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IOP Concise Physics

Gravity, Magnetic and Electromagnetic GradiometryStrategic technologies in the 21st century

Alexey V Veryaskin

Chapter 1

Gravity gradiometry

It is as simple as Hamlet’s flute, if you know how to play it. Just as the musiciancan coax entrancing melodies from his instrument, so the physicist, with equaldelight, can measure the finest variations in gravity. In this way we can examinethe Earth’s crust at depths that the eye cannot penetrate and the drilling rigcannot reach.

Lorand von Eötvös (1890)

1.1 IntroductionIn 1997, Robin Bell and co-authors, senior scientists at Columbia University’sLamont–Doherty Earth Observatory, published an article called ‘Gravity gradiom-etry resurfaces’ (Bell et al 1997). In the first paragraph they quoted an extract fromTom Clancy’s The Hunt for Red October, a fictional strategic nuclear-missilesubmarine story. This particular extract describes a ‘highly sensitive device calleda gradiometer’ that was able to pinpoint the submarine’s location to within 100 maccuracy.

Tom Clancy was quite right to use such a description in his famous novel. In the21st century, a sufficiently sensitive moving-base gravity gradiometer is the onlycandidate for so-called passive navigation, which is a highly desirable tool fornuclear submarines to be ‘up and running’ when all other means to navigatethemselves have been blanked out.

There have been a number of good publications about gravity gradiometry fornon-professionals. The second one by Robin Bell is ‘Gravity gradiometry’—aformerly classified technique used to navigate ballistic-missile submarines now helpsgeologists search for resources hidden underground (Bell 1998). Neil Fraser’s ‘Seeingwith gravity’—whether you’re Indiana Jones hunting for ancient tombs or asubmariner lost on the ocean floor, the Earth’s own A to Z could soon provide

doi:10.1088/978-1-6817-4700-2ch1 1-1 ª Morgan & Claypool Publishers 2018

https://doi.org/10.1088/978-1-6817-4700-2ch1

some three-dimensional help gave a good introduction to gravity gradiometry andpromoted the rise of so-called string gravity gradiometers (Fraser 1996).

Among the earliest professional reviews is Christopher Jekeli’s ‘A review ofgravity gradiometer survey system data analyses’ (Jekeli 1993), and among the latestis one from Lockheed Martin’s legendary team of gradiometrists, ‘Gravity gradi-ometer systems—advances and challenges’ (DiFrancesco et al 2008, 2009).

The Lockheed Martin Corporation (formerly Bell Aerospace) has pioneeredpractical gravity gradiometry from about 50 years ago. This has resulted in the so-called Falcon™-generation of gravity gradiometers that is still seen as the leadinggravity gradiometer technology in the world (Dransfield and Christensen 2013). Theso-called full-tensor gravity gradiometer (FTG), capable of measuring all gravitygradient components, has been under development at Lockheed Martin, resulting inthe FTG™-generation of gravity gradiometers. It was adopted to a commerciallydeployable version by Bell Geospace, Inc., and is currently available for end-users(Murphy 2010).

Being a defence subcontractor for the United States Government, the LockheedMartin Corporation mainly focused on the defence applications of gravitygradiometry.

However, there has been enormous interest in using such advanced technology forstrategic commercial applications. Figure 1.1 shows a graphical representation ofvarious applications of gravity gradiometry.

Early in the last century, oil was seen as the blood of human civilization, withoutwhich it would collapse and return to a stone age. The use of gravity gradiometers inoil exploration began in Europe as early as 1915, after the invention of so-calledtorsion balance (Gillies and Ritter 1993). After World War I, the first gravitygradiometers were imported to the United States. They were credited for the majoroil discoveries later in Texas.

However, these first gravity gradiometers were cumbersome, slow in operationand soon were completely abandoned to the favour of compact and fast-operatinggravimeters. The problem was that the torsion balance based gravity gradiometers

Figure 1.1. Gravity gradiometry applications compared on the sensitivity scale that is required to be reachedfor a particular application. Those on the far left are 1000× more sensitive than those on the far right. Adaptedfrom Evstifeev (2017) and reproduced with permission from Pleiades Publishing Ltd.

Gravity, Magnetic and Electromagnetic Gradiometry

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were capable of operating on land only. The stationary measurements, based on asit-down-and-measure approach, took hours to record data from a single station.That required an enormous amount of time to be spent on surveying the vast areashaving a potential for oilfield discoveries. The situation radically changed when thefirst moving-base gravity gradiometer arrived at some non-military market nichesafter being declassified by the USA Navy in 1994. Since then, the FTG and theFalcon generations of gravity gradiometers have been successfully used for oil, gasand mineral exploration (Dransfield 2007).

There is a standalone application of gravity gradiometry that is still waiting for itspractical realisation. Borehole gravity gradiometry requires a compact gravitygradiometer that is capable of operating in drilled wells at depth under extremelylimited mounting conditions. Currently, there are no commercially available gravitygradiometers that could fit in the downhole environment1.

However, work is in progress in the quest for a gravity gradiometer that cansatisfy such ‘exotic’ requirements and be sufficiently sensitive at the same time.Interestingly enough, the borehole gravity gradiometry, as a potential market niche,may look stronger than the airborne and surface-based markets that have beenestablished since 1994.

Finally, spaceborne gravity gradiometers have been under development fordecades. The recent success of the GOCE space mission (van der Meijde et al2015) has stimulated new ideas and new approaches to gravity gradiometry aidedexploration on the Moon (Carroll 2011), Mars (Cuperus et al 2009) and otherplanets. It is believed that compact and ultra-sensitive gravity gradiometers,specifically designed for various space missions, will soon be available for nationalspace agencies and private space enterprises.

1.2 History and recent developmentsThe father of practical gravity gradiometry was Baron Lorand von Eötvös, aHungarian nobleman and a talented physicist and engineer (figure 1.2(a)). Thephysics unit the ‘eotvos’ or Eo (1 eotvos = 10−9 s−2) is now standard for character-ising how sensitive different gravity gradiometers are. This quantity is equivalent toabout 1/1 000 000 of the angular acceleration experienced by a typical wristwatch’ssecond hand in a 1 s time interval.

What was invented by Lorand von Eötvös in 1890 was his famous ‘torsionbalance’. Eötvös himself considered his invention to be as an adaptation of theCoulomb balance (Coulomb 1784). The torsion balance consisted of two proofmasses hung at different heights from a horizontal beam suspended by a finefilament. If the force of gravity, acting on the proof masses, is not the same (whichmeans there is a gravity gradient around), this results in a torque being exerted onthe beam. This, in turn, gives rise to angular deflection of the beam. The deflection

1 Scintrex Ltd, a Canadian technology company, has developed the ‘Gravilog’—the first borehole gravimeterthat uses the same principle as that used in the famous LaCoste and Romberg gravimeters (Seigel et al 2007).By discriminating a gravimeter’s readings, it is possible, in principle, to derive a corresponding gravity gradientcomponent. However, the sensitivity of such a gradiometer will be limited to hundreds of eotvos at best.


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was read by a separate scale and telescope for mirror reading (see figure 1.2(b)below).

A sensitivity of about 1 eotvos can be reached with a torsion balance-type gravitygradiometer. However, the measurement requires several hours at a single stationand then a recalculation of gravity gradient components from at least fiveindependent measurements of the angular deflection at different azimuth angles.A recent review, ‘The history of the 125 year-old Eötvös torsion balance’ in Szabo(2016), and a comprehensive mathematical background for understanding thegradiometer’s operational principles (Jekeli 2011) are highly recommended for thoseinterested in such details. Since the 1960s there have been a number of different ideasabout how to make a gravity gradiometer that can operate much faster than theEötvös torsion balance. Some of these ideas have led to concrete developments.

The very first one was to mount a torsion balance-like device upon a fast-rotatingplatform. Not the original one, but a combination of two orthogonal horizontaldumbbells. In the 1970s, Robert Forward of the Hughes Aircraft ResearchLaboratory invented the first prototype gravity gradiometer for moving-baseapplications. It was called the rotating gravity gradiometer (RGG) and measuredthe differential torque caused by gravity gradients, as sensed by two centrallypivoted arms in a flexible cruciform structure with proof masses on each end (seefigure 1.3). One may call it a resonant rotating gravity gradiometer (RRGG). Thepivoted structure had a mechanical resonant frequency of about 35 Hz. The wholeassembly rotated at half the mechanical resonance frequency. This resulted in the

Figure 1.2. (a) Baron Lorand von Eötvös. Portrait by Gyula Éder (1941) after the photograph by AladarSzekely taken in 1913 (reprinted with permission from the Geological and Geophysics Institute of Hungaryand the Lorand Eötvös Museum). (b) A torsion balance schematic (reproduced from Fischbach and Talmadge1992).


