is coming from elsewhere, too. They
could reveal hidden geological structures and fault lines, and much of the
research into new approaches to measurement is being funded by companies that
hunt for oil and mineral deposits. With sensitive devices, archaeologists could
find lost tombs in Egypt, and military engineers could spot buried land mines in
Bosnia.

Ideally, all these people want a mobile device that makes sensitive
measurements of gravity. Until now, most commercial instruments have been
capable of measuring only large-scale changes in gravity. But this is changing.
Several groups of scientists are working on a new generation of detectors that
rely on superconducting technology to measure gravity with higher resolution,
and from a moving platform. Within the next few years, they say, superconducting
gravity measuring devices may change navigation and oil exploration for
good.

Their devices measure variations in gravity in one of two ways. The first is
simply to measure the strength of the gravitational field using an extremely
sensitive weighing device. Such an instrument, known as a gravity meter or
gravimeter, consists of a proof mass hanging from a spring. The stronger the
field, the further the spring extends (see
Diagram). The unit of
gravimetric measurement is the milligal, which is equivalent to an acceleration
of 10 micrometres per second per second or approximately the gravitational
influence of a five-storey office block at a distance of 1 metre. But
gravimeters have a major drawback: they cannot distinguish between acceleration
and a gravitational field, and so cannot be used effectively in moving vehicles,
where even the slightest acceleration tends to overwhelm the results.

A more promising approach is to measure how a gravitational field changes
with distance: its gradient (see
Diagram). The gravitational field
is three dimensional and can be described by three components acting at right
angles to each other, say, g_x and g_y horizontally and
g_z in the vertical direction. Gravity gradients are related to the complex
geometry of curved surfaces, but it is not hard to see that because g_x,
g_y and g_z can each vary in three directions, it takes nine
components to describe the gravity gradient. These can be expressed as
g_xx, g_xy, g_xz; g_yx, g_yy, g_yz;
and g_zx, g_zy, g_zz. Ideally, navigators and
prospectors want to know how the vertical component of the gradient, g
_zz, varies from place to place. Alternatively, they can calculate it by
measuring two of the so-called 鈥渙ff-diagonal鈥� components, such as g_xz
and g_yz.

In 1890, the Hungarian physicist Roland von E枚tv枚s developed the
first device capable of measuring components of the gravity gradient. Known as a
torsion balance, the instrument consists of two proof masses, each one fixed at
a different height from the end of a horizontal beam that is suspended by a
fibre. Because the gravitational field is not uniform vertically or
horizontally, there is a very slight difference in the force on the two masses.
This tends to rotate the suspended system about the fibre and the resulting
angle of twist gives a measure of one of the off-diagonal components of the
gravity gradient (see
Diagram). Turning the balance through 90掳 and
repeating the operation gives another. The unit of gradiometric measurement is
the E枚tv枚s (E枚), and it is tiny. If the difference in heights
between the two proof mass were a kilometre and the change in field strength
were 0.1 milligal, the gradient would be 1 E枚. It is this minuscule effect
that physicists have been struggling to measure.

Gravity gradiometers can in principle take measurements from a moving
vehicle. So long as the movement is in a straight line, any linear acceleration
will affect both masses equally and so cancel out. However, the same cannot be
said of the rotational acceleration that is created when a vehicle turns. This
causes problems because the strength of the centrifugal force that arises
depends on the distance of the proof mass from the vehicle鈥檚 centre of rotation,
and this will usually be different for each mass. In practice, even on solid
land, an E枚tv枚s torsion balance takes hours to calibrate and settle
down.

Despite this drawback, gradiometers were used extensively in gravitational
survey work and oil exploration in the 1920s and 1930s. The instruments are even
credited with the discovery in 1924 of the first major oilfield in Texas.
However, interference from the gravitational fields of nearby hills and
mountains, and the hours it took to set these instruments, eventually proved
their downfall. By 1950, oil companies had switched to quicker survey methods
such as core drilling and seismic surveys. Consequently, little research on
gradiometry was carried out for the following twenty years.

The impetus for new research came in the 1970s, when scientists in the US and
Russia recognised gradiometry鈥檚 potential for improving inertial guidance
systems. In particular, physicists turned to the superconducting quantum
interference device (SQUID), which can measure minute changes in magnetic
fields.

The breakthrough came in the early 1980s, when two physicists, Ho Jung Paik
at the University of Maryland in College Park and Alexey Veryaskin at Moscow
University, independently developed working superconducting instruments. Both
machines detect the tiny changes in a magnetic field caused by the displacement
of a proof mass by measuring tiny changes in a magnetic field, and are sensitive
enough to pick up displacements of around 10^-13 metres. This is one-thousandth
the diameter of an atom, and only ten times the size of its nucleus. These two
devices opened the way for a new generation of gradiometers.

Disturbing movements

Paik鈥檚 gradiometer consists of two 1-kilogram blocks of niobium, suspended by
springs inside a large vessel of liquid helium cooled to 4 kelvin. The blocks
are surrounded by a reference magnetic field. When they move, currents induced
in the niobium generate their own magnetic fields, which disturb the reference
field. The SQUIDs monitor the amount of disturbance, which gives a measure of
the relative movement of the proof masses and hence a measure of the vertical
gradient g_zz. In this configuration each mass acts independently, like a
gravimeter. The instrument is so sensitive that it can detect a moving human
fist at a distance of 50 centimetres.

