super conducting gravimeter
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REVIEW ARTICLE
The superconducting gravimeter
John M. Goodkinda)
Department of Physics, University of California, San Diego, La Jolla, California 92093-0319
Received 13 April 1999; accepted for publication 28 June 1999
The superconducting gravimeter is a spring type gravimeter in which the mechanical spring is
replaced by a magnetic levitation of a superconducting sphere in the field of superconducting,
persistent current coils. The object is to utilize the perfect stability of supercurrents to create a
perfectly stable spring. The magnetic levitation is designed to provide independent adjustment of the
total levitating force and the force gradient so that it can support the full weight of the sphere and
still yield a large displacement for a small change in gravity. The gravimeters provide unequaled
long term stability so that instrumental noise can be either below geophysical and cultural noise or
indistinguishable from it over periods ranging from years to minutes. This article reviews the
construction and operating characteristics of the instruments, and the range of research problems to
which it has been and can be applied. Support for operation of the instruments in the United States
has been limited so that operation of multiple instruments for periods much longer than a year has
not been possible. However, some of the most appropriate applications of the instrument will requirerecords of several years from arrays of instruments. Commercial versions of the instruments have
now been purchased in sufficient numbers elsewhere in the world so that a world-wide array has
been organized to maintain instruments and share data over a period of six years. © 1999
American Institute of Physics. S0034-67489900111-2
I. INTRODUCTION
Gravity meters are devices which measure slow varia-
tions in gravitational force or acceleration. They differ from
accelerometers or seismographs in that they are designed to
operate at lower frequencies with lower noise levels. Datafrom gravimeters are typically obtained at frequencies below
about 0.1 Hz. Ideally they would provide instrumental noise
levels below ambient geophysical noise at arbitrarily low
frequencies and this was the objective in developing the su-
perconducting gravimeter SG. In circumstances where en-
vironmental influences on gravity have been well accounted
for, the best records from SG have shown gravity variations
over a year of the order of 1 gal (1 gal1 cm/s2103 g).
Gravity at the surface of the earth changes by about 1 gal
for a vertical displacement of 3 mm. For periodic signals, the
SG provides uniquely low noise from periods of a few thou-
sand seconds to the monthly and annual solid earth tides andthe Chandler wobble 1 cycle/434 days. Measurements of
the diurnal and semidiurnal earth tides with a year long
record yield amplitudes at the various frequencies to within
103 gal1012 g). The resolution available with the in-
strument has provided new information for geophysics and
fundamental gravity studies. With increasing numbers of the
instruments distributed around the globe and with some lo-
cated to study specific problems, new fields of research and
new discoveries are likely to appear during the coming de-
cade.
Section II of this article describes the physical principles
and practical realization of the device along with some of the
ancillary equipment that is required to make it work. Section
III describes procedures for setting up and operating the in-
struments. Section IV describes a range of geophysics and
physics problems to which the unique capabilities of the in-
strument have been applied. Section V describes the perfor-
mance achieved by the SG and compares the characteristics
of the two other types of gravimeters currently in widespread
use. It is suggested how their combined use would provide
more information than any of them used alone. Section VI
speculates about possible future applications of high resolu-
tion gravimetry.
II. PRINCIPLES OF OPERATION ANDINSTRUMENTATION
All gravimeters other than the early pendulum types and
the absolute meter see Sec. V, use the equivalent of a mass
on a spring. The spring must provide an upward force equal
to the time averaged value of the downward force of gravity.
Small changes in gravity are measured through the extension
of the spring or the resulting changes of position of the mass
relative to the support structure. As will be discussed below,
much of the work that has been done or is anticipated for the
SG requires measurement precision of at least 1 gal so thataElectronic mail: [email protected]
REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 70, NUMBER 11 NOVEMBER 1999
41310034-6748/99/70(11)/4131/22/$15.00 © 1999 American Institute of Physics
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the upward force of the spring must be stable to at least one
part in 109. Mechanical spring type gravimeters have not
achieved this stability. The SG was conceived to make use of
the, in principle, perfect stability of superconducting persis-
tent currents to provide a perfectly stable magnetic suspen-
sion. The fundamental design of the gravimeter has not
changed since it was first reported in the Review of Scientific
Instruments nearly 30 years ago.1 However, modifications
that have yielded improvements in performance were ac-
tively developed in this laboratory at the University of Cali-
fornia San Diego UCSD until 1990 and are continuing forcommercially available instruments at GWR Instruments.2
The design of the instrument is illustrated in Fig. 1. A dia-
gram of a recently developed dual sensor instrument3 is
shown in Fig. 2. Its purpose will be described in Sec. V.
A. Superconducting levitation
The basic element of the device is a superconducting
sphere suspended in the magnetic field gradient generated by
a pair of superconducting coils with persistent current
switches. That is, the coils are shorted with a superconduct-
ing shunt after a current is established so that the current is
permanently trapped as long as the superconductor remains
at temperatures below its critical temperature, T c . Themethod for trapping the current is standard for superconduct-
ing magnets. A voltage is applied to a heater to raise the
temperature of the shunt above T c . Current is then applied to
the coil to generate the desired magnetic field. When the
desired field is reached the heater voltage is removed so that
the shunt becomes superconducting. Then the current from
the external supply is reduced to zero and disconnected,
leaving the original current flowing in the coil and the shunt.
In order to minimize heat input that evaporates liquid he-
lium, the current leads between room temperature and liquid
helium temperature are connected through a plug located in
the liquid helium. Once the current is trapped in the coils, the
leads are unplugged and removed from the cryostat. In prac-
tice, the precision required for adjusting the currents is
greater than can easily be achieved by this simple procedure.
Therefore short pulses are applied to the heaters with the
external current close to the desired value as described in
Sec. III.
The levitation force is due to the interaction between the
inhomogeneous magnetic field from the coils and the cur-
rents induced by it in the superconducting sphere. The effect
does not depend on the Meisner effect4 of superconductors in
which magnetic field is excluded from the interior of a su-
FIG. 1. Diagram of the cryogenic portion of the superconducting gravime-
ter.
FIG. 2. Diagram of the dual sensor superconducting gravimeter developed
and produced by GWR Instruments. Extra coils are added to trim the null
positions of each sensor to provide the same tilt sensitivity.
4132 Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 John M. Goodkind
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perconductor even if it becomes superconducting while in amagnetic field. Rather it depends only on the zero resistance
property of superconductors so that the Faraday induction
law guarantees that flux is excluded from inside of the sphere
if a field is applied after the sphere becomes superconduct-
ing.
The levitation force on the sphere is proportional to the
product of the field and the field gradient produced by the
coils. Two coils, close to the Helmholtz configuration along
a vertical axis are used and the sphere is levitated just above
the plane of the upper coil. In this way the levitating force
and the force gradient can be adjusted independently so that
with the sphere levitated at its desired location, the restoring
force for departures from that position can be adjusted asclose as desired to zero. This would be equivalent to an
infinitely long spring. In practice there is an optimal range
for the force gradient which is discussed in Sec. III. A quali-
tative description of the levitating force as a function of po-
sition for various ratios of currents in the two coils is pro-
vided in Ref. 1 along with measurements made with an ac
analog of the superconducting device. Computations of the
force on a superconducting sphere in an arbitrary magnetic
field can be performed using spherical harmonics5 or finite
element numerical methods.6 For the case of axial symmetry,
without the magnetic shield, it can be computed using the
method of images.7 Figure 3 shows the force, computed by
the finite element method, as a function of position of the
sphere along the axis relative to the plane of the upper coil
for three different current ratios in the two coils.
Some experimental gravimeters constructed at GWR
fixed the force gradient permanently by winding the two
coils with the appropriate turns ratio so that the same current
passed through both connected in series would yield the de-
sired gradient. This would simplify the levitation procedure
and therefore shorten the time required for setup. However,long term stability and other characteristics of this arrange-
ment have not been adequately tested. In the initial develop-
ment of the instrument NbTi alloy wire was used for the
coils to take advantage of its high critical current and strong
flux pinning. Contrary to expectations it was found to allow
flux creep such that the field would initially decay at a few
parts in 109 per day. Consequently, pure Nb wire has been
used on all instruments since it does not exhibit this flux
creep at the fields and currents required.
In addition to the main current carrying coils it was
found, in the earliest work, that independent single layer
windings on the same form, underneath the main coils, re-
duced the temperature dependence of the levitation field
Sec. II D. These stabilizing coils also include a persistent
switch so that the switches can be opened heated when the
currents through the main coils are created. In this way the
stabilizing coils initially carry no current and are under no
magnetic stress. Very small currents are subsequently in-
duced in the stabilizing coils if there are correspondingly
small changes in the flux through the current carrying coils.
These induced currents then cancel the change of magnetic
field which would occur without them but, because the
changes are small, the magnetic pressure is small, and there
is no decay due to flux creep. For the same reason they also
reduce the temperature dependence of the total field. In theearliest work the gravimeter was not thermally isolated from
the liquid helium bath1 and had many other design features
that were less exacting than the first field instruments. Recent
tests at GWR have remeasured the shielding factor provided
by these coils8 against temperature changes and current
changes in the main coils and found that the coils may no
longer be necessary.
Mechanical stability is essential for the windings of the
coil and their position relative to the position detection sys-
tem of the sphere. Displacements of the sphere as small as
1010 cm are detected so that displacements of this order in
the structure can lead to spurious signals. For this reason the
coils are tightly layer wound in a form machined into a solidcopper block which also houses the detection system see
Fig. 1. The coil windings are further secured either by wind-
ing a layer of nylon monofiliment on top of the coil or by
bonding the windings with epoxy.
The sphere is hollow so as to reduce its weight and thus
reduce the magnetic field required for levitation. The field
required with solid spheres, of this diameter, is greater than
the lower critical field4 (Hc1) so that flux will creep into the
sphere and it will drop. With the hollow spheres the maxi-
mum field on their surfaces is between 0.025 and 0.04 T for
masses between 4 and 8 g. This is well below Hc10.13 T
for Nb at the gravimeter operating temperature. A variety of
fabrication techniques have been used to make the spheres.
FIG. 3. Levitating force as a function of position of the sphere relative to the
plane of the upper coil. The force gradient is the slope of the curve and can
be adjusted arbitrarily close to zero by adjusting the ratio of the currents in
the two coils. The ratios of the upper coil currents to lower coil currents for
the three curves are 0.870, 0.884, - - - 0.892 and the corre-
sponding force gradients are 1.1103, 5.1104, 1.3
104 N/m. The instruments are operated with a force gradient between
103 and 104 N/m.
4133Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 Superconducting gravimeter
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The earliest versions plated Pb onto thin walled, hollow alu-
minum spheres. These would deteriorate in time if left at
room temperature due to continued oxidation of the Pb. Cur-
rent instruments use Nb spheres. For the UCSD gravimeters
a high temperature salt bath was used to electroplate9 Nb
onto precision ground,10 solid steel spheres. The steel was
then chemically dissolved through the small hole left after
removing the copper rod which supported and provided a
conducting path to the sphere in the bath. A small hole in the
finished sphere is desirable since it eliminates the change of stress that would occur on a sealed sphere due to condensa-
tion of the air trapped inside of it when cooled to cryogenic
temperatures. It also reduces the bouyant effect of the helium
gas around the sphere by about an order of magnitude. In the
commercial instruments, two thin walled hemispheres of Nb
are machined, e-beam welded, and finally ground to yield an
accurate sphere. Chemical vapor deposition was also tested
for the manufacture of the commercial instruments but pro-
vided no advantages and was more costly.