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resonant excitation of the dumbbells and increased sensitivity of the gradiometer byQ times (Q is the quality factor in all oscillatory systems (Pain 2005)).

This type of gravity gradiometer can also be called the resonant modulatinggravity gradiometer (RMGG), since its output signals are recorded as a result oftheir being demodulated at the carrier frequency. The latter one, in the case of anRMGG, is the doubled revolution rate of the rotating platform. This developmentwas intended for spaceborne and airborne missions, with a performance goal ofachieving 0.3 Eo/√Hz noise spectral density at the carrier frequency.

The RMGG had demonstrated a gravity gradient noise floor of about 3 Eo/√Hzin the laboratory environment and was never taken out for moving-base testing. Thedevelopment of this instrument was halted in the early 1980s, when the USADepartment of Defense chose the Lockheed Martin (Bell Aerospace) gravitygradiometer for long-term development. Some time ago, a revamped version ofthe RRGG was under development at Carson Geoscience, Inc. (Gleason and Shaw1999). The present status of this development is unknown.

The most important effect inherent to rotating gravity gradiometers is the factthat whilst many of the error and noise sources are modulated at the rotationfrequency or are not modulated (1/f noise is an example), the useful signal ismodulated–demodulated at double the rotation frequency. This is a result of thetensorial geometric properties of gravity gradient components, which represent asecond rank tensor (Jekeli 2011).

Robert Forward deserves a few additional words. He is the legendary scientistwho was among the first to publish the equations describing gravitoelectromagnet-ism (Forward 1961) and pioneered experimental antigravity research (Forward1963). He also pioneered the idea of applying electronic cooling effects to gravitygradiometry research in order to improve the signal-to-noise ratio in RMGGs(Forward 1979).

Interestingly enough, there was also a forgotten attempt to design a rotatinggravity gradiometer consisting of just a single proof mass. In 1968, the Chobotov ofAerospace Corporation (USA) published the article, ‘Radially vibrating, rotating

Figure 1.3. The RMGG developed at the Hughes Aircraft Research Laboratory. (a) Basic principle: twoorthogonal dumbbells are set to rotate uniformly around a mutual pivot representing a torsional spring.(b) A real RMGG prototype.


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gravitational gradient sensor’ (Chobotov 1968). This considered a linear mechanicaloscillator mounted on a rotating platform with just the radial degree of freedom. Ifthe platform was set to a uniform rotation, the oscillator experienced a parametricexcitation with a modulation index proportional to a gravity gradient in the plane ofrotation. The intention was to deploy the sensor from a low-orbit satellite and use itas an accurate attitude control sensor, an orbital altimeter, or a navigation aid in avariety of satellite applications.

Another rotating instrument was developed in the 1970s and early 1980s byMilton Trageser of Draper Research Laboratory (USA), the floated gravitygradiometer (FGG). The sensor used the ‘floated gyro’ technology developed atthe Massachusets Institute of Technology (MIT) (Trageser 1984). It was suspendednear neutral buoyancy in a low-viscosity fluid. Like the RGG, the FGG sensedgravity gradient-induced differential torques on its dumbbell-like proof masses (seefigure 1.4). Isolating vibrations through a buoyant, viscous and magnetic (orelectrostatic) suspension of the proof masses achieved the gravity gradient measure-ment. To cancel any platform acceleration effects, more than one matched sensorwas needed. The orientation of the floated proof masses was maintained by torquefeedback loops fed by external gyroscopes, which were integrated into the system. Itshould be noted that neutral buoyancy supports the float perfectly, no matter what

Figure 1.4. Floated gravity gradiometer system (reprinted from US patent US3731537, assigneeMassachusetts Institute of Technology).


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linear acceleration is experienced by the whole assembly. The acceleration propor-tionally affects both float weight and hydrostatic pressure gradients.

The floated gradiometer performance was shown to be much superior to that ofthe other demonstrated devices in the following ways:

• quick time response;• low level of self-noise;• relative insensitivity to angular vibration, 0.006 × 109 eotvos (rad s−1)−2;• low level of fluid unbalance;• reasonably low sensitivity to linear vibration, temperature and magneticfields.

The FGG was also intended for satellite and aircraft applications. Its perform-ance goal of l Eo/√Hz was actually demonstrated in the laboratory environment. Nomoving-base field demonstration was ever conducted, however. As for the RGG,FGG development was halted in the 1980s.

The third rotating gradiometer, designed in the 1980s by Ernest Metzger of BellAerospace, yields the full-tensor of gravity gradients (FTGs). Its basic designconsists of electronically matched pairs of accelerometers. The signal outputs aredifferenced to produce a gravity gradient. The United States Navy selected the Bellgradiometer as the gravity compensation aid for its Trident submarine inertialnavigation systems. The system’s performance was not sufficient for a completelypassive navigation solution at that time. However, later in the 1990s, a passivenavigation demonstration was successfully conducted in a submarine installation.The FTG system was declassified in the late 1990s and allowed to be used forproposed regional airborne gravity surveying systems (Bell 1998).

The full gravity gradient tensor is sensed by an umbrella configuration of threerotating discs (see figure 1.6). Each disc, called a gravity gradient instrument (GGI),is mounted on a gyro-stabilized platform. On each disc, two opposing Bell modelVII-G accelerometers are separated by a 15 cm baseline (L). Hence, the detection ofa gradient of a few eotvos requires accelerometers to be accurate to 10−10 m s−2. Themodel VII’s null bias error, caused by material’s creep and temperature variation, isonly 10−5 to 10−6 m s−2. However, the null bias error at the frequency of the discrotation (Ω) is considerably lower, in fact, near the requirement stated above. This isachieved as follows (Gleason and Shaw 1999).

As shown in figure 1.5, pairs of accelerometers are mounted in diametricopposition such that their sensitivity axes are in the plane of the disc, perpendicularto the spin axis (which goes through the disc’s centre). The sum of the twoaccelerometers’ signals yields the gravity gradient at the centre, eliminating thecommon linear platform acceleration. The difference of two such sums from twoorthogonally oriented accelerometer pairs further cancels the rotational accelerationabout the spin axis (thus there are four accelerometers on each disc).

The entire gravity gradient tensor is obtained from a set of three such discs (orGGIs) mounted in an umbrella configuration. The three GGls are mounted inmutual orthogonality on the inner element of the gyro-stabilized inertial platform.Each GGl has the same orientation with respect to the vertical.


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This requires less space than mounting the GGls in an orthogonal triad. EachGGI makes an angle of arccot(√2) = 35.264° with the horizon, as depicted in figure1.6. In addition to reducing the platform size, the umbrella mount enhancesinstrument calibration because each GGI senses similar amplitudes of the gravityfield. Interchanging or replacing GGIs within the triad is also made easier.

Figure 1.5. GGI rotating platforms with pared accelerometers are shown in horizontal and vertical spin axes.

Figure 1.6. (a) A full-tensor gravity gradiometer, consisting of three GGIs, was designed for airborne and shipoperations. (b) The GGIs are mounted in an orthogonal triad configuration at an angle of approximately 35°to each other’s spin axis. Reproduced from Murphy (2004) with permission from Geoscience Australia.


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Disc rotation at a frequency Ω modulates the gradient signals at 2Ω because eachpair of accelerometers senses a particular gradient twice per revolution. Extraneouslinear accelerations perpendicular to the spin axis, caused mainly by scale factorimbalances between accelerometers within a pair, are modulated at the rotationfrequency Ω because they are only sensed, in effect, by one accelerometer of the pair.Demodulating the output signal at Ω thus generates a detection signal that is ameasure of these imperfections (error sources). This signal is used in a feedback loopto adjust the proof mass in one of the accelerometers in each pair to null the signal.

Other error sources include mismatches between radial distances to the accel-erometers, misalignments, sensitivities to acceleration caused by the non-linearitiesthat every complex system possesses, and individual component vibrations. Theseerror signals are nulled out by the following.

• Superimposed motions, non-harmonic to Ω, namely angular oscillations ordithers about the spin axis and axial shakes along the spin axes, are applied toeach disc.

• Demodulating the outputs at these frequencies yields detection signals thatare used to adjust the proof mass of an appropriate accelerometer to null thesignals.