The trouble with Paik鈥檚 device is that it is susceptible to tiny changes in
the properties of the masses and their springs. This causes the instrument to
drift, so it must constantly be recalibrated using a mass that produces a known
gravitational field strength. In addition, each block feels the full force of
the gravitational field, which is many orders of magnitude greater than the
difference in the force on them鈥攖he gradient. This means the instrument
must be capable of making measurements over a huge range of scales. It is rather
like measuring the size of a mountain and the size of pea on its summit with the
same measuring stick. Not an easy task.

But there are times when this problem does not look so large. Paik hopes to
place a version of his instrument aboard a space shuttle flight. The centrifugal
force of an orbiting spacecraft virtually cancels out the Earth鈥檚 gravity, but
the subtle changes that make up the gradient are still present. Under these
conditions, the gradient is easier to measure. In the 鈥渨eightlessness鈥� of space,
instrument drift is also less of a problem. 鈥淚n a spacecraft, both of these
errors will be reduced by an order of magnitude,鈥� says Paik. The mission is
called GEOID and Paik hopes it will fly in 2001. He is now waiting to hear from
NASA whether it will get the go-ahead.

At the University of Western Australia in Perth, the physicist Frank van Kann
has pioneered a different approach to gravity gradiometry, funded by the oil
company BP and the mining firm RTZ. Like E枚tv枚s, van Kann measures the
difference in gravity at two ends of a beam, but his setup is quite different.
Van Kann鈥檚 gradiometer consists of two horizontal bars a few centimetres long,
mounted like a pair of scissors (see
Diagram). The beams, which are
cooled to about 4 kelvin, start off at right angles and are free to rotate about
a vertical axis, Although difficult to imagine, the off-diagonal components of
the gradient tend to close the scissors. The movement is once again detected by
SQUIDs.

Sagging under their own weight

In principle, van Kann鈥檚 device should be immune to rotational motions, since
any angular acceleration has the same effect on both bars. However, this is only
true if their mass is identical, and in practice small differences in the size
and density of the superconducting bars are inevitable. To overcome this
problem, the experiment has to be mounted in a computer-controlled system of
gimbals, reducing the angular disturbances by a factor of 10 000. 鈥淭his gives
the required stability and robustness,鈥� says van Kann.

Another problem is that the bars tend to sag under their own weight. 鈥淥n that
scale, materials are more like foam rubber than solids,鈥� says van Kann. The
sagging of a 10-centimetre bar can create an effect equivalent to 1000 E枚,
which wipes out the results. 鈥淔ortunately, although the bars are flexible, they
are at least predictable when cold,鈥� he says.

Although Paik鈥檚 and van Kann鈥檚 teams have scored major successes in recent
years, they share a significant problem: vibration. This tends to make the
components of their instruments jiggle about, making precise measurement of
their positions very difficult. Without this knowledge, the machines sense a
gravity gradient but cannot say exactly where in space it applies鈥攁
crucial failing.

This problem could be solved with a radically different approach developed by
Veryaskin, who is now working independently in New Zealand. Instead of freely
suspended proof masses or bars, Veryaskin鈥檚 gradiometer consists of a single
vertical superconducting string which is fixed at both ends and has a current
flowing through it. Differential forces in the gravitational field generate
atomic-scale deformations in the string, which are detected by two sets of
SQUIDs placed perpendicular to each other. This setup allows Veryaskin鈥檚 machine
to measure two off-diagonal components of the gradient at once. Veryaskin says
his device is immune to errors created by linear acceleration, and that problems
caused by angular acceleration can be corrected easily.

Superconducting string

By placing the string inside a superconducting tube, Veryaskin has eliminated
external electromagnetic interference, and a custom-made feedback system
eliminates other forms of noise. The device is also more portable than the
others. Veryaskin鈥檚 gradiometer is a cylinder the size of a relay baton. But
perhaps the main advantage of Veryaskin鈥檚 approach is that by not using two
proof masses he doesn鈥檛 have to keep recalibrating his device.

All three groups are now looking for financial backing to take their work
forward. This is most likely to come from oil and mineral companies, which spend
around $5 billion every year hunting for new reserves. An airborne
gradiometer could revolutionise the prospecting process by producing accurate
gradient maps of large areas quickly and cheaply. Gradient maps show geological
features such as faults, changes in rock type and other structures associated
with the presence of oil and minerals. And a gradiometer lowered down a borehole
would measure the density at that depth, a characteristic that is directly
related to the rock鈥檚 mineral composition, porosity and the kind of fluid it
holds. Both these approaches would speed up survey methods and greatly reduce
costs.

Elsewhere, superconducting gradiometry could find a home in geodesy and for
experiments into general relativity. It could also be used to detect buried land
mines, archaeological remains and volcanic activity. For the all-but-blind
submariners, the gravitational gradient map provides a grid reference system for
navigation. Every point in the ocean should have a characteristic gradient
value, allowing a submarine with a gradiometer to identify its position with
just one reading.

Given funding, Veryaskin believes he could have a working gradiometer capable
of taking measurement from an aircraft within two years. Van Kann and Paik could
be hard on his heels. If they succeed, many secrets of the rocks beneath our
feet and the unseen world beneath the waves will finally be revealed.