Accurate sphericity of the outer surface guarantees that
the levitating force will not depend on orientation of the
sphere relative to the coil axis so that they have been ground
spherical to within at least 3 m. Departure of the inner andouter surfaces from concentricity is actually desirable since it
is used to maintain the sphere at fixed orientation with the
small hole on top where the magnetic field is minimum. The
spheres determine the ultimate size of the instrument and
almost all of the instruments have used 2.54 cm diameter.
Their mass has ranged between 4 and 8 g with no clear
difference in performance within this range. Attempts to
make smaller instruments by using smaller spheres resulted
in greater sensitivity to ground noise and poorer signal-to-
noise over the entire spectrum. This was first discovered at
UCSD when an instrument was built using a 6.35-mm-diam
sphere and it is probably responsible for the higher noise
level of an instrument built at GWR using a 1.27-cm-diam
sphere.11 The reason for this is apparently that the horizontal
ground motions remain the same but a given horizontal dis-
placement is a bigger fraction of the sphere diameter and
spacing between the sphere and the capacitor plates. Conse-
quently, a given horizontal displacement leads to a larger
apparent vertical displacement. Conversely, this implies that
still larger spheres would yield instruments less sensitive to
ground noise. Alternatively, the addition of constraints of the
horizontal motion of the sphere would accomplish the samething and will be mentioned later in another context.
The electronic component for the levitation procedure is
a dual current supply capable of delivering the required 4 to
6 A for each coil. Panel meters are included to confirm the
settings of the current control knobs. In addition it includes
two pulse generators for the persistent switch heaters, each of
which generates one pulse per second. The voltage and du-
ration of the pulses are adjustable from the front panel. Four,
normally open, momentary switches are used to apply the
pulses to the heaters for the two coils and their two stabiliz-
ing coils so that the operator can easily control the number of
pulses applied. This provides an additional control on the
total energy input to the heaters.
B. Position detection and feedback
Once the sphere is levitated and the gradient adjusted,
the sphere will move relative to the coils in response to local
gravity changes. This displacement is measured as an unbal-
ance of the capacitance bridge formed by the three plates and
the sphere as shown schematically in Fig. 4. The plates are
machined to form the interior of a sphere, 1 mm larger radius
than, and enclosing the levitated sphere. The plates are con-
structed by bonding cylindrical bars and rings of aluminum
together with epoxy which serves as insulation between the
FIG. 4. Circuit diagram for the capacitance bridge displacement detection for UCSD gravimeters. The components on the left side are located inside of thecryostat. The components on the right side are located on top of the cryostat at room temperature.
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finished capacitor plates and between the plates and
grounded rings shielding the center plate from the end plates.
Then hemispherical cavities are machined into the pieces.
The mating surfaces of the two halves are machined to fit
tightly into each other and to align accurately along the axis
of the cylinder. Half of the center ring plate is on each piece.
The outer diameter of the assembly is machined into a cyl-
inder to fit into the cavity of the copper block on which the
coils are wound.
The two halves of a capacitor assembly, along with a
2.54 cm sphere in the upper half are shown in Fig. 5. Clear-
ance holes, countersunk for screw heads, are drilled through
the upper half of the ring plate for the bolts which secure theassembly to the top of the cavity in the copper block Fig. 1.
The lower half has similar clearance holes for bolts to attach
the lower half to the upper half. Copper rods, threaded at one
end, are screwed into blind tapped holes on the top of the
center plate and ring plate to serve as the center lead of rigid
coax cables. The outer conductor of these coaxes is formed
by holes drilled the length of the copper block. The copper
rods protrude through tubes soldered into the top of the cop-
per block. The rods are then sealed, vacuum tight, to the
block using Stycast 2850 epoxy. A third hole and rod
through the copper block forms the coax cable to the lower
plate which is connected by a lead between the end of the rod
and a terminal screwed into the center of the lower plate. Thesphere is placed in the lower half of the assembly before the
lower half is bolted in place.
A copper plate covers the bottom of the cavity and is
sealed vacuum tight with an indium ‘‘O’’ ring. An annealed
copper capillary tube is soldered into this plate to allow
evacuation of the cavity and backfilling with helium gas.
After backfilling the copper tube is pinched off. To further
ensure that the helium does not leak from the cavity the seam
of the pinch-off is covered with epoxy or soldered with in-
dium.
The optimal signal-to-noise ratio for the bridge is ob-
tained by operating at about 1 kHz. Cables that run from
room temperature at the top of the Dewar to 4.2 K at the top
of the vacuum can are subjected to changing temperature
gradients as the liquid helium level changes and changing
pressure since the Dewar is vented to the atmosphere. Tests
at UCSD with a sphere rigidly clamped in the center position
indicated that this was a measurable source of noise in the
capacitance bridge. In order to eliminate this problem, the
UCSD gravimeters place the bridge transformer and a cryo-
genic preamplifier in the liquid helium on top of the vacuum
can Fig. 4. In this way low impedances are presented to the
cables so that the signals are not effected by small changes of
the high capacitive impedances of the cables. The drive sig-
nal for the bridge is generated by the internal oscillator of alock-in amplifier and the output of the preamplifier is con-
nected to the input of the lock-in. This provides the signal-
to-noise advantage of the lock-in and the sign reversal of the
output with sphere position above or below null as required
for feedback. The normal range of force gradients used are
such that electronic noise from the bridge as measured with
the clamped sphere is much less than the signal generated
by mechanical noise with the sphere floating. The cryogenic
portion of the preamplifier is shown on the left side of the
circuit diagram of Fig. 4. The room temperature portion of
the circuit is shown on the right side of the diagram and is
placed on the top plate of the cryostat. Figure 6 is a photo-
graph of this plate, bolted to the flange of the Dewar. Thephoto shows the box containing the preamplifier with cables
clamped by the lid, a second box that clamps additional
cables on the opposite side, the pumping line to evacuate the
vacuum can, the openings for the liquid helium transfer tube,
a vent tube, and a large opening in which a closed cycle
refrigerator is inserted Sec. II F.
The gravimeter is operated in feedback so that the sphere
remains in a position that nulls the capacitance bridge. Feed-
back provides the usual advantages of increased linear dy-
namic range and rapid response relative to open loop opera-
tion. An additional advantage of holding the sphere in the
null position of the bridge is that the mechanical force from
FIG. 5. Photograph of the two halves of the capacitor plate assembly with a
sphere placed in the upper half. The top half is bolted to the top of the cavity
in the copper block of Fig. 1. The large clearance holes allow the bolt head
to touch the upper ground ring without touching the ring plate. The lower
half is then bolted to the upper half using the small threaded holes in the
upper half of the ring plate. The lower half of the assembly has clearance
holes through its ground ring.
FIG. 6. Photograph of the flange on top of the Dewar of the UCSD gravime-
ters showing the room temperature portion of the capacitance bridge pre-
amplifier, the pump out, and valve for the vacuum can, cables, and feed
throughs for all other wiring. The small openings are for the liquid helium
transfer tube, the magnet plug for applying the current to the levitating coils
during setup. The large opening at the center is for the closed cycle refrig-
erator placed as illustrated in Fig. 8.
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the 1 kHz sensing field is null. This can be seen by consid-
ering the sphere as the center flat plate capacitively coupled
to the ring plate between two other parallel plates so that the
force on the center plate due to a voltage, V , applied to the
end plates with the center plate at ac ground is given by
F 1
2 0 AV drive
2 1
d x 2
1
x 2 . 1
Here A is the area of all of the plates, d , is the separation
between the end plates, and x is the variable distance be-
tween the center plate and one end plate. For the sphere
centered, xd /2 and this force is zero, so that relatively
large bridge drive voltages can be applied without applying a
voltage dependent force. In practice a bridge drive of 10 V
peak-to-peak is used.
The feedback force can be generated either by a low pass
filtered voltage, dc coupled to the capacitor plates or by acurrent applied to a 5 turn superconducting coil wound on
the copper block below the position of the sphere Fig. 1.
The capacitance bridge plates are wired so as to allow the
application of an electrostatic force but this is normally used
only to monitor the force gradient during setup or for a rela-
tive calibration of the instrument after setup. It is imple-
mented as shown in Fig. 7. Equal and opposite fixed poten-
tials are applied to the top and bottom plates and the
feedback voltage is applied at their common connection
point. The effect of this is to vary the potential difference
between the top and ring plates relative to that between the
bottom and ring plates, or equivalently, to apply a variable
potential to the ring plate. It was found empirically in the
early work at UCSD that the magnetic feedback is inherently
very linear whereas the electrostatic feedback requires care-
ful balancing of the bridge to both ac and dc potentials.12,13
The reason for this is that for fixed potential, V dc , and a
feedback voltage of V , the equation for the force on the
sphere becomes
F 1
2 0 A V dcV 2
d x 2
V dcV 2
x2 . 2
For the sphere on center so that xd /2, this reduces to a
force linear in V
F 1
2
0 A
d /22 4V dcV . 3
However, the null of the capacitance bridge for the 1 kHz
signal can occur for the sphere at a different position than
that for which there is no force with V 0. This is due to
stray reactive impedances in the bridge circuit. In that case,
when the ac bridge is nulled, xd /2 and the terms quadratic
in V of Eq. 2 will not cancel. For a variety of reasons, Vcannot be very much less than V dc so that the quadratic terms
can be non-negligible. Thus, it is necessary to trim the ca-
pacitance bridge so that the null for detection occurs at the
same position of the sphere as the null for the force with
V 0.
Magnetic feedback, on the other hand, is highly linear
and is automatically nulled when the bridge output is zero.
The force in this case is given by, F aIibi i, where I is
the current induced in the sphere by the levitation field and i
is the current induced by the feedback field. Since i / I is at
most the ratio of the tide forces to g, i / I107 whereas a
and b are of the same order of magnitude, the second term is
negligible for any measurable signal. Thus, during normaloperation, magnetic feedback is used. The output voltage of
the lock-in amplifier is fed back to the current loop through
an integrator and a stable resistor which determines the feed-
back factor .
Magnetic flux detectors called superconducting quantum
interference devices SQUIDs are used in other applications
to detect very small displacements14 and can be used in the
SG as well. They have been used at different stages of the
development of the SG for diagnostic purposes but are more
complicated and expensive. Since they measure changes in
magnetic flux, and not uniquely the position of the sphere,
magnetic feedback could not be used with SQUID detection.
They are used with a superconducting transformer with one
loop placed underneath and close to the sphere and the other
around the SQUID at some location shielded from the levi-
tation field. As the sphere moves relative to the transformer
loop, in the levitation field, it changes the flux through the
loop and therefore the current through the entire circuit. This
is measured as a flux change by the SQUID. It was used to
test for stability of the magnetic field when the sphere was
removed, when it was mechanically clamped, and when it
was held in fixed position by electrostatic feedback. It was
also used to measure the shielding effect of the stabilizing
coils.