• A total of nine active servo feedback loops continuously compensate for all ofthe imperfections mentioned above.

In the 1987 US Air Force test flight the discs revolved once every four seconds(Ω/2π = 0.25 Hz). Final signal processing steps attempted to compensate the gravitygradient signals for self-gravity and centrifugal force effects. The signals were thendemodulated at 2Ω with a low-pass filter (LPF) to produce gravity gradientmeasurements at intervals of 1 s. The cutoff frequency of the filter used for thistest flight was 0.06 Hz. The filtering limited the spatial resolution of the finalgradient outputs. This is a key problem for high-speed mobile applications.

The first full-tensor GGI was intended for aircraft, land vehicle and shipapplications. In the laboratory environment, it had performed at a level of about6 Eo/√Hz. During the l987 test flight, it performed at about 30 Eo/√Hz level. TheAir Force system received a partial refurbishment (replaced GGls) in the mid-1990s,but is currently idle. It resides in a full size Winnebago-type land vehicle. If its bulky1980s support electronics were replaced by modern chip-scale components, thesystem could easily fit in the bed of a pickup truck.

In the early 1990s Bell Aerospace had proposed design improvements. Theseincluded doubling the baseline length to 30 cm (to strengthen signal), placing eightaccelerometers on each disc instead of four, and increasing the rotation frequencyand filter cutoff frequency to enhance sampling and spatial resolution for high-velocity aircraft applications. The first two improvements were applied to the armscontrol verification gravity gradiometer (ACVGG) that Bell Aerospace built for theDefense Special Weapons Agency (1947–97) in the 1990s. The ACVGG was astationary, tripod-mounted, single (vertical) spin axis device. It successfully distin-guished between conventional and nuclear warheads when they were placed inidentical casings and rolled past the ACVGG in a railcar approximately 10 feet


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away. The ACVGG was also used by the Air Force in 1997 to successfully detectunderground missile silos at Vandenberg AFB, CA, USA and part of the abandonedsuper-collider tunnel in Texas.

In the late 1990s, BHP Billiton, an Australian mining giant, undertook anexclusive agreement with Lockheed Martin to develop a gravity gradiometerspecifically designed for airborne use. In parallel, Lockheed Martin had developeda simplified version of the early Bell Aerospace and Lockheed Martin FTGtechnology designed for the gravity gradiometer that aided the Trident nuclearballistic missile submarine autonomous navigation system.

This was a single-axis rotating, eight-accelerometer based device, with somecritical improvements compared to the FTG generation of gravity gradiometers (seefigure 1.7 below). After being adopted for commercial airborne deployment, thesystem was successfully delivered to BHP Billiton in late 1999 (van Leeuwen 2000).Trademarked as Falcon, the BHP Billiton AGG system performed the world’s firstcommercial airborne gravity gradient survey in October of that year (Dransfield et al2001). BHP Billiton took delivery of two more Falcon systems in 2000 and 2002.

The Applied Physics Laboratory (APL) at Johns Hopkins University hadproposed a full-tensor gravity gradiometer consisting of 12 of sapphire resonatortransducer accelerometers. The APL gradiometer is illustrated in figure 1.8. It wasdesigned to be enclosed in an 18″ diameter sphere and to be made up of sixaccelerometer pairs placed on a symmetric dodecahedral mount (figure 1.8(a)). Thesix baselines were 30 cm. The total weight was around 40 lb (each suspended proofmass weighs around a kilogram). The most attractive feature of the APL instrumentis the high bandwidth/sampling rate capability of its individual accelerometers(0.1 μg when sampled at 100 Hz). The accelerometers work as follows:

Figure 1.7. (a) The 1990s LockheedMartin single spin axis gravity gradiometer system evolved into the Falcongeneration of gravity gradiometers. (b) The bulky and heavy power station fed the first Falcon gravitygradiometer that was delivered to BHP Billiton in 1999. Reproduced with permission from Lockheed MartinCorporation.


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Figure 1.8. (a) The APL gravity gradiometer configuration, showing six pairs of collinear accelerometersplaced on a dodecahedral mount. (b) The accelerometer’s cross-section, showing the spring and proof massdisplacement phase detector circuit. (c) The accelerometer prototype assembly. (d) A simplified schematicof a single accelerometer. (e) The laboratory set-up of the prototype one-axis gradiometer, sapphire cavityresonator, spring and proof masses. Reproduced with permission from the Johns Hopkins Applied PhysicsLaboratory.


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As shown in figure 1.8(b), a proof mass is attached to a tuning disc. A referencesignal is sent from an external frequency synthesizer to an RF input on theaccelerometer/sapphire resonator (housed in a vacuum chamber). Acceleration inputsinduce proof mass displacements. The displacements modulate, or cause a small changein, the microwave resonance frequency of the accelerometer/resonator (9.6 GHz).

This resonant frequency is then waveguide-coupled to the external referencefrequency. As a result, the amplitude and phase of the reference signal are alsomodulated by the proof mass displacements. The demodulation was performed by adetection package with an output phase noise level of −135 dBc/√Hz (i.e. below themicrowave resonance carrier). The detected phase shift on the RF output referencesignal is then correlated to a measurement of acceleration change. The entire process isrepeated for the next iteration. Individual accelerometer noise floors were reached atsampling frequencies between 100 and 200 Hz (from the microwave resonance carrier).The performance goal of the proposed full-tensor gradiometer was 1 Eo/√Hz, whichhad not previously been realised. In the 1990s, the APL project was halted and nofurther information has been provided in the public domain relating to it.

1.2.1 Quantum gravity gradiometers

The first quantum gravity gradiometer, based on laser-manipulated atom interfer-ometry, was developed at Mark Kasevich’s laboratory, based at Yale University(Snadden et al 1998). The device used a light-pulsed magneto-optical atom trappingtechnique to simultaneously measure the absolute accelerations of two proof masses,each free falling along a ballistic trajectory (figure 1.9). Each proof mass was a laser-cooled ensemble (cloud) of cesium (Cs) atoms. The gravity gradient was thenextracted by dividing the difference of the two acceleration measurements by thebaseline distance between the two ensembles (set between 1 and 10 m).

Figure 1.9. The principle of absolute gravity gradient measurement based on cold atom interferometry.Reproduced with permission from the American Physical Society. Reprinted from Snadden et al 1998 withpermission from the American Physical Society.


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The measurement axis passes through both atom ensembles, virtually eliminatingsensor misalignment errors. Since the absolute accelerations are measured simulta-neously at both positions, many systematic errors are effectively cancelled out.Moreover, the proof masses are individual atoms rather than precisely machinedand suspended macroscopic objects. This reduces the ‘classic’ systematic errorsinherent to traditional gravity gradiometer concepts. Proof mass imbalances due toscale factor and null bias errors, which in turn are caused by material instabilitiesdue to temperature variations, will no longer be applicable. In fact, the physicalproperties of all atomic proof masses will be identical for all such gravitygradiometers made in the future. These properties will be immune to temperatureand magnetic field variations. The gradiometer set-up is immune to kinematic andangular disturbances, if placed on a moving platform, while atoms are in freefall.The gradiometer is only susceptible to the platform’s motion at the drop instancesand laser interrogation instances. Finally, the calibration of such measurements isreferenced to the wavelengths of a pair of frequency-stabilised laser beams, and theyare identical for both atomic proof masses.

Although the Yale prototype device only measured absolute accelerations alongthe vertical axis, it can be extended to a full-tensor capability (Carraz et al 2014).The practical sensitivity limits set upon such quantum gravity gradiometers areroughly a few eotvos at an integration time of 1 s (Sorrentino et al 2014).

In 2013, Lockheed Martin patented the concept of an atom-interferometricstepped-gravity gradient measuring system (Rice et al 2013). Each axis in thethree-axis measuring system is served by a different gravity gradiometer, with eachgradiometer comprising three pairs of atom-interferometric accelerometers. Theaccelerometers in each pair are mounted on opposite sides of the gradiometer’srotation axis from each other. The three accelerometer pairs are step-rotated, insteadof being continuously rotated. This provides enhanced signal-to-noise performance.

The three gradiometers in the overall measuring system are mounted orthogo-nally with respect to one another on a local-level platform, in order to achieve a full-tensor measuring system. The measuring system can be step-rotated as an overallunit around an axis that is perpendicular to a local-level reference. As was claimed inthe patent, the multiple levels of stepped rotation, as enabled by the atominterferometry, yield improved results with lower costs than are achievable withsome prior techniques. There are no publications in the public domain to supportthis claim.

