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

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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




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




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.





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.





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.





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-





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.





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.





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





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-





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.





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





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.





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.





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





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.





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.





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





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.





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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