The fundamental choice that has been made in the de-sign of the SG is to use a weak restoring force so that rela-
tively large displacements result from small changes in grav-
ity. As a consequence, the sensitivity of the capacitance
bridge displacement measurement is more than adequate. By
contrast, detectors that were developed for gravity wave
antennas14 and used in a gravity gradiometer15 measure
much smaller displacements in very stiff restoring forces.
C. Magnetic shielding
Since the levitation is magnetic, stray magnetic fields
would cause the sphere to move and yield a false gravity
signal. Magnetic shielding is provided by a superconducting
FIG. 7. Circuit diagram for electrostatic feedback. The center tap of the
transformer is ac 1 kHz ground for the capacitance bridge position detec-
tion but not at dc ground. The slowly varying feedback signal is dc coupled
to the center tap through the bias batteries. The ring plate is maintained at dc
ground.
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cylinder with hemispherical closure on one end see Fig. 1
and by a metal can outside of the vacuum can. The metal
shield reduces the magnetic field of the earth so as to mini-
mize the amount of flux trapped in all of the superconducting
elements. The metal is demagnetized in situ just prior to
cooling the instrument to liquid helium temperature. This
reduces the field on the superconducting shield to a few
times 107 T. The superconducting shield prevents any
changes in the environmental magnetic field from changingthe field on the levitated sphere. The effectiveness of this
shielding is improved by eliminating trapped flux through
the use of the metal.
The superconducting shields for the UCSD gravimeters
were made by plating Pb onto copper. The copper pieces
were electroformed onto a stainless steel mandril of the de-
sired shape. The shield is mechanically and thermally at-
tached to the copper block with bolts around the circumfer-
ence, near the top of the block, and with a single bolt through
the center at the bottom. In this way the shield is thermally
and mechanically anchored to the copper block which is tem-
perature regulated and it cannot move relative to the coils.
The commercial gravimeters use welded Nb shields which
are also attached to the copper block as described.
D. Temperature control
The effective diameters of the sphere, the coil windings,
and the superconducting shields depend on temperature
through the temperature dependence of the superconducting
penetration depth. In fact, the dependence that was measured
in the early development was about an order of magnitude
larger than what one would calculate from the known pen-
etration depth for a smooth surface. It was assumed to arise
from the fact that the relevant surfaces are rough on themicroscopic scale so that the effective penetration depth is
greater then that measured in ideal circumstances. This was
later confirmed by explicit measurements of the effect.16,17
Consequently the levitating force varies with temperature by
roughly 10 gal/mK. An additional temperature dependence
can arise from the paramagnetism of the copper block and
other materials inside of the superconducting shield but this
is apparently smaller than the penetration depth effect. For
this reason the copper block is thermally isolated in a
vacuum chamber with weak thermal contact to the liquid
helium bath through the stainless steel collar Fig. 1 and is
electronically regulated to within a few K. The temperature
is measured using a doped Ge thermometer resistor18 as onearm of a Wheatstone bridge. The other three arms are wire-
wound fixed resistors whose values are chosen so that the
bridge will balance when the temperature is at about 0.1 K
above the liquid helium bath. All four resistors are located in
the cryogenic environment, inside of the vacuum can so as to
eliminate any influence of changing cable impedances on the
bridge balance. Standard techniques of lock-in detection and
feedback to a heater are used for the rest of the control sys-
tem.
The thermometer resistor is in thermal contact with the
top of the copper block close to the control heater. In this
manner the temperature of a point close to the weak thermal
link is regulated so that if there are no other heat leaks be-
tween the copper block and the liquid helium, the entire
block should be regulated independent of the temperature of
the liquid helium bath. The liquid helium bath is vented to
the atmosphere through a narrow tube so that it is always
slightly above atmospheric pressure but varies with the at-
mosphere. For this reason residual helium gas in the vacuum
can must be at very low pressure so that temperature varia-
tions of the bath are not transmitted to the lower portions ofthe copper block. If 4He exchange gas is placed in the
vacuum can for the initial cool down, it is pumped after cool
down with a diffusion pump or cryopump until a helium
mass spectrometer leak detector at its highest sensitivity can
barely detect the presence of the gas. If hydrogen exchange
gas is used, then no pumping is required and the hydrogen
atoms are all adsorbed on the walls at the 4.2 K operating
temperature. The copper used for the block is 99.999% pure
so that it will have the highest possible thermal conductivity.
This minimizes changes of temperature gradients along the
block which result from weak thermal exchange between the
block and the walls of the vacuum can, due to radiation or
residual He gas.
E. Tilt control
An ideal gravimeter would respond only to forces along
its axis and would be perfectly rigid or have infinite restoring
force perpendicular to its axis. If its axis were not aligned
with the vertical then it would respond to the component of
gravity along its axis so that the apparent acceleration due to
gravity would be g apparentg cos , there where is the angle
between the vertical and the axis of the instrument. Horizon-
tal accelerations, a horizontal will also have a component along
the instrument axis given by a horizontal sin which will there-fore also contribute to gapparent if 0. The restoring force in
the direction perpendicular to the axis of the SG under nor-
mal operating conditions is several hundred times larger than
in the vertical direction but finite. If the instrument is tilted
the sphere moves off of the axis of the instrument. For a
given tilt angle, the levitating force along the axis of the
instrument decreases, as the sphere moves off center, by
more than the component of gravity along the axis decreases.
Consequently, the sphere passes over a high point when
0. The apparent force displacement of the sphere along
the axis has the same dependence on tilt angle as an ideal
device but with the opposite sign, so that the apparent change
in gravity, gg(1cos )g( 2 /2). If artificial signals dueto tilt are to be less than 1012 g then the tilt must be main-
tained within 1.4 rad. Large scale geophysical tilts are of
this order but local tilts due to changes in temperature
ground water, or cultural effects can be much larger.
Changing temperature gradients in the neck of the
Dewar can cause tilting of its inner wall and therfore of the
gravimeter. For this reason, two pendulum type tiltmeters
with their sensitive axes aligned along orthogonal axes, are
mounted directly on top of the gravimeter vacuum can, in the
liquid helium. In principle, the signals from these tiltmeters
could be used to correct the gravity signal. In practice, be-
cause of the quadratic dependence on , this would be pos-
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sible only if the gravimeter and tiltmeters were exactly
aligned so that the tiltmeter nulls corresponded to 0. In
addition the tiltmeters would need to be linear. These condi-
tions are difficult to meet so that active feedback of the tilt
signals is used to hold the alignment of the gravimeter con-
stant. A variety of displacement transducers can be used for
the purpose so long as they can translate over a distance of
order 1 mm. Thermal expansion devices of various designs
ranging from solid bars of aluminum to bellows filled with
high thermal expansion coefficient oil have been used.
For most of the instruments, the Dewar containing the
gravimeter is bolted to a metal frame supported at three
points in a horizontal plane as indicated in Fig. 8. Variation
of the elevation of two of the points varies the tilt along
orthogonal directions parallel to the directions measured by
the tiltmeters. Micrometer screws at these positions are used
for initial alignment along the vertical prior to placing the
system in feedback. The transducers for automatic tilt control
are placed under the micrometers, on a concrete block pier.
Current versions of the commercial instruments have re-
placed the metal frame with a band around the Dewar as
shown in Fig. 9 so that the transducers can be placed directly
on the floor and there is no need to construct a pier. This
version appears to respond less to the horizontal accelera-
tions of ground noise.
F. Cryostat design
The SG, as any equipment that operates at liquid helium
temperature, requires a support structure, electrical wiring,
and vacuum pumping lines that extend from room tempera-
ture to 4.2 K. In order to minimize the heat conduction be-
tween these temperatures, and therefore minimize consump-
tion of liquid helium, they must be made of materials which
are poor thermal conductors and of sufficient length and
small cross section to reduce the total heat input to the he-
lium bath to less than 100 mW. The UCSD gravimeters are
supported from the top by thin-walled stainless steel tubes
which also double as a pumping tube for the vacuum can and
as rf shielding for cables. Vibrational modes of this support
structure can degrade performance of the instrument if they
occur at inopportune frequencies. For this reason, the
gravimeters take advantage of the relatively stiff and massive
inner wall of the Dewar by pressing the cryostat against the
bottom of the Dewar in addition to bolting it to the topflange. The early UCSD and GWR gravimeters used a stiff
bellows as a spring attached to the bottom of the metal
shield to make contact at the bottom Fig. 8. Current UCSD
instruments use a solid aluminum cone pressed against the
aluminum bottom inside wall of the Dewar by the weight of
the gravimeter. The stainless steel support tubes connect to
the top plate of the cryostat through a slip joint that allows a
small vertical displacement so that the cryostat is not under
compression when the plate is bolted in place. The current
commercial models have eliminated the support structure
and some of its heat leak by building the gravimeter into the
Dewar, rigidly attached to its inner wall.
Since long term, undisturbed operation of gravimeters isimportant for the type of data that they obtain, the total heat
leak into the Dewar must be minimized so that the time
between transfers of liquid helium is maximized. For this
purpose all of the instruments currently incorporate closed
cycle refrigerators which provide 1 W of cooling power at 10
K recent models at 6.5 K so as to absorb most of the heat
flowing in from room temperature.19 In this manner the cur-
rent commercial instruments run for more than a year be-
tween transfers. The Dewars for the UCSD gravimeters were
purchased before reliable refrigerators were available at af-
fordable prices. The cryostat support structure was revised to
accept refrigerators in these Dewars during the late 1980s.
FIG. 8. Diagram of the system supported from a frame on top of a cement
wall pier. In this design the tilt control points were at two corners of an
isosceles right triangle so that the tilt controllers operated along orthogonal
directions.
FIG. 9. Photograph of the complete system of the current model GWR
gravimeter. The compressor and cooling water system for the refrigerator is
on the right. The refrigerator is mounted on its own stand and is mechani-
cally isolated from the Dewar. The expansion devices for tilt feedback are
placed directly on the floor underneath the micrometer heads which are
attached to a band around the center of the Dewar. This arrangement leads
to less coupling of horizontal accelerations into the gravity signal. In this
arrangement the tilt control points are at the corners of an equilateral tri-
angle so that the tilt control axes are not orthogonal.
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This is accomplished by leaving an opening through the lid
of the cryostat that allows insertion of the refrigerator into
the neck of the Dewar with the gravimeter in place and in
operation as shown in Fig. 6. A mechanical diagram show-
ing the placement of the refrigerator in the Dewar neck of thecommercial instruments is shown in Fig. 10. The heat leak-
ing into the Dewar through the neck is transferred to the
refrigerator through the helium gas and the copper heat ex-
change plates. This arrangement allows removal or replace-
ment of the refrigerator for servicing without interrupting
operation of the gravimeter.
All of the current refrigerators operate on the Gifford–
MacMahon cycle which employs a reciprocating piston so
that they generate mechanical vibrations ranging from fre-
quencies of 2 Hz up to hundreds of Hz. Consequently the
systems must be constructed so as to include vibration isola-
tion of the refrigerator from the gravimeter. The refrigerator
is suspended from an independent frame which is vibrationisolated from the floor or the gravimeter pier. The refrigera-
tor is aligned in the opening to the cryostat so that it does not
touch Fig. 10. The opening into the Dewar around the re-
frigerator is sealed by a rubber diaphragm.