Since 2001, there have been further developments of the gravity gradiometersbased on quantum matter-wave interferometry (Asenbaum et al 2017). However,these developments have mostly shifted towards academic fundamental physicsresearch, rather than practical applications such as mineral exploration and passivenavigation.

Currently there are two known commercial entities that have been established tocreate commercial instruments based on atom interferometry. One is AOSense Inc.(USA), which has been funded mostly by US defence agencies and does not providemuch information about the latest developments in this area. A patent applicationpublished in 2016, for which AOSense is the assignee, discloses a gradiometer


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configuration that is invariant to laser phase noise and sensor rotations (Kasevichet al 2016). Another commercial entity is Muquans (France), which is the assignee ofanother recent patent application disclosing a cold atom gravity gradiometer(Bouyer et al 2014).

The UK’s Defence, Science and Technology Laboratory (DSTL) is developinga quantum technology-based industrial base, which is an academic, industrialand cross-governmental effort with a current value of approximately £350 million(500 million US dollars).

Two development programmes—a gravity imaging programme and a quantumimager—have been initiated along with the DSTL’s academic partners, namely, theUniversity of Birmingham, Imperial College London and the National PhysicalLaboratory. The concept of the imager involves taking an array of gravitygradiometers that use cold atom physics, measuring a gravity gradient across aregion of space and then by inverting the data reconstructing the density profile thathas generated that gravity field (Bongs 2017).

1.2.2 Recent gravity gradiometer developments at Lockheed Martin

In August 2016, the Australian Society of Exploration Geophysicists (ASEG) incollaboration with the Petroleum Exploration Society of Australia (PESA) and the

Figure 1.10. A quantum gravity sensor developed at the UK National Quantum Technology Hub (reprintedwith their permisison).


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Australian Institute of Geoscientists (AIG) organised a gravity/gravity gradiometryworkshop which highlighted the recent advances in airborne gravity and gravitygradiometry since the last airborne gravity forum of the 21st InternationalGeophysical Conference and Exhibition held in in Sydney on 22 August 2010.

The first talk by Thomas Meyer of the Lockheed Martin Corporation, ‘Recentadvances in Lockheed Martin’s gravity gradiometer technology’, was something of asensational one. The Lockheed Martin’s gravity gradiometry team has developedthe next generation of the full-tensor gravity gradiometer (FTG plus), which, asclaimed, possesses specifications it was thought would never become practicallyfeasible.

Lockheed Martin has made several advances with respect to its gravity gradi-ometer technology since 2010 (Meyer 2016). Substantial improvements in terms ofinstrument sensitivity and noise performance have very recently become available toindustry in the form of an enhanced full-tensor gradiometer system called eFTG(figure 1.11(a)). This full-tensor system is a scaled-up version of the standard FTG,with increased sensitivity and lower noise to help resolve smaller and deeper geologicfeatures. The initial performance of the eFTG is 2.5–4 Eo/√Hz, with follow-onimprovements expected over time as the system is fielded.

The rotational motion of the host aircraft is attenuated at its source by mountinggradiometers to the stabilized and pointed element of an aircraft interface platform.This minimizes the motion’s influence on measurements, which is necessary becausethe deviatoric portion of the angular rate feeds through in just the same way as thegravity tensor. Small residual rotations are directly measured and compensated forpost-survey.

The interface platform comprises a series of servo-driven nested gimbals for allpresently fielded gradiometer systems, full-tensor or partial-tensor, including eFTG

Figure 1.11. (a) Enhanced full-tensor gradiometer (eFTG) system during dynamic factory tests. (b) Digitalfull-tensor gradiometer (dFTG) system represents a 41% volume reduction and a 32% weight reduction fromearlier analogue versions. Reprinted from DiFrancesco and Meyer 2017 with permission from LockheedMartin Corporation.


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and the recently designed digital version of FTG (dFTG, see figure 1.11(b)). This isto the analogue FTG systems what digital Falcon is to its early analogue precursor.The roughly 30% and 40% reductions in volume and weight, respectively, offerfuture customers the flexibility to install dFTG in helicopters and other smallaircraft, perhaps alongside additional geophysical equipment. Further, virtually allhardware and firmware is now common among digital Falcon, dFTG, eFTG and anew factory test station. The test station is configurable for the same hardware,firmware and software as for these systems, enabling better field support and theability to recreate particular scenarios in the laboratory and test updates prior tosending these out to fielded systems.

Lockheed Martin began conceptualising a new gradiometer system architecture afew years ago with internal research and development efforts. The initial studiesfocused on qualifying the gradiometer accelerometers for use in non-rotating systemarchitectures. With this requisite confidence in hand, the primary objective thenloosely became to maximize full-tensor measurement performance within theconfines of Falcon and FTG system size, weight and power, thereby enabling theuse of small fixed-wing aircraft and helicopters (see figure 1.12).

Other objectives include a greater proportion of monolithic construction, fewerinterfaces, certain athermal design considerations and acoustic isolation—all towardincreased reliability and availability. The new concept and set of draft performancegoals/system characteristics eventually cohered based upon a spherical air-bearinginterface platform with accelerometers arranged near the periphery of the systemenvelope. The group of accelerometers is non-rotating, thereby alleviating the needfor rotor spin assemblies with associated slip rings, electronics and parasitic bearingdisturbances, and flex capsules associated with nested gimbals.

The performance goals for FTG plus are 0.5 Eo/√Hz over a pass band from0.1 mHz to 5 Hz, representing a 20× improvement over Falcon plus. New physics-based

Figure 1.12. Notional installation layout for the FTG plus system in a B3 helicopter. Reproduced withpermission from the Lockheed Martin Corporation and Geoscience Australia.


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error filtering methods are used for compensation, which leverage detailed modellingand tests of the core sensors. The spherical air bearing passively provides greaterthan 1000× attenuation of rotational disturbances. An arrangement of custom non-contact/non-coupling sensors and actuators is used to level and point the instrumentblock while further isolating it from rotational disturbances and preserving thebearing’s inherent isolation down to DC. A minimal tether for power andcommunications mechanically couples the instrument to the survey vehicle’s rota-tional motion environment.

The geometry and alignment of the gradiometer accelerometers are designed forinternally balanced retrieval of the full gravity tensor, which amounts to all tensorcomponents being measured at a common centre point with equal fidelity. Thearrangement is ideally conditioned so the determination of gradients does notamplify unwanted noise.

Once again, the Lockheed Martin Corporation has proved to be the world leaderin developing a sophisticated technology at the edge of the impossible (DiFrancescoand Meyer 2017).

1.2.3 Superconducting gravity gradiometers

The development of superconducting gravity gradiometers (SGGs) was pioneeredby Ho Jung Paik of the University of Maryland and Frank van Kann of theUniversity of Western Australia (the University of Western Australia) in the 1980s.

Superconducting technologies possess several unique advantages, which, whenexploited properly, offset the complications associated with cryogenic equipment.Perhaps the most annoying complication is the need to use a bulky vessel (Dewar) tohouse the cryogen.

Beyond the obvious reduction in thermal noise, superconductivity leads to nearperfect magnetic shielding, a very high degree of mechanical and electrical stability,the virtual elimination of thermal gradients and unprecedented mechanical displace-ment measurement sensitivity using superconducting quantum interference device(SQUID) amplifiers (Fagaly 2006). Magnetic flux is conserved and quantised inclosed superconducting loops. In the SGGs, a SQUID senses any superconductingcurrent change caused by proof mass displacements. Superconducting (niobium-made) proof masses are positioned in the close vicinity of such superconductingloops, resulting in a mirror image of the primary loops inside the bulk ofsuperconducting material due to the Meissner effect (Tinkham 2004). The gapbetween a real loop and its Meissner counterpart is twofold of the physical distancefrom the loop’s plane to the superconductor’s surface, which is parallel to the latter.

The superconducting current, stored in the loop when the system is stationary,will compensate any magnetic flux change due to the relative motion of thesuperconducting proof mass (the loop’s mirror image) with respect to the loop’splane. The measurement principle for a single superconducting linear accelerometerdeveloped at the University of Maryland is illustrated in figure 1.13.

With NASA funding, highly sensitive SGGs were developed at the University ofMaryland in the 1980s and early 1990s. The first gradiometer developed at the


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University of Maryland in the early 1980s demonstrated a gradient resolution of0.7 Eo/√Hz (Chan et al 1987a), a level yet to be surpassed by a room-temperaturedevice on Earth. A later version demonstrated common mode rejection (CMR) tobetter than one part in 107, which led to a demonstrated noise level of 0.02 Eo/Hz−1/2

(Moody et al 2002; figure 1.14(a)).Extraterrestrial mission studies showed that an SGG of 10−3 E Hz−1/2 sensitivity

at 250 km altitude could resolve Earth’s gravity with 100 km resolution in sixmonths. Because 4K space-qualified cryocoolers were not available in the 1990s, theduration of the SGG mission would have been limited to a year. Therefore, with the

Figure 1.13. A simplified schematic of the superconducting accelerometer developed at the University ofMaryland (adapted from Paik et al 1997).

Figure 1.14. (a) Original in-line three-component SGG. (b) Cross-component SGG. Courtesy of Ho JungPaik.


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goal of monitoring seasonal and annual gravity changes over five years, NASAselected the SST mission, GRACE, as the first gravity mission for the Earth.

The focus for continued development of the SGG at the University of Marylandswitched to its application in airborne gravity surveying (Paik et al 1997). A single-axis SGG, based on the concept of pivoted test masses, was tested fully in thelaboratory (Moody 2011). This cross-component SGG (figure 1.14b) has beenintegrated with a stabilized platform and is undergoing flight tests at Gedex, Inc.,a Canadian technology company (see figure 1.15)

Gedex, Inc. has been developing its high-definition airborne gravity gradiometer(HD-AGG™) for a long time. The system measures the gravity gradient utilising apair of balance beams, each of which is centred on a pivot spring. The systemcomponents and the performance of the prototype elements were described inCarroll et al (2010). Based on simulator and airborne trials of the individualelements integrated as a system, Gedex reconfigured and built a new two-axissystem, with improvements designed to further improve the noise performance in theairborne environment. While the primary objective was the improvement ofbalancing techniques to position the centre of mass on the axis of rotation in thegravity gradiometer sensors (balance beams), improvements were also made to theisolation mount, the cryostat, the auxiliary measurements used in the post-processingand the final data processing. Due to the benefits of measuring more than onecomponent, and the orientation of the sensor, the system was also upgraded to atwo-axis system, which effectively responds to (Gzz − Gxx)/2, and (Gzz − Gyy)/2. Thecommercial target for the system is a post-processed performance of 1 Eo/√Hz in thebandwidth from 0.001 to 1 Hz (Baker et al 2017). A performance of less than

Figure 1.15. Flight components of the Gedex HD-AGG™ installed in a Cessna Caravan 208 plane.Reproduced with permission from Gedex, Inc.


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10 Eo/√Hz was demonstrated in a Cessna Caravan and there is a plan to move thesystem to a Dash-8 plane, where a further increase in performance due to a morestable platform is expected (Main 2017).

Fundamental assessments of the SGG architecture occurred concurrently withthese efforts. By replacing the relatively stiff mechanical springs used in earlierdevices with soft magnetic levitation, the sensitivity of the device could be improvedby two to three orders of magnitude. The development of an SGG based on thelevitated test masses started in 2012, with support from NASA. The objective of thisprogramme is to develop a full-tensor SGG that measures all six components ofgradient tensor for Earth and planetary science applications. Significant advances inspace-qualified cryocoolers have been made in recent decades. The use of acryocooler will enable mission durations in the 10 year range.

Another SGG (the VK-1 orthogonal quadrupole responder) was originallydeveloped by Frank van Kann at the University of Western Australia in the1980s. The prototype instrument was described in van Kann et al (1994). Itmeasured an off-diagonal XY component of the gravity gradient tensor andconsisted of an orthogonal pair of quadrupole-like proof masses pivoted about acommon vertical axis (see figure 1.16(a)).

Each quadrupole mass was a rectangular bar made of niobium, which becomessuperconducting below −264 °C (∼9 K). Superconducting niobium inductive sensecoils and SQUID magnetometers—similar to those used in the University ofMaryland design—formed the basis of a read-out transducer system. The coilsalso provided supplementary magnetic springs to enable matching of mechanicalparameters.

Figure 1.16. (a) The original OQR prototype developed and tested at the University of Western Australia in1990. (b) The latest design of a balanced quadrupole beam as the primary gravity gradient sensor. Courtesy ofFrank van Kann.


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The original OQR (see figure 1.16(a)) was mounted on gimbals driven bydiamagnetic actuators in order to provide three-axis attitude control. Rotationsabout the X and Y axes were measured optically and referenced to a room-temperature custom-designed inertial system. The rotation about the OQR’sZ-axis was sensed directly by the OQR itself. The original gradiometer packagehad been studied extensively under controlled environment conditions, i.e. mountedon a shakeable platform on the laboratory floor. The sensitivity target for the VK-1instrument was 1 Eo/√Hz in a frequency bandwidth from 1 mHz to 1 Hz.

With financial backing and technical support from Rio Tinto, a global explorationand mining Company, the VK-1 instrument had been constantly modified andimproved over almost 30 years. In its most recent version (figure 1.16(b)), a pair ofbalanced quadrupoles, oriented orthogonally to each other, are aligned in the verticalplane but are free to be oriented in any horizontal direction by the operator.Therefore, the VK1 is sensitive to both the vertical gravity gradient and the gravitygradient along some fixed definable horizontal heading.

In recent years, VK1 had undergone extensive laboratory testing on a six-axis flightsimulator, in addition to ground-based moving-platform field trials (Aravanis et al2016). These tests indicate that the quality of VK1 gravity gradient data is potentiallycompetitive with that of the best existing moving-base gravity gradiometer systems,while it is also able to deliver data at higher frequencies. Laboratory-based flightsimulation tests achieved noise levels of ∼15 Eo in a 0.5 Hz frequency bandwidth(∼60 mg turbulence), while field tests in a closed van achieved levels of 25 Eo in thesame bandwidth.

Richard Warburton of GWR Instruments, Inc. (USA) developed a super-conducting gravity gradiometer for the US Department of Energy that closely

Figure 1.17. The latest version of the VK1 orthogonal quadrupole responder being tested on a flight simulator.Courtesy of Frank van Kann.


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followed the principles pioneered by the University of Maryland. Its plannedapplication is to detect underground structures from a mobile land vehicle.Effectively, the instrument consists of two superconducting gravimeters separatedby 20 cm and mounted with collinear sensitivity axes. Each gravimeter is a1″ diameter niobium sphere levitated in a magnetic field produced by superconductingcoils (Goodkind 1999). The sensitivity achieved for the device is ∼50 Eo/√Hz. Theclassic ‘two-gravimeter’ design cannot be extended to become a full-tensor gradiom-eter. Airborne applications are not being envisioned either. The programme wasabandoned years ago and currently no material relating to this development isavailable in the public domain.

1.2.4 String (ribbon) gravity gradiometer developments

On 11 October 2011, His Royal Highness Prince Philip, the Duke of Edinburgh,arrived in Perth, Western Australia, while visiting Australia along with Her MajestyQueen Elizabeth II. While planning his visit, he expressed his desire to see a gravitygradiometer that had been developed at the University of Western Australia. ‘I haveno idea how the Duke found out about the gravity gradiometer,’ Frank van Kann,the inventor of the VK-1 instrument and the leader of the University of WesternAustralia team, said. ‘I was approached by somebody from the Western AustraliaPremier’s Department a couple of months ago, then, later I had a meeting withrepresentatives from the Buckingham Palace.’

In fact, there had been two gravity gradiometers under development at theUniversity of Western Australia in parallel and completely independent of eachother at all times since 2005. In 2011, there was Gravitec’s ribbon gravitygradiometer, which had been under development since 1995.

Gravitec Instruments Ltd was formed by a group of private investors in 1995 inLondon (UK) and registered in the Commonwealth of the Bahamas as an offshorecompany. The reason for establishing an offshore company was, perhaps, the hopeto escape from defence export control restrictions and capitalise freely on thedevelopment of the completely new design of a gravity gradiometer, i.e. the stringgravity gradiometer.

The original concept was first patented in 1995 in New Zealand (Veryaskin 1996)and was then reassigned to Gravitec Instruments in exchange for establishing aNew Zealand-based laboratory and financial backing for the development of thegradiometer’s working prototype.