Refrigerators are also manufactured which operate at 4
K so that, in principle it would never be necessary to transfer
liquid helium in the field. Two systems incorporating these
refrigerators have been delivered by GWR and one has been
operating for five months without loss of liquid helium. The
necessary time between preventive maintenance of these re-
frigerators is not yet well established but there is reason to
expect them to run for as long as four years. A major disad-
vantage of all of the refrigerators for field operation is that
they require about 2 kW of power. The 4.2 K machines re-
quire 3 or 4 kW but this requirement could be reduced if
there is sufficient economic motivation for manufacturers to
undertake the development effort. New developments, such
as the pulse tube refrigerator,20,21 which have no moving
parts, could lead to gravimeters and other cryogenic devices
that can operate indefinitely in the field with maintenance
intervals of several years. They would also eliminate or sub-stantially reduce the need for mechanical isolation. The first
commercial pulse tube refrigerator to run at 4.2 K has be-
come available this year.22
G. An undesirable degree of freedom
As stated above, the restoring force in the horizontal
direction is finite so that the sphere can move in the horizon-
tal direction as well as the vertical. Due to the near cylindri-
cal symmetry, this means that the center of mass can move in
an orbit around the stable equilibrium point. A normal mode
of the system is indeed excited by tilting the instrument
Evidence that it is this orbital motion, rather than a purerotation of the sphere about its axis, is provided by the fact
that the viscous damping of the mode by helium gas is too
large to be explained by a pure rotation. Due to slight asym-
metries in the levitation and detection systems, there is a
small apparent or real vertical displacement associated with
this motion. The period of this mode can be decreased from
close to 1 h to less than a few seconds by trapping magnetic
flux in the sphere and then applying a small magnetic feild,
both in the horizontal plane. This is done by deliberately
applying a small magnetic field to the sphere, while it cools
through the superconducting transition using some small
coils glued onto the copper block. These same coils are then
used to apply a field, during operation, so as to break the
cylindrical symmetry. The damping of the mode is also in-
creased by increasing the amount of flux trapped in the
sphere since the moving sphere then induces eddy currents in
the capacitor plates. The damping of the mode is also in-
creased by viscous damping of helium gas sealed into the
cavity with the sphere. The cavity in the copper block is
sealed at room temperature with helium gas at a pressure of
1 atmosphere or less. With no gas in the chamber, the Q of
the mode is several thousand so that it is always excited and
the instrument is not usable. By contrast, the vertical mode,
which is the useful degree of freedom, is heavily over-
damped under normal operation conditions and has a period
of about 5 s.
H. Electronic and digital filtering
Although the SG provides unique signal-to-noise only at
frequencies below about 103 Hz, optimal data can be ob-
tained only if data is sampled at least every 10 s. This is
because there are undesirable high frequency components to
the signal that result from environmental, cultural, or instru-
mental events. These can be in the form of rapid spikes or
sudden offsets of the signal which are not of interest to in-
vestigators using the gravimeters and must be removed from
the records so as not to degrade the long term signals that are
FIG. 10. Drawing showing the placement of the closed cycle refrigerator in
the neck of the Dewar of a GWR gravimeter.
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of interest. This can be done with greater precision and less
influence on the long term data, by removing these artifacts
from data sampled at the higher rates. Some investigators
sample at 1 s intervals so that the electronic antialiasing pre-
filter can then use a time constant as short as 2 s. Shorter
time constant filters use smaller capacitors which are likely
to be more stable than large ones. For tidal analysis and
measurement of secular changes in gravity these records
would normally be digitally filtered and decimated to 10 minor hourly samples. The UCSD gravimeters sampled and re-
corded at 10 s intervals with 20 s Butterworth prefilters. In
addition the data acquisition software included a real time,
symmetric digital filter to record at 2 min intervals. This
allowed relatively high resolution real time monitoring of the
data.
In order to compare signals from different instruments it
is important that gain and phase shift as a function of fre-
quency of the antialiasing filters be identical. Specifications
for this filter have been agreed upon by the participants in the
Global Geodynamics Project23 GGP, discussed in Sec. IV,
and are available on the Web page for that organization.
However, the force gradient of the gravimeter, and therefore
its intrinsic response time, can be adjusted over a wide range.
The force gradient must be set sufficiently weak to provide
sufficient open loop electromechanical gain, A, so that geo-
physical noise dominates the signal and A 1, but not so
weak that the closed loop time constant is comparable to the
antialiasing filter. If the latter were the case then the gain and
phase shift of the data from various instruments would not be
the same even with well matched electronic filters. In prac-
tice the necessary conditions are well satisfied over the range
of force gradients that have been used.
I. rfi shielding and temperature controlAlthough the electronic components all operate only at
audio frequencies or dc, early experience demonstrated that
rf interference from local radio broadcasts could degrade the
data. In addition, it was found that a measurable dependence
of the system on room temperature resulted entirely from
temperature dependence of the electronics. Consequently,
the electronics for the UCSD instrument, SGB, were placed
inside of an rfi shielded enclosure which is also insulated and
temperature regulated at 33 °C. All of the cables leading into
the cryostat from the rfi enclosure pass through braided cable
shielding that is grounded to both the enclosure and the
Dewar.
J. Data acquisition
The largest temporal variations of gravity are from the
tides and they are approximately 300 gal peak-to-peak at
mid latitudes. Short term noise at quiet locations can be as
small as 0.1 gal so that an analog-to-digital A/D converter
with resolution of 1 part in 3103 12 bits might seem
adequate. However, to prevent the signal from exceeding full
scale of the A/D in the event of offsets from earthquakes or
other disturbances, the instruments are usually run so that the
tides are no more than 1/2 of full scale. Thus a 12 bit A/D
converter is not quite adequate. Analysis of a year long
record can yield amplitudes of the various tidal frequencies
to within about 103 gal so that it would be desirable to
have resolution of better than one part in 3105 of full
scale. In practice, high quality digital voltmeters can provide
six decimal digits of resolution but their specified long term
stability is no greater than 16 bits. All work with the UCSD
instruments thus far has been done with 16 bit A/D boards
which plug into the computer bus. Users of GWR gravime-
ters have used bench top commercial digital voltmeters.In contrast to most laboratory experiments, timing of the
data acquisition must be at accurate universal times, not sim-
ply even intervals. Analysis of tide signals or their removal
from the data to reveal other gravity variations requires that
the universal time of the data points be known to within
about 1 s. A shift of less than 5 s in the absolute time of a
year long record can lead to differences in the best fit tidal
amplitudes that are greater than the uncertainty due to geo-
physical noise. A variety of methods have been used to syn-
chronize the computer system clock with UT in the field. The
UCSD data systems at one time used commercial plug-in
boards to receive the time signal from the radio broadcast
station, WWV, of the National Institutes of Standards and
Technology NIST. More recently a plug-in GPS receiver
was found to be much more reliable and is useful worldwide.
Both systems require an outdoor antenna. In either case the
PC system clock was automatically updated from the plug-in
board whenever the difference between them reached one
second.
III. SETUP PROCEDURES AND OPERATION
Starting a gravimeter with the resolution of the SG is not
as simple as throwing a switch. There are a few well defined
procedures which must be followed, some are peculiar to theSG and some would be required of any gravimeter with com-
parable precision.
A. Cool down and levitation
In order to optimize the magnetic shielding, the metal
shield is demagnetized after the instrument is installed at its
operating location and before the system is cooled below the
superconducting transition temperature. When the instrument
has cooled to liquid helium temperature, the currents in the
coils are increased in steps until the sphere levitates. The
drive voltage and gain of the capacitance bridge are both set
100 to 1000 times lower than for the operating conditions so
that it can be used to monitor the sphere position over theentire range of its motion. With the sphere always levitated
close to its centered position the force gradient is then de-
creased by successively reducing the current in the lower coil
and increasing the current in the upper one. As the force
gradient is decreased, the displacement of the sphere for a
given change in current becomes greater so that increasingly
fine adjustments are needed. This is accomplished by de-
creasing the power in the pulses applied to the persistent
switch heaters and by setting the power supply current suc-
cessively closer to the final desired current. The current in
either coil is increased or decreased by setting the supply
current respectively higher or lower than the trapped current
4140 Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 John M. Goodkind
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and pulsing the heaters. The decrease in the force gradient is
qualitatively evident since the time constant for the sphere to
approach its equilibrium position increases with decreasing
force gradient. Gravimeters have been operated with this in-
trinsic time constant as long as 30 s. In the initial levitation
all four heaters are pulsed simultaneously but for final cen-
tering of the sphere it is easier to adjust only the current in
the lower coil. The position is less sensitive to current
changes in the lower coil and, for small changes, this adjuststhe position of the sphere with little effect on the force gra-
dient.
When the currents are adjusted to the desired values the
current from the external supply is turned off. This causes a
small displacement of the sphere since the persistent current
after the external supply is removed is not exactly the same
as the the current through the coil when current is still flow-
ing from the supply. It is then recentered by turning the
current on again and readjusting the position of the sphere to
be offset by the same amount but in the opposite direction to
the shift caused by turning off the current.
B. Tilt adjustment
Coarse alignment of the gravimeter along the vertical is
done before the final adjustments of the coil currents since
the vertical position will change with gross changes of the
tilt. Adjustment of the two tilt axes is iterated until it is clear
that tilt in any direction will lower the sphere. Adjustment
requires measurement of small changes of the position of the
sphere so that it is complicated by the fact that turning the
micrometers subjects the gravimeter to relatively large hori-
zontal acceleration which will usually excite the orbital
mode. The oscillations of the mode will then be superim-
posed on the tide signal. In order to determine shifts of the
mean position accurately, it is necessary to observe several
cycles of the mode so that the entire process can take up to a
few hours depending on the damping of the mode.
The final step is to ‘‘anneal’’ the superconductors by
raising the temperature above the normal operating tempera-
ture. The irreversible creep of flux into the superconductors
seems to be eliminated by deliberately heating them above
the operating temperature with the levitating field turned on.
The temperature is raised until the sphere drops irreversibly
by a small fraction of the distance to the lower capacitor
plate. After returning T to its normal operating value, the
sphere is again centered by increasing the current in the
lower coil.
C. Maintenance
There is no mechanical wear of the instrument since it
has only one moving part and that part is magnetically levi-
tated. There is no other degradation of the instrument over
time since it operates at T 4.2 K where chemical processes
are virtually eliminated. Therefore the only maintenance is
that which is required to maintain the cryogenic tempera-
tures. This means that at some intervals the liquid helium in
the Dewar must be replenished. The time between such
transfers of liquid helium is maximized through the use of
the closed cycle refrigerators. The refrigerators require re-
placement of an oil separator once a year. Every two years
the refrigerator must be removed for preventive maintenance
which can be done without interrupting the operation of the
gravimeter. The most efficient procedure is to swap the re-
frigerator with one that has been serviced.
The UCSD instruments use 160 liter Dewars and require
filling every four months. Current commercial instruments
are built into smaller, more efficient Dewars as discussed
above. These instruments can run for more than one yearbetween refills with liquid helium. They also are mounted
directly on the floor so that no pier need be constructed. A
photograph of this instrument is shown in Fig. 9.