Some years later, major players from over the globe who were interested incommercial applications of gravity gradiometry got in touch with Gravitec’stechnical team in order to understand the place the new concept would takeamong the other developments. Among these were Industrial Research Ltd(New Zealand), Halliburton (USA), Schlumberger (USA), Rio Tinto (Australia),BHP (Australia), Western Mining Corporation (now BHP Billiton, Australia),CGG (Canada), Lockheed Martin Corporation (USA), Shell International (theNetherlands), NIMA (now the National Geospatial Intelligence Agency, USA),CSIRO (Australia), QinetiQ Ltd (United Kingdom). This resulted in a decade of


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external investment opportunities for Gravitec being provided by some of theentities listed above.

In 2005, Gravitec Instruments established a subsidiary company in WesternAustralia, Gravitec Instruments (AU) Pty Ltd, which took over the one establishedin New Zealand. The latter one, i.e. Gravitec Instruments (NZ) Ltd, had been thedeveloper of different versions of string gravity gradiometers before it ceasedoperations in 2005. The reason for this relocation was the fact that the Universityof Western Australia, in collaboration with Gravitec, had won two successiveAustralian Research Council linkage grant applications for the development ofanother string-based instrument, an intrinsic string magnetic gradiometer (see themagnetic gradiometry section below). This programme had been supported by twoof Gravitec’s Australian industry partners, namely the Western Mining Corporation(now BHP Billiton) and FUGRO Australia (now CGG-Multiphysics).

The new gravity gradiometer concept was not a torsional (dumbbell) or accel-erometric one. A string, which is inherently subjected to certain boundary con-ditions, represents a sensor that does not possess localised proof masses that areresponsive to the force of gravity. The entire length of such an object is a continuumof spatially distributed mass per unit length. Therefore, the force of gravity per unitlength is the only quantity that the string is responsive to, and this is indeed a gravitygradient-related quantity (Veryaskin 2000). Such devices are called intrinsic gravitygradiometers, as they do not differentiate signals from paired sensors such asaccelerometers or gravimeters.

Another interesting feature of objects such as strings or long strips, is the fact thatthey possess some distinct mechanical degrees of freedom, which are similar to violinmodes (see figure 1.18). At every instance the string’s shape is a superposition of allsuch modes. However, some of them are only coupled to a gravity gradient due totheir asymmetry with respect to the string’s mid point. If a particular mode is excitedby an external force per unit length, then each point along the string’s length movessynchronously in the time domain. Effectively, the string represents an infinitenumber of point-like accelerometers responding coherently to any externaldisturbances.

If no force per unit length is applied to a string, it forms an absolute line in space.This line passes between the points where the string does not move, such as fixedends. A round string has only one such well-defined direction in space (say theZ-axis) and it can be deflected in both the X and Y directions. A ribbon whose length(along the Z direction) is much longer compared than its width (along the Ydirection), and whose width is much greater than its thickness (along the Xdirection), has a well-defined intrinsic coordinate system X, Y and Z. It can onlybe deflected along the X-axis and therefore represents a one-dimensional multi-modemechanical oscillator.

A gravity gradient component, say Gxz (see figure 1.19), is measured by twodisplacement sensors, which are positioned at one-quarter of the string’s length fromthe string’s mid-point. At these particular locations, the string’s displacements fromits unperturbed state (straight line) are maximum and opposed to each other for thegradient-only coupled S-mode.


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Figure 1.18. Elementary vibrations (modes) of violin strings. If it is being excited, a string’s instant shape is asuperposition of all possible modes.

Figure 1.19. All in one—basic principles for using string-like objects as gravity gradient sensors. The typicalboundary conditions are shown in the bottom left corner.


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The displacement sensors could be either SQUIDs, as in the case of a super-conducting string gradiometer (Veryaskin 1999), or inductive/capacitive pick-offsfor room temperature-based instruments. The displacement sensors do not need tobe strictly identical. They can be included into complementary arms of a Mach–Zehnder interferometer, as described in Veryaskin and McRae (2011).

A common mode rejection (CMR) scheme is also easy to implement by summingthe sensor’s output signals and using a piggy-back connection to the main datastream. In the latest version of Gravitec’s gradiometer, a flat metal strip (ribbon)with its mid-point partially clamped is implemented. This implementation leads tothe complete surpression of the first violin mode (the C-mode) while the gradient-coupled S-mode remains free to rotate around that particular position. A closeanalogy to this arrangement is a flexible torsion balance with its ends fixed. An RFphase-sensitive read-out was also incorporated into the gradiometer system in 2011,and this was a step forward in getting the best performance quantified at about30 Eo/√Hz in a noisy laboratory environment with limited protection from back-ground noise (see figure 1.20).

In 2013, Gravitec moved its gravity gradiometer development programme to theUniversity of Strathclyde (Glasgow, UK), and this was active until October 2016.

Figure 1.20. The latest version of Gravitec’s ribbon gravity gradiometer assembly being tested in thelaboratory at the University of Western Australia in 2010–11.


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No data highlighting the outcome of the final stage of Gravitec and Strathclyde’sjoint efforts are available in the public domain.

A novel minituarised ribbon gravity gradiometer with more advanced designfeatures than Gravitec’s one has been recently patented by a team of scientists basedat the University of Western Australia (Veryaskin et al 2016). Project TAIPAN (thenickname of the new gravity gradiometer) is currently underway and the new gravitygradiometer design is undergoing laboratory testing in order to verify its perform-ance. This is the gravity gradiometer design that has the potential to be deployedfrom UAVs, both airborne and submersibles, and inside drilled wells. It is a leadingcandidate for borehole applications of gravity gradiometry.

1.2.5 Conventional absolute gravity gradiometers

An absolute gravity gradiometer is made up of two classic absolute free-fallgravimeters that have been developed at the Joint Institute for LaboratoryAstrophysics (JILA) (Niebauer et al 1995). A vertical gravity gradient componentGzz is calculated as the difference between the gravimeters’ outputs divided by thevertical baseline (in metres). Each individual absolute gravimeter used laserinterferometry to measure the acceleration of a freely falling test mass in the formof corner cube retroreflector accurately. The instrument employed a Michelson-typeinterferometer, in which one end mirror was falling freely and the other wassuspended from a long period isolation device called a ‘super string’. The timeinterval between the zero-crossing of the interference fringes are fitted to a parabolawhich yields the acceleration of the falling retroreflector relative to a reference testbody. The latter was isolated from vertical accelerations above ∼30 mHz. Thisoperational principle allowed for the absolute accuracy of the gravimeter to belimited by a systematic error of about 3 microGal.

The most advanced FG5 generation of absolute gravimeters is being developedby Micro-g LaCost & Romberg, Inc. (USA). Two such absolute gravimeters can beuseful for determining variations in the Earth’s gravity field. The variation in gravitynear the surface of the Earth is normally dominated by the nearly constant verticalgravity gradient of the Earth itself. The gradient from a homogeneous Earth is about3000 eotvos. This causes the gravity at the bottom of a 20 cm drop to be about60 μGal larger than it is at the top (see figure 1.21)

In 1999, a method to determine the vertical gravity gradient from raw data takenwith an FG5 was reported (Hipkin 1999). It was possible to recover a gradient valuewith a standard error of about 1% after averaging over about 14 000 drops. Theseresults proved that the FG5 absolute gravity meter could be used to measure thevertical gravity gradient directly, as well as the gravity value at a point at the top ofthe drop without having to move the gravity meter. In contrast, other methods tomeasure the vertical gravity gradient require either two different vertically separatedgravity sensors or a sequence of two different gravity measurements, with the samesensor being moved between two different vertical locations.

Another attempt to improve absolute gravity gradient measurements was madeusing a different FG5 gravity meter (Robertson 2001). Sparse matrix techniques


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were used to solve a non-linear least-squares fit for many thousands of measure-ments at one time. Each least-squares fit included about three million optical fringesfor 5000 different drops to estimate 24 000 parameters. These results for the gradienton a single fit of about 5000 drops had a formal error of better than 1% (about20 eotvos), but the gradient itself varied by 10 times this amount or about 300 eotvos.The lack of repeatability in the sequence of these gradient measurements wasthought to be the presence of low-frequency damped sinusoids in the data,presumably caused by recoil of the dropping chamber. The repeatability of thesemeasurements had been improved to about 100 eotvos after the removal ofsystematic sinusoidal noise terms.

These works provided motivation to develop a new dropping chamber with itsadditional free-fall length and reduced recoil to determine the vertical gravitygradient (Niebauer et al 2011). The new dropping chamber incorporates counter-weights to compensate recoil effects. It has the same physical length as the standardFG5 dropping chamber, but the free-fall distance has been increased from 20 to25 cm. The new drive train pulls on the centre of the system to reduce unwantedhorizontal velocity and rotation of the free-falling test mass. The test-massmaterial was chosen to reduce possible magnetic eddy-current damping causedby external magnetic field gradients. External lead masses were used to change thegravity and vertical gravity gradient. The measurements agree well with thetheoretical gravity field changes derived from the position of the external weights.