D. Data analysis
The last step in using the instrument is, of course, analy-
sis of the data. The initial steps in the analysis are common
to almost any ultimate use of it and include removal of some
artifacts as well as environmental influences on gravity
which may not be of interest. The principle artifacts are noise
spikes and offsets or ‘‘tares’’ in the data that are a wellknown problem to users of all types of gravimeters. These
are apparent sudden changes in gravity that usually result
from subjecting the instrument to large accelerations but they
have also resulted from lightning strikes and can occur with-
out any apparent cause. They normally appear as changes
between successive data points even when sampling at 10 s
intervals and consequently are too rapid to result from any
real change in gravity. They are removed from the data by
fitting straight lines to a short segment of good data on each
side of the affected segment and subtracting the difference
between the two intercepts from all data after the tare. If one
or more data points on either side of the tare are also far from
the smooth time dependencies, they are replaced by interpo-lating the straight line fit to the data prior to the tare. If there
is a longer segment of data that is damaged or missing, with
or without a tare, a periodic signal containing the major tidal
frequencies can be fit to the good data and used for interpo-
lation in place of a straight line.
Tares that are smaller than about 1 gal may not be so
easily removed from the raw data since they can be difficult
to identify in the presence of the much larger tide signal. For
such cases the tides must be removed first, as discussed be-
low. The size of the offset can then be determined by the
method described above and removed from the raw data be-
fore detailed analysis is attempted. The noise on data
sampled at 10 s intervals may be too large to reveal tares ofthis size so that in some cases they are more clearly revealed
in data filtered to 1 or 2 min samples.
Another artifact that has been significant on some of the
SG is an exponential approach of the sphere to its final equi-
librium position with a time constant as long as 300 days.
Since it is very regular in time it can be fit to the data along
with tides, ocean load, and atmospheric gravity see Sec. IV
and subsequently subtracted from the time series. More dis-
cussion of the influence of offsets and exponential drift on
the data is included in Sec. V. Beyond the removal of these
artifacts from the data, the methods of analysis depend on the
purposes of the investigator. Some of these methods are de-
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scribed in Sec. IV as part of a discussion of the uses of the
instruments.
E. Calibration
For some purposes, such as testing models of the interior
of the earth through measurements of the solid earth tides, it
is essential to calibrate the gravimeter accurately. The SG
can be calibrated to an accuracy of about 1% by applying adc potential to the capacitor plates as described above but
this is not sufficient for present day work. There are three
methods that are currently used for the purpose. An accu-
rately calculated gravity signal can be generated by moving a
known mass near the gravimeter over known distances, as-
suming the validity of Newton’s gravitation law, and assum-
ing previously measured values of the gravitation constant
are correct.24–26 The gravimeter can be subjected to an accu-
rately determined acceleration.27 Simultaneous measure-
ments of the tides at the same location with an absolute
gravimeter and the SG discussed below are compared. All
of these methods are capable of an accuracy of 0.1% or
better. The latter two were checked against each other andagreed within close to this limit.28
IV. PAST AND PRESENT APPLICATIONS
The capabilities of the SG have provided data which are
not obtainable with other gravimeters. Some of the topics
which have been investigated with this data are discussed
below. Some of them will not be well resolved until local
and global arrays of SG are used and the data are used in
conjunction with that from other types of instrumentation. A
global array of such data is the objective of the current
GGP23 in which operators of SG at 17 sites distributed
around the world have agreed to maintain and share stan-dardized records between July 1, 1997 and July 1, 2003. No
attempt has yet been made to use local arrays for engineering
purposes or to study hydrology as discussed below. In this
section some of the phenomena which cause changes in
gravity that are measurable by the SG are described. Collec-
tively they illustrate that continuous gravity records of this
precision are required to distinguish the various causal rela-
tionships and thereby measure each of them with precision.
Repeat survey measurements of short duration cannot serve
this purpose no matter how accurate the instrument.
A. Tides of the solid earth and studies of the deepinterior of the earth
When the instruments were first deployed, the clearest
demonstration of their new capabilities was necessarily a
measurement of the tides of the solid earth since the largest
contribution to the time variation of g is the tides.13 Solid
earth tides continue to be an important subject of study with
the SG because they can provide unique information about
the interior of the earth. Records of length one year or longer
from SG measure the amplitudes of the various tidal period-
icities to within about a nanogal (1012 g). The major por-
tion of the gravity tide signal is due to the force gradient
from the sun and the moon. Due to the complexity of the
orbits of the moon and the earth, the spectrum of the forcing
function is very rich. The terms fall into groups split succes-
sively by a cycle per day, a cycle per month 28 days, and a
cycle per year plus some small terms at other frequencies.
However, 16% of the tidal gravity signal results from the
elastic yielding of the earth in response to these forces. This,
geophysical, portion of the solid earth tide results from
change in elevation distance to the center of the earth and
from a shift in the distribution of mass.29 However, other
phenomena influence gravity at tidal frequencies so that pre-
cise measurement of the solid earth response requires mea-
surement of these other phenomena as well. The principal
contributions to the gravity signal are illustrated in Fig. 11and described in the following paragraphs.
The traditional approach to the study of earth tides has
been the ‘‘harmonic analysis’’ in which sinusoids at the
known tidal frequencies are fit to the data to determine am-
plitudes and phases. The tidal potentials or forcing functions
as a function of time can be determined with the very high
accuracy of astronomical data for the orbits of the earth and
moon.29–33 Long time series of these potentials can then be
developed and analyzed into spectral components with accu-
rately determined amplitude and phase. By comparing the
amplitudes and phases of the sinusoids fit to the data with the
computed tidal forcing functions at those frequencies, a fre-
FIG. 11. The gravity signal at Fairbanks, Alaska during September and
October 1990 and its major components. a The raw gravity data is at the
top, the computed theoretical solid earth tide is next, and the computed
ocean load tide is at the bottom. The signals are artificially offset for better
display. b The solid line is the residual after subtracting the theoretical
solid earth and ocean load tides from the raw signal. The dotted line is the
barometric pressure. The strong correlation between the two is typical of all
locations.
4142 Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 John M. Goodkind
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quency dependent amplitude and phase of the overall re-
sponse of the earth is determined. Two software packages,
ETERNA,34 and BAYTAP-G35 designed for various types of
tidal analysis and removal of tides are now widely used in
this field. The problem then becomes one of identifying the
various contributions to this response. The direct effect of
the forcing function combined with the elastic response of
the solid earth is the largest term and has been calculated
using specific geophysical models of the earth.36–38 The nextlargest contribution is from the ‘‘loading’’ of the ocean tides
discussed below. In the harmonic method of analysis one
must subtract a calculated ocean load effect for each tidal
frequency from observed data in order to compare data to
geophysical predictions of solid earth tides. Therefore, in
order to search for deviations from predictions concerning
the solid earth one must assume that computed ocean loads
are accurate. An alternative approach fits the full time depen-
dencies predicted for the ocean load tide and for the solid
earth tide to the data.24 This yields the amplitude of both
predicted effects and the residual signal is then analyzed for
frequency and time dependent departures from the geophys-
ical predictions.
1. Influence of ocean tides
The tidal motion of the oceans contributes as much as
10% of the total measured diurnal and semidiumal gravity
tides at mid latitudes. At the poles it is 100% since there are
no diurnal or semidiurnal tides there. The ocean tides are
approximately 90° out of phase with the tidal driving force
but both amplitude and phase vary substantially with loca-
tion. Measurement of the solid earth portion of the tides
therefore requires that the influence of the ocean loading ef-fect be calculable to the same absolute accuracy as the de-
sired precision of the measurement. Calculation of the effect
requires detailed knowledge of the ocean tides everywhere
and a method for calculating the response of the solid earth
to the shifting mass of the ocean tides. The accuracy of our
knowledge of the ocean tides has improved dramatically in
the past two decades as a consequence of satellite data.39
Using a global model for the height of the ocean tides based
on these data,40 the influence on gravity is computed by in-
tegrating a Green’s function for the response of the earth to a
point load at its surface.41 A suite of computer programs to
allow computation of the ocean load effect anywhere on the
globe on this basis has been made available by Agnew.40
One test of the accuracy of these computed ‘‘ocean load’’
tides indicated that they agree with measurements to within
0.1 gal at the south pole42,43 where all of the measured
diurnal and semidiumal gravity tide is due to the ocean load
effect. However, by using the nonharmonic method of tidal
analysis mentioned above at mid latitudes, where both grav-
ity tides and load tides are large, a significant difference
between calculated and measured values was found.24 None-
theless, the computed values are now sufficiently accurate so
that when they are subtracted from measured tide signals, the
result can be analyzed for a number of other phenomena
discussed below. The global array of instruments involved in
the GGP will provide the best opportunity yet to test the
ocean models and optimally remove the ocean load from the
solid earth tides.
If nontidal signals are of interest, the objective is to re-
move all periodic terms at tidal frequencies, rather than to
measure them. This is done by fitting and subtracting sinu-
soids at tidal frequencies to the full gravity signal. The opti-
mal number of frequencies to fit to the data depends on the
length of record to be analyzed. More than one hundredterms can be used for records of one year or longer. For
records of less than one month the optimal removal is ob-
tained by fitting somewhere between 8 and 12 frequencies.
An alternative is to subtract the full time series of the theo-
retical computed solid earth gravity tide and ocean load ef-
fect from the signal and then fit and subtract sinusoids from
the remaining ‘‘residual’’ signal. The latter method requires
fitting many fewer terms to achieve equivalent results. Using
either method, some small periodic terms always remain in
the data. The cause of these remaining periodic terms is
probably due to amplitude modulation of the tides by atmo-
spheric influence on the ocean tides but definitive identifica-
tion will be important for further study of the tides and re-
lated geophysical problems.
In spite of the major advances in the computation of the
response of the earth and the influence of ocean tides, the
predictions of the total time dependence differ from measure-
ments by as much as a few gal. Consequently, measure-
ment of nontidal changes in gravity to within a few gal at
any given location may require measurement rather than
computation of the tides at that location. For most purposes,
at noncoastal sites, the tides are determined to sufficient ac-
curacy with one or two months of measurement. The ampli-
tudes and phases determined are then sufficiently stable so
that they can be used to correct future short duration surveymeasurements at the same site to within 1 gal. However, in
coastal regions the influence of storm surges and seasonal
variations in sea level might not be predetermined with com-
parable precision. In that case concurrent measurement of
sea level along the coast near the gravimeter station would
be needed since very local influences of harbors and changes
in bottom topography would render future predictions unre-
liable at the 1 gal level.
2. Gravity variations due to the atmosphere
After the gravity tides and the ocean load effect, the next
largest influence on gravity is due to the atmosphere.44–49
This is of interest for its possible contribution to atmosphericphysics but also must be removed from the gravity signal
before properties of the solid earth can be deduced. Its effect
on tidal amplitudes and phases is small but measurable ex-
cept at periods close to 1 and 2 cycles per solar day where
the effect can be large. The irregular distribution of the mass
of the atmosphere due to weather systems produces changes
in gravity in the same manner as the oceans by gravitational
attraction of the shifting atmospheric mass and by distortion
of the surface of the earth. The largest portion of the effect
from the atmosphere is the local direct gravitational attrac-
tion of its mass above the gravimeter. As pressure increases,
the density increases so that the total mass above the
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gravimeter increases and consequently gravity decreases. A
small contribution of the opposite sign results from the local
depression of the surface of the earth with increasing pres-
sure. Periodic variation of atmospheric pressure due to diur-
nal heating and cooling also produces a measurable gravity
variation. Most if this is a local effect but part is due to the
global atmospheric tides49 due to solar radiation rather than
tidal forces. Both effects vary with the seasons and location.
The gravity/atmospheric pressure admittance for the local ef-
fects varies in time according to the size and shape of weather system but is normally close to 0.3 gal/mbar. The
correlation between gravity, after earth and ocean tides have
been removed, and barometric pressure, measured at the site
of the gravimeter, is normally very high as indicated in Fig.
11. Thus it can normally be removed from the gravity
records to within about 1 gal by fitting and subtracting a
single pressure record. Since the admittance changes in time
the atmospheric effect can be better fit in shorter segments of
data. It can also be better fit if low passed and high passed
barometer records, with a crossover at about five days, are fit
separately to the gravity data. Using pressure records from an
array of locations, accounting for the response of the oceanto atmospheric pressure and for the stratification of the atmo-
sphere further improves the agreement with measured grav-
ity changes.46,47
Further demonstration of the dominance of atmospheric
noise is provided by comparing the power spectra of gravity
and barometric pressure. Figure 12 shows the spectra for a
two year period at Cantley, Quebec.50 Very recently, analysis
of 11 years of data from the International Deployment of
Accelerometers IDA network of Lacoste–Romberg
gravimeters discussed below has shown that seismic noise
in the 2–7 mHz frequency range is due to atmospheric
turbulence.51,52
3. The interior of the earth
Most of the present knowledge about the interior of the
earth has been obtained through analysis of seismic data and
from the ringing of the normal modes of the earth after earth-
quakes. However, data from the SG can provide information
that is not available by any other means. These include some
properties of the liquid core and the low frequency visco-
elastic properties of the mantle and crust. One of the long
standing unsolved geophysical problems is the frequency de-
pendence of the dissipation in the solid earth. The dissipation
has been determined at seismic frequencies and for the nor-
mal modes of the earth roughly 1 to 100 cycles per hour. It
can also be determined at the very long periods correspond-
ing to glacial rebound. However, for the wide range in be-
tween there are no simple means for measuring it. In prin-
ciple the dissipation at tide frequencies could be measured by
the phase shift relative to theoretical gravity tides but this
would require more accurate computed ocean loads than are
currently available. Another approach is through the mea-
surement of the Q of the nearly diurnal free wobble and other
internal modes of the earth.
53–56
The nearly diurnal freewobble is observed by gravity through the resonant response
of the earth to tidal forcing at frequencies close to the wobble
frequency.
A closely related phenomenon is the Chandler Wobble57
with a period of 435 days.58–62 This is a wobble of the axis
of rotation of the earth relative to its body axis. One of the
problems here has been to determine what excites the wobble
since its Q is finite but the oscillations never damp out com-
pletely. It alters latitude and therefore the centrifugal force
due to the rotation of the earth. Both of these phenomena are
due to oscillations of the interior of the earth due to the
ellipticity of the boundary between the liquid core and the
mantle of the earth. Prior to the SG the Chandler Wobble hadbeen measured only by astronomical observations using ze-
nith tubes. Currently the rotation effects can be measured
most accurately using satellite data and by very long base
radio interferometry.63 However, even at this low frequency
there is evidence that the ocean responds differently than the
solid earth. Gravity measures a combination of the shifts in
rotation, the response of the ocean mass to them, and the
distortion of the crust due to the ocean response. A combi-
nation of satellite data and gravity data of sufficient accuracy
could allow identification of these different effects. Removal
of the gravity effect of the polar motion is essential for mea-
surement of secular changes in gravity since it can amount to
several gal, depending on latitude.The solid inner core can also oscillate with respect to the
body center of the earth. Due to the rotation of the earth this
should lead to a triplet of frequencies.64 Detecting and mea-
suring these oscillations would provide additional constraints
on the properties of the liquid core. Long records from the
SG offer the only present hope of confirming this prediction.
One analysis65,66 found evidence for the triplet in records
from SG but the conclusion is contested.67 Additional infor-
mation is being obtained.68 Much more data from a wider
geographical distribution of SG are anticipated from the
GGP so that if the triplet will ever be observable above geo-
physical noise it should appear in that data.
FIG. 12. Power spectra of gravity and atmospheric data at Cantley, Canada
for a two year record indicating that the dominant source of gravity noise
over the frequency range shown is from the atmosphere. Data from Ref. 50provided by David Crossley.
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The normal modes of the earth are excited by
earthquakes69 and, due to their high Q, some will ring at
measurable amplitudes for several days after large, deep
events. Their frequencies and the splitting of the modes due
to rotation and ellipticity can be calculated from specific
models of the interior of the earth70–72 so that measurements
of the frequencies can be used to constrain these models.73 A
global effort to measure the frequencies, splittings, and
damping of all of the modes has been underway since 1975by the IDA network.74 This effort has used large numbers of
Lacoste–Romberg, spring type gravimeters placed around
the earth. A recent study has found that, at periods shorter
than about 1 h, the best spring type gravimeters can be less
noisy than the compared SG.75 Nonetheless, the modes are
clearly measured by the SG so that the global array of the
GGP will contribute to the field. Discussion of the causes for
the higher noise level at high frequencies in the SG and
possible remedies is provided in Sec. V.
4. Tectonophysics: Vertical crustal motion along
plate boundaries According to Newton’s gravitation law, local gravity de-
pends on the distance to the center of the earth. Thus g
changes as the surface moves up and down in response to
loading from the ocean or atmospheres, as discussed above,
or due to tectonic processes and the buildup of seismic strain.
The dependence of g on elevation above an idealized spheri-
cally symmetric earth is 3 gal/cm. The SG has been shown
to be able to distinguish real gravity changes of about 1 gal
from those due to ocean, atmosphere, and ground water see
discussion in Sec. V. This means that changes in elevation
as small as 3 mm can be measured. Displacements of the
order of 1 cm/year or greater are known to occur at plate
boundaries and in regions of glacial rebound. However, suchsecular gravity changes can result from shifting of mass be-
neath the surface as well as from vertical displacement. GPS
measurements of surface displacement can be made to about
1 cm accuracy so that the combination of gravity and geo-
detic measurements can now determine both vertical dis-
placement and displacement of mass beneath the surface.76
Displacement of mass can result from changes in meteoric
groundwater discussed below or from compression or ex-
pansion due to stress. Measurement of these small, slow
changes require reliable determination of any possible instru-
mental drift. This is also discussed in Sec. V.
5. Hydrology: Effects of rainfall
An infinite sheet of water 1 cm thick produces a gravi-
tational field of 0.4 gal. Thus 1 cm of rainfall will increase
gravity by 0.4 gal at locations where it falls more rapidly
than it can drain away laterally. Clear correlations with rain-
fall at this ratio are observed at locations where lateral drain-
age is slow77–80 Fig. 13. The ratio of gravity change to
rainfall during the rain in such locations, if it is greater than
0.4 gal/cm, measures the area from which rain is collected
into an aquifer beneath the gravimeter. The rate at which
gravity decreases after rainfall has ceased, measures the net
flow rate out of the aquifer. At The Geysers, California and
at the Hawaiian Volcano Observatory,78 the time dependence
of the gravity signal from rainfall was accurately modeled
using simple models with discrete aquifers and fixed flow
rates between them.
Gravity variations with rainfall such as these measure
the integrated effect of the total mass of water in the ground
around the gravimeter. Water table measurements using
drilled wells measure only at the point of the well and there-
fore provide incomplete information in inhomogeneous ter-rain. An array of gravimeters could map the areal extent of a
large aquifer, identify its sources and sinks, and measure the
total change of mass from season to season. The information
obtained in this manner would greatly exceed what can be
obtained by episodic gravity surveys, as a consequence of
the continuous records and the higher resolution of the SG.
Only with continuous records can all environmental influ-
ences on gravity be identified so that measurements of a
specific influence such as groundwater can be made with
better than 1 gal precision.
For purposes other than hydrology, the influence of
groundwater is a signal that must be removed from the data.
FIG. 13. Rainfall and gravity as a function of time through two rainy sea-
sons at The Geysers geothermal field in northern California. The ratio of
gravity change to rainfall is slightly larger than 0.4 gal/cm indicating that
the gravimeter was on top of a small basin into which water drained rapidly
from a wider area during the rainstorms. The gravity signal does not de-
crease immediately after the rainstorms until late in the season during the
first year. During the second year the measurements were terminated before
gravity began to decrease. Apparently when total rainfall reached 100 cm inthe first year, the pressure in a local aquifer became sufficiently great to
force a rapid drainage. The total rainfall during the second year was only 60
cm.
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At most locations, measurements of rainfall, water table, and
soil moisture above the water table are required. At Rich-
mond, Florida the terrain was flat, uniform, and highly po-
rous and the combination of these three measurements al-
lowed the removal of the gravity effect with high
confidence.78 In Fairbanks, Alaska a well was used to moni-
tor the water table hourly, two capacitive soil moisture
gauges recorded every 2 min were buried at depths of 1 and
2 m, and precipitation was recorded daily. Apparently due tothe permafrost, topography, and the relatively small amount
of precipitation, no influence of ground water on gravity was
detected there.
B. Fundamental gravity
The earliest use of the SG for an experiment in funda-
mental gravity was a test for the existence of a universal
preferred reference frame and an anisotropy of the gravita-
tional constant.81–83 A detailed investigation of the frequency
dependence of tidal amplitudes and phases was used to set an
upper limit on a parameter that represents the influence of a
preferred reference frame on the laws of physics. These testscould be improved with the use of longer records from mul-
tiple instruments and by examining additional tidal constitu-
ents. More recently, experiments have looked for departures
from the gravitational inverse square law.25,26
Another potential use of the gravimeters is the detection
of gravity waves using the earth as an antenna. Selective
excitation of normal modes of the earth that can respond to
the quadrupole nature of gravity waves, at times when no
seismic events are detected would provide the evidence.84,85
An early claim to have observed gravity waves in this man-
ner was performed with an unsuccessful redesign of the su-
perconducting gravimeter which had a higher noise level
than the Lacoste meters of the IDA network.73,74,84 The re-
sults have not been confirmed with better instruments. The
method has serious difficulties which have not yet been sur-
mounted. One is the difficulty of distinguishing excitations
caused by ‘‘silent’’ earthquakes from those caused by gravity
waves. These are earthquakes which occur sufficiently
slowly so that they do not create teleseismic waves but none-
theless excite low frequency normal modes.86 A second dif-
ficulty is that the anticipated energy density of gravity waves
at these low frequencies is very low.