Figure 1.21. An absolute gravity gradiometer based on two FG5 absolute gravimeters. Reproduced withpermission from Micro-g & LaCoste.


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The experiment clearly demonstrates the efficacy of using an absolute gravitymeter to measure both the gravity and the gravity gradient signals caused byvariations in the external gravity field. This technique shows promise for passivegravity-monitoring applications.

1.2.6 MEMS gravity gradiometers

Micro-machined electro-mechanical systems (MEMS) have been explored intensivelysince the late 1990s. They are fabricated using integrated circuit (IC) batch processingtechniques and can range in size from a few micrometres to millimetres. These devices(or systems) have the ability to sense, control and actuate on the micro scale, andgenerate effects on the macro scale. The interdisciplinary nature of MEMS utilizesdesign, engineering and manufacturing expertise from a wide and diverse range oftechnical areas, including integrated circuit fabrication technology, mechanicalengineering, materials science, electrical engineering, chemistry and chemical engi-neering, as well as fluid engineering, optics, instrumentation and packaging.

The complexity of MEMS is also shown in the extensive range of markets andapplications that incorporate MEMS devices. MEMS can be found in systemsranging across automotive, medical, electronic, communication and defence appli-cations. MEMS-based accelerometers, where both a test mass attached to a springand a capacitive displacement transducer are integrated together in a tiny micro-machined structure, have been under construction since 1999 (Jiang et al 2002).They have demonstrated their potential to provide sensitive mechanical displace-ment measurements quantified at a few picometres/√Hz (10−12 m/√Hz). A pair ofsuch micromachined accelerometers, or a single angular accelerometer (a micro-torsion balance) can serve as an ultra-miniature gravity gradiometer, as depicted infigures 1.22 and 1.23.

The first MEMS-based gravity gradiometer research began at the University ofTwente (the Netherlands) (Flokstra et al 2009) as a potential technology for future

Figure 1.22. A comparison of the principles of operation of differential-accelerometer and torsion-balancegradiometers for measuring the vertical gravity-gradient component. Adapted from Liu et al (2016) withpermission from the American Institute of Physics.


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space missions. This was the only option that was feasible for using MEMS gravitygradiometers, since they could hardly tolerate the full-g environment inherent to allterrestrial applications.

Recently, progress has been made in attempting to adopt MEMS-based technol-ogy for terrestrial applications. A group of scientists at Imperial College London(UK) have presented the design, fabrication and characterization of a seesaw-leverforce-balancing suspension for a silicon gravity gradient sensor, a gravity gradi-ometer, which is capable of operating over a range of gravity from 0 to 1g (Liu et al2016). This allows for both air and space deployment after ground validation. Anoverall rationale for designing MEMS gravity gradiometer has been developed,indicating that a gravity gradiometer based on a torsion balance, rather than adifferential accelerometer, provides the best approach. The fundamental micro-machined element, a seesaw-lever force-balancing suspension, is designed with a lowfundamental frequency for inplane rotation in response to gravity gradient, but withgood rejection of all cross-axis modes.

During operation under 1g, a gravitational force is axially loaded on two straight-beams that perform as a stiff fulcrum for the mass-connection lever without affectingsensitive in-plane rotational sensing. The dynamics of this suspension are analysedby both closed-form and finite element analysis, with good agreement between thetwo. The suspension has been fabricated using through-wafer deep reactive-ionetching, with the dynamics verified in both air and vacuum. The sensitivity of agravity gradiometer built around this suspension is expected to be limited by thermalnoise of about 10 Eo/√Hz.

Figure 1.23. Schematics showing the operating principles of EPFL’s monolithic MEMS gravity gradiometersbased on the torsion-balance approach with gap-variation differential capacitive sensing. The gravity vector, g,is shown with the proof masses labelled m and the capacitive transducers c1 and c2. Adapted from Liu et al(2016) with permission from the American Institute of Physics.


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1.3 Classification of existing gravity gradiometersThere have been a few attempts to characterise gravity gradiometers using differentclassification schemes in accordance with their working principles and methods ofmeasuring gravity gradients. One of the early efforts in this direction was under-taken by Victor Nazarenko in 1982. He was a talented Soviet-era physicist whograduated from the famous Vladimir Braginsky group at Moscow State University(Thorn 2016). He was also among the first to publish a detailed noise analysis and aread-out optimisation algorithm based on the maximum plausibility functionmethod applied to his classification of gravity gradiometers (Nazarenko 1982).This is a classic situation in statistical radiophysics, for example, when one needs toestimate a useful parameter in a signal received along with narrowband orbroadband noise with a priori known or unknown statistical properties (Levy2008). A ‘toy model’ of a horizontal torsional oscillator was rigorously analysed(see section 4.3). This analysis, however, can be applied to a much broaderspectrum of real gravity gradiometers, such as the MEMS-based micro-torsionbalance.

According to Nazarenko, all gravity gradiometers can be broken down by themethods used to extract useful information from broader content, includingunknown parameters and noise2. There are static, dynamic and modulating gravitygradiometers. The latter can be further broken down to rotating, rotating resonantand non-rotating ones. A more detailed version of the Nazarenko classification issummarized in tables 1.1 and 1.2 below.

Another attempt to characterise different gravity gradiometers was made byDavid Gleason (Air Force Research Laboratory, USA) and Gerald Shaw (SRIInternational, USA) in 1999. They had composed a detailed review titled‘Systematic analysis of gravity gradiometry developments’ and submitted it to apeer-reviewed journal. The review was never published for unknown reasons. Theauthor of this book served as a referee and obtained a full copy from the publisher.Years later, by personally communicating with David Gleason, the author waspermitted to use some fragments of the review in this book.

There are essentially two classes of gravity gradiometer. One can be designated asthe ‘direct’ or ‘intrinsic’ class (IGG). Another one is the ‘differencing’ class (DGG).In the first case, a single sensing element measures a gravity gradient componentdirectly. A direct gravity gradient means the true first spatial derivative of thegravitational acceleration vector along the sensitivity axis of an IGG (see table 1.3for an example).

In the differencing class, two different sensors are paired up and their outputsignals are subtracted from one another in real time. This represents a significantchallenge, which is a well-known ‘common mode rejection’ problem in gradiom-etry. In order to underline the seriousness of this problem, let us consider thefollowing.

2 Both classic and cold atom gradiometers based on free fall of the test masses are exempt from this analysis.


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Tab

le1.1.

Different

cryo

genicinstruments

classified

bytype

andprinciples

ofop

eration.

Cryog

enic

Static

Dyn

amic

Mod

ulating

(rotating,

non-resona

nt)

Mod

ulating(rotating,

resona

nt)

Mod

ulating(other)

Torsion

alRioTinto

&Universityof

Western

Australia

VK-1

Ortho

gona

lQua

drup

ole

Respo

nder

(OQR)

Universityof

Marylan

dan

dGEDEX

Differentialan

gular

accelerometer

Accelerom

etric

ARKeX

Twovertical

supercon

ducting

accelerometerssepa

ratedby

aba

selin

e(nolong

erun

der

developm

ent)

Gravimetric

GWR

instruments

Tworelative

supercon

ducting

grav

imeterssepa

ratedby

aba

selin

eDistributed

GravitecInstruments

supercon

ducting

string


1-31

Tab

le1.2.

The

sameas

table1.1ab

ove,

butforroom

-tem

perature

operatinginstruments.