V. PERFORMANCE OF THE SG AND COMPARISON
TO OTHER GRAVIMETERSThe SG is unique for the low noise level it provides over
a broad range of frequencies but two other types of gravime-
ters are in widespread use for the unique features they pro-
vide. At present, no instrument exists which combines all of
the advantages of all three. A brief comparison of these fea-
tures is provided here along with a discussion of how they
should be used in complementary fashion for a rigorous
gravity research program. The SG has been used primarily to
obtain high resolution measurements of gravity as a function
of time at a fixed location. However, relative changes as a
function of location gravity surveys also provide very im-
portant geophysical information and have constituted the
bulk of gravity work in the past. Most gravimeters were de-
signed for survey work.87 Complete understanding of time
dependent variations measured by the SG will also require
measurements of their location dependence on both a global
and local scale. Since all three instruments are too costly to
anticipate deployment by the thousands, surveys relative to
the locations of the SG will provide a useful alternative to
such arrays for many purposes. The high resolution time de-
pendent measurements of the SG will allow accurate deter-mination of the influence of ocean tides, atmosphere, and
groundwater at a given site. If the data reveal a gravity
change in addition to these effects, a survey around the site
would use the accurately measured ocean, atmosphere, and
in some cases groundwater effects, to correct the survey
measurements and determine over how large a region the
additional effect appeared. The two other types of meters are
used primarily as survey meters and each has its special ad-
vantages.
A. LaCoste–Romberg and other spring types
The LaCoste–Romberg gravimeter is the most widely
used of the spring type gravimeters described briefly in
Refs. 29 and 87 and therefore the most widely used of any
gravimeter. It is used for airborn, shipboard, and borehole
surveys as well as the more common ground based surveys.
Its virtues are that it is small, light weight, and can be setup
for measurements in a few minutes. Some of these instru-
ments have been modified to include a capacitive detection
system analogous to that of the SG along with feedback for
use as a tidal gravimeter. As a ground based survey instru-
ment it can provide accuracy and resolution of a few gal
over short distances and short time periods. For high preci-
sion work two or more of them are used simultaneously 88
and the survey is done in a closed loop to check for closureupon return to the starting point.
Their defects relative to the SG are that they drift ran-
domly, the calibration varies in time and with position of the
nulling screw, and when operated out of feedback they are
nonlinear.89 They are also susceptible to tares from shock
and are temperature sensitive. These all limit the accuracy of
measurements made over long time intervals, large distances,
or at different elevations. However, for rapid local surveys
over short distances they are an excellent complement to the
SG.
B. The absolute gravimeterThe absolute gravimeter90 AG measures the accelera-
tion of an object falling in vacuum. It uses laser interferom-
etry to measure the position of a falling mirror. The accuracy
and precision of the instrument has improved over time with
improvements in laser stability and the development of ac-
tive vibration isolation.91 It has been used primarily for re-
peat gravity measurements over widely separated locations
but can also be used to make continuous measurements. Its
major virtue is that its measurements are absolute, to within
an accuracy which in some cases approaches 1 gal92–94 see
Fig. 14. However, some measurements strayed from con-
tinuous records with the SG by as much as 8 gal.94 A
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measurement of g at a particular location on the earth can be
compared with later measurements at that location no matter
how far into the future. When used as a survey meter, its
accuracy is not degraded by the time, distance, or elevation
change between measurements.
In order to realize these advantages over the LaCoste–
Romberg survey meter, more time is required to setup the
instrument and to make measurements. Its disadvantages for
long term continuous measurements relative to the SG are
that it does not provide sub-gal noise level and that it has
many moving parts so that it would not operate for manyyears without interruption. Typically the mirror is dropped
about every 10 s so that the data is sampled at this interval
but without the possibility of antialiasing prefiltering of the
data.
As in the case of the LaCoste–Romberg meter it can be
used as an excellent complement to the SG. Repeat measure-
ments at the site of a SG can provide a cross check on mea-
sured secular changes to determine whether they are real or
instrumental and can eliminate ambiguities from offsets in-
duced by earthquakes or other large mechanical disturbances
see Fig. 14. It has also been used to calibrate the SG28,95,96
by simultaneous measurements with both instruments at the
same location for about 2 weeks. The full time dependence
of gravity Fig. 11a measured by the SG is then fit to the
variation measured by the AG and the single parameter of
the fit is the calibration constant.
C. The superconducting gravimeter
The virtues of the SG relative to the other two types are:
Its noise level is lower over a very wide range of frequencies.
Long term drift when it occurs is a well determined function
of time so that it can in most cases be unambiguously re-
moved from the data. The calibration constant is fixed by the
geometry of the coils and suspended mass so that it remains
the same if the instrument is turned off and on again no
matter how long the time between. It is simple mechanically
with only one moving part, which is magnetically levitated
so that very long term, uninterrupted operation is possible.
The most important property of the SG is its low fre-
quency performance so that it would be useful to be able to
specify its noise power as a function of frequency and com-
pare it to natural or cultural noise. The impediments to doing
so are that this noise cannot be measured by any other in-strument in this frequency range and that some SG have drift
and tares that were mentioned above. Although these effects
cause uncertainties of at most a few parts in 10 9 they are
entirely absent in some of the records so that it is clear that
essentially drift and tare free SG have been and can be pro-
duced. It has been difficult to find instrument modifications
to completely eliminate them from all SG because of the
large amount of resources and time required to explore all of
the possible parameters. Progress has been made by testing
for the most likely causes8 which include; the cool down and
magnetic field history of the initialization procedure, the sta-
bility of the magnetic field produced by the supercurrents,
the temperature control, the capacitance bridge, tilt control,
gas adsorption and desorption from the levitated sphere, and
the method of manufacturing the sphere.
Regardless of what the causes may be there is a large
amount of field data from more than 20 instruments operated
during the past 20 years which defines the limits of perfor-
mance. It demonstrates that with both drift free and drift
corrected records, atmospheric and ground water gravity sig-
nals can be identified and subtracted from the data. When
tares and drift are also removed the residual peak variations
are about 2 gal over periods of years.97,58,59,50 In some
cases, long term drift cannot be unambiguosly identified as
either true gravity changes or instrumental drift. The use ofmultiple instruments, the new dual sphere instrument from
GWR, or the combined use with the AG is currently allow-
ing resolution of the ambiguity.94 Some examples of field
data illustrate these statements.
For 10 commercial instruments that have reported long
term behavior, three set upper limits on the instrumental drift
of 2 gal year,98–100 two showed exponential drifts which
decreased to less than 1 gal/year after less than 1
year,101,102 two measured drifts of about 5 gal/year for
which real changes in gravity were not eliminated,103,104 one
showed a linear drift of 3 gal/year which also was not con-
firmed as instrument drift,105 two gravimeters at Boulder
Colorado showed the same drift of 8 gal/year59 but dis-agreed with the absolute measurements over that time.94 A
two year record at Boulder Colorado94,106 revealed 4 tares
triggered by power outages and a helium transfer.
Analysis of one year of data from an instrument of the
current generation of GWR gravimeters (C 021) at Mem-
bach, Belgium, revealed106 13 tares, all but one triggered by
electrical disturbances. This small number of offsets is accu-
rately removed from the data so that the long term variation
of gravity at the site could be measured by both the SG and
an AG. The two measurements agreed within 1 gal while
both showed an apparently real increase in gravity of about 8
gal during the period of measurement. The full 3 1/2 years
FIG. 14. Data from Membach, Belgium compared with measurements by
AG model FG5. A tidal model, atmospheric gravity, polar motion, and a
linear drift of 4.8 gal per year have been subtracted from the SG data.
The AG data from May to December 1997 have been corrected for an offset
of 4 gal due to a problem in the timing electronics which was corrected.
There was a gap of one month in the SG data during 1996 so that long term
comparison of the instruments is valid only within the two continuous data
segments. Data provided by Olivier Francis of the European Center forGeodynamics and Seismology.
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of data from this instrument along with AG measurements is
shown in Fig. 14. Maximum deviation of the AG from the
SG record is about 1 gal except for one point and isconsistent with the error bars on the AG data. A 30 day
simultaneous record of the Membach SG and another GWR
instrument before shipment showed maximum deviations of
0.3 gal over 30 days under relatively unstable operating
conditions.8 This level of stability was reached within short
periods after cool down and setup ranging from one day to
two weeks.
Three of the original seven UCSD instruments were up-
dated in the early 90’s. One showed no measurable drift for
two years of operation.25 A second measured large changes
that appeared to result from ground water effects.78 The third
was operated at San Diego, California, Richmond, Florida,
and Fairbanks, Alaska. At Richmond, the operation was in-terrupted twice by refrigeration failures. Upon restarting the
instrument an exponential approach to equilibrium was
found each time but with different time constants.97 This
record was the first to be compared to an AG and the total
change in gravity after correcting for the exponentials and
offsets agreed with the AG within the 3 gal error of the
absolute measurements at that time. Upon termination of the
work at Richmond, SGB was moved to Fairbanks without
warming above 4 K. No drift was measurable for the first
100 days until the data was interrupted and the instrument
needed to be restarted. After the interruption there was again
an exponential drift.
A better indication of the instrument capabilities is ob-tained when two or more instruments are run simultaneously
at the same place.94,96,97 In that case any differences between
the records are necessarily due to the instrument or its
mounting. The noise on the difference is indeed much
smaller than on either instrument alone, proving that the
noise on the individual SG records is dominated by real
gravity changes. With two or more instruments, instrumental
tares not simultaneous on both instruments as small as 0.1–
0.2 gal are clearly identified in individual instrument
records and can be removed from both records. A detailed
example of the difference signal between two instruments is
shown in Fig. 15. The data is for the month of September
1990 with a UCSD instrument, SGB, and GWR instrument,
T 001, in Richmond, Florida. The two instruments were in
the same building on separate piers located about 5 m from
each other. The data have been filtered and decimated to
samples at 1 h intervals. T 001 displayed a large exponential
drift97 It was later rebuilt. and the SGB record was on the
tail of an exponential, drifting at about 2 gal/month at this
time. The curve in Fig. 15 was obtained by first fitting the
T 001 raw data to the SGB data to find the ratio of theircalibration factors from the tide signal, and then subtracting
the T 001 signal times the ratio from SGB. The resulting
difference data then consisted of the relative drift of the two
instruments, one tare of about 5 gal and four tares less than
0.2 gal plus the noise of undetermined origin. The tares
were removed by fitting straight lines to small segments of
data on either side of the tare and subtracting the difference
between their intercepts from all data after the tare. A single
exponential was then fit to the patched difference data and
subtracted from it. The result shows that peak differences
between the two instruments are mostly less than 0.2 gal
except for one excursion to about 0.4 gal which occurs at
the time of a heavy rainfall also shown in Fig. 15. It is not
correlated with atmospheric pressure or temperature or with
temperature in the building. This implies that the pier of one
of the instruments moved relative to the other as a result of
the rainfall. Indeed, during rainstorms a puddle formed at the
corner of the building closest to SGB. The soil at Richmond
was found to be highly porous.78,79 The standard deviation
from the average for the month is 0.09 gal and the statisti-
cal uncertainty in the average for the 30 days is 0.003 gal
These data demonstrate the ultimate limits of performance of
the SG but also provide warning that at the level of 0.5
gal, very local effects can change gravity. This emphasizes
the point that continuous records of gravity and environmen-tal variables are necessary for identifying the source of such
changes.
The noise on most individual residuals after performing
the best possible subtraction of atmospheric and ground wa-
ter gravity is 2 gal, an order of magnitude larger than the
differences between colocated instruments. Some of this 2
gal residual is almost certainly due to inadequate removal
of atmospheric and ocean gravity signals. Better prediction
of the atmospheric effects will result from and contribute to
better understanding of the atmosphere. However, other geo-
physical noise sources are also likely to be involved.
In the new dual sphere instrument produced by GWR
Fig. 2 the two gravity sensors are rigidly connected in thecryogenic environment so that there can be no influence of
the support structure of the instrument. This instrument pro-
vided data that identified a temperature dependence of the
GWR electronics and transformer for the capacitance bridge.
The UCSD instruments place the transformer in the cryostat
and the electronics are placed in an rfi shielded, temperature
regulated enclosure. One tare on the difference signal was
observed during testing and the data showed that tares of one
sensor relative to the other as small as 0.05 gal can be
identified and removed.3
The primary disadvantage of the SG is that, in its present
form, it cannot be subjected to large accelerations without
FIG. 15. The difference between gravity signals from two SG at Richmond,
Florida solid line and rainfall dotted line for the month of September
1990. The largest discrepancy occurred at the time of a heavy rainfall. This
implies that the rain moved the pier under one of the gravimeters differently
than the other.
4148 Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 John M. Goodkind
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inducing tares in the record or exciting the orbital mode. For
this reason it is not currently useful as a survey instrument.
Another disadvantage is that it is a relative instrument so that
if it is turned off and on again, there is no way to determine
whether gravity has changed while it was off. This disadvan-
tage could be eliminated by using more than one instrument
at a given location so that one or the other is always running,
or by bridging gaps between SG records with absolute mea-
surements.The use of both AG and the SG together will improve
the measurements made by both. The long, high resolution
records of the SG will provide an accurate determination of
the gravity admittance of ocean, atmosphere, and ground wa-
ter at a given site. The ocean effect will be largely indepen-
dent of time so that a determination of total gravity tide
variations at a given site should be valid indefinitely. The
admittance of the atmosphere, as measured by a single pres-
sure station, varies by as much as 30% over time and the data
in Fig. 11 show that this can lead to errors of 2 gal or
greater. However, if a network of pressure measurements is
available a correction to greater precision is possible.107 Cor-
rections for ground water can be 10’s of gal Fig. 13.
Since the water is in the soil and in various aquifers beneath
the surface it would not be possible to correct absolute mea-
surements for it without continuous records that determine
the time dependence of gravity after rainfall or the relation
between water table level, soil moisture, and gravity. Thus if
the absolute measurements are to be useful at the 1 gal
level that they are capable of, continuous records of gravity
and environmental variables must first be made at the sites in
order to develop the algorithms for relating environmental
variables to gravity. Conversely, if SG records are to be use-
ful for decades or centuries, the AG will be necessary to tie
records together that may be separated by many years.
VI. POTENTIAL FUTURE USES
There is a wide range of geophysical and fundamental
gravity topics which might be approached with high resolu-
tion, continuous gravity records such as those provided by
the SG. Work on some of them has begun but will not be
completed until more data is obtained from more instru-
ments. Major new opportunities will result from improve-
ments of the instrument to allow surveys to be made to the
same sub-gal accuracy as are time dependencies at a fixed
location.
A. Potential advances in instrumentation
A major advance toward sub-gal survey capability
would result from elimination of the orbital mode. Doing so
would allow rapid recovery from the mechanical disturbance
of moving the instrument and rapid adjustment of the tilt and
the sphere position. This can be accomplished either by ap-
plying mechanical constraints to hold the sphere on the in-
strument axis or by winding additional coils to apply mag-
netic fields in the horizontal plane. In order to eliminate all
barriers to use as a survey meter, the instrument would also
need to be free of tares that result from mechanical shocks.
There is no doubt that this is possible since one of the com-
mercial instruments has satisfied the requirement. It remains
to be determined what particular properties of that instru-
ment were responsible. Alternatively, a removable clamp for
the sphere could be developed which would immobilize the
sphere when the instrument was to be moved.
Simplification of setup of the instrument would be desir-
able both for possible survey work and for measurements of
a few months duration at a large number of sites to determine
tidal parameters. This can be accomplished by automatingthe tilt adjust procedure through computer control and by
connecting the two support coils in series with correct turns
ratio so that no adjustment of the force gradient is required.
An important advance for long term operation at remote sites
will arise from the development of closed cycle refrigerators
which operate at 4.2 K and use less than the current 2–4 kW
of power.
Long term drift and tares degrade the performance of the
instruments even though, in most circumstances they can be
clearly identified and removed from the data. The source of
these problems and the means to solve them clearly exists
since instruments have been made which show no measur-
able drift and very small numbers of tares. However, even
without solving the problem, the use of two instruments at a
site or of the dual sensor instrument will identify nearly all
instrumental tares.
Some of the recently discovered high T C superconduct-
ors have critical temperatures above 77 K liquid nitrogen.
In principle, the complexity of the refrigeration requirements
for the device, and therefore the cost, complexity, and power
requirements for field operation, could be reduced by oper-
ating at this temperature. In practice thermal excitation of
flux jumps will be greater at the higher temperature so that
the noise level and long term stability of such a gravimeter
cannot be predicted. Flux pinning might be sufficientlystrong in some of the materials to overcome this problem.
However, the advantages over operation at liquid helium
temperature and the likelihood of success are, thus far, too
small to motivate the required development effort.
B. Potential new research
It is not possible to anticipate new discoveries that might
result from measurements at a new level of precision such as
that of the SG. However, a few which are suggested by pre-
vious work are suggested here without describing detailed
proposals.
One of the original objectives in developing thegravimeter was to be able to measure vertical motion of the
crust. Elevation changes of order 1 cm can now be measured
by GPS data. If there were no associated displacement of
mass beneath the surface this would result in a change of 3
gal which is now measurable over any period of time if all
of the techniques described above are used to remove other
effects. Departures from this ratio-of-elevation change to
gravity change will determine whether mass was also added
or removed beneath the surface and how much. One example
is the measurement of sea level changes over periods of
years. A direct measurement of water depth does not neces-
sarily measure a change in sea level since it could also be
4149Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 Superconducting gravimeter
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due to a vertical displacement of the land. A gravimeter on a
platform attached to bedrock beneath the water will measure
a gravity change due to sea level change plus that due to
vertical displacement of the land. The depth of water can be
measured directly so that its contribution to the change in
gravity can be calculated accurately from its measured den-
sity. If this computed change agrees with the measurement,
the change of water depth is a real change in sea level andnot due to vertical crustal motion. Although GPS measure-
ments can, in principle measure the vertical crustal motion
directly, it does not yet provide the precision that can be
achieved with the SG. Another approach to sea level change
will use the global array of SG in the GGP to detect a world
wide change in gravity due to sea level change.108
Earthquakes occur when sufficient strain accumulates in
the crust to cause blocks on either side of a fault to slip.
Some of the strain will always lead to compression and
therefore to shifts of local gravity. This could arise from
uplift or subsidence near the fault line or from changes in
porosity and pore pressure in the rock. Hints of measurable
effects associated with earthquakes have been observed in
the records obtained with UCSD gravimeters at two sites
with very different types of seismicity77,109 Fig. 16. These
were in contradiction with the gravity changes that might be
expected from straightforward models of earthquakes.110
Confirmation of them at additional sites would provide a
powerful new tool for studying earthquake mechanisms.
The influence of groundwater on gravity has, thus far,
been mainly a nuisance that obscures the measurement of
other phenomena. However, the potential for application to
specific hydrological problems remains to be exploited. For
example, continuous gravity measurements coupled with
gravity survey measurements could measure the total mass
change in a deep aquifer drawn down for cultural use, the
rate at which it is replenished, and the rate of its response to
climate changes.
The ratio of local barometric pressure change to the cor-
related gravity change varies by as much as 50% at a given
location. The time dependence of this ratio has not been
adequately explored. The ratio measures primarily the size of
the weather system associated with the pressure change.
However, it also depends on the vertical distribution of the
mass displacement. Since gravity measures a three dimen-
sional 3D integral of the mass distribution it provides a
different measurement than other tools of atmospheric phys-
ics.
In fundamental physics, the gravitational field is the least
understood of any of the fundamental forces. Questions
which may be approachable using high resolution gravity
measurements in the laboratory include measurements of the
gravitational constant, G, such as further tests for a distance
dependence, a time dependence, a spatial anisotropy, and
improved measurement of its absolute value. Others might
be, improved tests for a universal preferred reference frame,
direct detection of gravity waves, and improved tests of the
equivalence principle.
VII. DISCUSSION
The long term stability of the SG has provided previ-
ously unobtainable data about time variations of gravity at
the surface of the earth. These data have provided new infor-
mation about phenomena as diverse as the global ocean tides
and variations of ground water. In order to reach the new
levels of precision continuous records are compared to si-
multaneous records of environmental variables and models
of the earth tides. Much of what has been learned is limited
by narrow geographical distribution of the instruments and
by natural and man made accelerations of the surface of theearth rather than by instrument capabilities. In the past few
years a sufficient array of the instruments around the globe
has been created to allow improvements of previous mea-
surements and to search for new phenomena. Some improve-
ments of the instrument are still possible to remove the small
influence of tares and drift and to make it portable, but these
defects have not limited the information obtained thus far.
Thorough exploitation of gravity measurements will require
deployment of gravimeters in numbers similar to current de-
ployment of seismometers. Ideally they would have the long
term stability of the SG, the absolute capability of the AG,
and be portable like the Lacoste–Romberg. In order to de-
FIG. 16. Gravity changes at Fairbanks Alaska corresponding to earthquakes
within 500 km. a The dashed line is at the time of an earthquake of
magnitude 4.6, at a depth of 10 km, and distance 63 km. Gravity decreased
sharply before the earthquake and the quake occurred at about the time
gravity reached a maximum. b A month during which there was a large
amount of seismic activity and large fluctuations in gravity. The solid
squares represent the cumulative sum of the magnitudes of all earthquakes
in central Alaska during the month. The two largest events in the region
were on May 16, magnitude 4.0, depth 106 km, distance 126 km, and on
May 17, magnitude 4.7, depth 130 km, distance 450 km. In this case gravity
also decreased prior to the events and they occurred when gravity reached a
peak value.
4150 Rev. Sci. Instrum., Vol. 70, No. 11, November 1999 John M. Goodkind
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ploy them in large numbers they must also cost about the
same as seismometers. Given sufficient demand the SG
could be developed into such an instrument. It is very likely
that some technology, possibly the SG, will achieve these
goals in the future so that the new possibilities demonstrated
by the current SG will be realized. In the meantime, the
present instruments are creating an archive of precise data
that will serve as reference points for phenomena that will
evolve over decades or centuries in a manner analogous toancient astronomical observations.
ACKNOWLEDGMENTS
The author would like to thank Richard Warburton for
reading and commenting on the text, for pointing out addi-
tional references and for providing photographs and draw-
ings from GWR Instruments. I also wish to thank Olivier
Francis of the European Center for Geodynamics and Seis-
mology for providing the data from Membach.
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