Roo

mtemperature

Static

Dyn

amic

Mod

ulating

(rotating,

non-resona

nt)

Mod

ulating

(rotating,

resona

nt)

Mod

ulating(other)

Torsion

alMEMStorsionba

lance

Imperial

College

Lon

don

Hug

hesAircraftResearch

Lab

oratory

Accelerom

etric

DelftUniversityof

Techn

olog

yMEMS

baseddifferential

accelerometer

Imperial

College

Lon

don

MEMSba

sed

differential

accelerometer

App

liedPhy

sics

labo

ratory

Sapp

hire

Oscillator

Lockh

eedMartin

FALCON™

FTG,eF

TC,dF

TC

Lockh

eedMartin

FTGPlus

Gravimetric

Micro-g

solution

sTwoab

solute

free-fall

grav

imeters

Distributed

GravitecInstruments

Ribbo

nGravity

Gradiom

eter

Universityof

Western

Australia

TAIPAN

Gravity

Gradiom

eter

Floa

ted

DraperLab

Floated

Gravity

Gradiom

eter


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Let the Earth’s ambient vertical acceleration of gravity be ⊗g at a point O inspace. One wishes to measure its gradient with 1 eotvos accuracy. If two Z-sensitive‘ideal’ accelerometers are used to measure an YZ gravity gradient component, whichis a change in ⊗g along the Y-axis over an L metre baseline, their differential outputis as follows:

δ δφ

δ δφ

Δ = − + +

≅ − −⊗ ⊗

⊗ ⊗⎡⎣ ⎤⎦( ) ( )

V kg L k k g

kL G k k g L g L

( ) ( )(1 ) (0)

( / ) (0)/ (0)/,

ZY

where k is the ‘ideal’ accelerometers’ scale factor, δk is a systematic error resultingfrom a mismatch of the real accelerometers’ scale factors and δφ is a systematic errorresulting from angular misalignments of the real accelerometers’ sensitivity axes, i.e.S1 and S2, as depicted in figure 1.24.

Then the 1 eotvos gravity gradiometer’s capability assumes the followinginequalities:

δ δφ≈ ⩽ −⊗k k L g/ 10 ( / ),9

which are equivalent to a one-sigma error level. For the Earth’s full-g environment( ⊗g = 9.8 m s−2) and L = 0.5 m (the best case scenario) one obtains

Table 1.3. An example of differencing and intrinsic gravity gradiometers. Their sensitivity axes are chosen tobe aligned along the X direction. However, a gradiometer can have multiple sensitivity axes and measure allfive independent gravity gradient tensor components.

Gravity gradiometer type Sensitivity axis Measured quantity Major problem

Differencing (twosensing elementsseparated by abaseline)

X (gz2 – gz1)/(x2 − x1) Mismatch andmisalignment ofsensing elements

Intrinsic (a single sensingelement)

X Gzx = ∂gz/∂x = ∂gx/∂z Read-out sensitivitylimitations

Figure 1.24. Two ‘identical’ sensors with angular misalignment of their sensitivity axes (S1 and S2) andinfinitesimally different scale factors (k and k + δk).


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δ δφ≈ ⩽ × −k k/ 5 10 .11

The bad news is that these requirements must be provided over the wholegradiometer run time, i.e. must be stable within reasonably long time intervals.To date, there are no differencing gravity gradiometers that are capable of operatingin the Earth’s full-g environment in cases where the accelerometers’ sensitivity axesare aligned with ⊗g .

The situation becomes more plausible when a gradiometer’s sensitivity planecoincides with the horizontal plane or is slightly tilted from the latter by a smallangle, as in the case of the Falcon generation of gravity gradiometers. However, inthe moving-base environment, a gradiometer will need to reject so-called dynamic ortotal acceleration, which includes the kinematic acceleration if the carrier’s speed isnot constant. The latter may reach the same order of magnitude as the full ⊗g , andmay have non-zero projections in the gradiometer’s sensitivity plane.

Further, if the moving platform experiences spatial rotations, which is always thecase in the real world, so-called dynamic gravity gradient components will bemeasured instead of the ones related to the spatial distribution of the acceleration ofgravity. They include non-inertial terms containing the platform’s angular velocitiesand angular accelerations as shown below (Chan et al 1987a):

δ ε= + Ω − Ω Ω + Ω∼G G

ddt

,ij ij ij i j ijkk2

where Gij is the true gravity gradient tensor (sections 4.1 and 4.2),Ω = Ω Ω Ω{ , , }X Y Z

��is the platform’s angular velocity vector, δij is the Kronecker

delta and εijk is the totally antisymmetric Levi-Civita symbol (Tyldesley 1973).Below is a summary of the problems that one must deal with whn developing

gravity gradiometers intended for operation on moving carriers (Evstifeev 2017).1. Detection of gravity gradient tensor components mixed with a background

of considerable dynamic gradients of inertial forces at the gravity gradiom-eter position. The measurement error of 1 eotvos corresponds to the gravityacceleration change of 2 × 10−10 m s−2 (2 × 10−11 ⊗g ) along a 0.2 m baseline.Note that some mobile objects may undergo intensive linear vibrations withamplitudes of up to 1 ⊗g , kinematic acceleration up to 10−1–10−2 and angularaccelerations that may be equivalent to billions of eotvos. Therefore, ameasurement error that is about 10 orders of magnitude lower than the levelof the measured signal value may be desirable. In order to mitigate theseeffects, special vibration isolation techniques and linearly and angularlystabilised platforms are being designed at reasonable cost. Such stabilisedplatforms are an integral part of all existing gravity gradiometers.

2. Providing a minimum of dynamic errors associated with the structuralinstabilities (harmonic self-oscillations) inherent to all cumbersome stabletables. For example, the dynamic error created by platform’s tosionalharmonic oscillation, which is as large as 1 arcsec at a frequency of 1 Hz,is equivalent to 80 million eotvos.


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3. Providing matching parameters (and keeping them stable over the wholeoperation interval) for accelerometric (paired) gravity gradiometers. Theaccelerometers must be noiseless down to about 3 × 10−11 ⊗g , if one wants todetect a 1 eotvos gravity gradient with a 2 sigma confidence level.

4. Providing thermal stabilisation of all critical parts that constitute a gravitygradiometer. It is important that for metallic dumbbells with a thermalexpansion coefficient of about 10−5 1/°C, temperature variations in thestructure must not exceed 10−6 °C. Zero-point drift (1/f noise), caused bytemperature instabilities is a profound problem for all static gravity gradi-ometers. Cryogenic gravity gradiometers are far more stable in that regard.However, operation of cryogenic systems on board small moving vehicles,such as light aircraft, UAVs and the like, does not seem feasible at this time.

5. Providing ultra-sensitive and stable displacement measurements for torsionalgravity gradiometers such as orthogonal dumbbells.

6. Providing ultra-stable rotating platforms with a constant speed of rotation, foreither accelerometric or torsional modulating (rotating) gravity gradiometers.

7. Providing real-time data processing based on advanced Kalman adaptivefiltering algorithms. Such procedures must not significantly reduce theresolution of gradiometric measurement.

8. Providing metrological equipment and calibration stations for moving-basegravity gradiometers. The in situ gravity gradients must be determined andcontinuousely monitored with an accuracy of at least 0.1 eotvos accuracy.

The development of gravity gradiometers capable of measuring gravity gradientsin a moving environment is a tough challenge. One can say this: the problem-solvingpotential of those involed in this business would require the highest grade ofexpertise, similar to that of the Impossible Missions Force in the Mission Impossiblefilms.

Finally, all measurements can be classified as absolute, relative and those that canbe calibrated in absolute units (see tables 1.4 and 1.5). Absolute gradiometers, eithertwo absolute (freefall) gravimeters or two absolute magnetometers, separated by abaseline, do not require changes of the physical quantity they are designed to

Table 1.4. Gravity measuring devices are broken down into ‘absolute’, ‘relative’ and ‘can be calibrated inabsolute units’ categories.

Devices Absolute RelativeCan be calibratedin absolute units

Gravimeter and static accelerometer No Yes YesDifferential (doubled) static accelerometer No Yes YesTorsion balance No Yes YesTree fall gravimeter Yes NoClassic pendulum Yes No


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measure. A relative instrument, while stationary, does require time variation of thequantity it measures. It can only measure the difference between, say, a gravitygradient at an instance of time A and an instance of time B. The true absolute valueof that gradient at any instance of time remains undetermined.

Confusion often occurs when a static gradiometer, which can only provide relativegradient measurements, is moved continuousely along a survey line, say, while beingused aboard an aircraft.

Its output signal is proportional to the running difference between a gravitygradient at a current position and that of the starting point when the instrument wasswitched on. Effectively, relative gradiometric measurements are equivalent tomeasuring the second spatial derivatives of the physical quanities of interest. It isa useful tool in mineral exploration, for example, when a moving gradiometerapproches an ore body. The latter creates a local anomaly in the gradient spatialdistribution and the situation when a gradiometer sweeps over ‘no-anomaly-to-anomaly’ course works well here.

Interestingly enough, a static instrument calibrated in absolute units (a singleaccelerometer, for example), if moved from one spatial position (station) to anotherone, can determine an absolute value of a gradient tensor component of the physicalquantity it does measure. In order to achieve that, one can take the measured relativedifference in the instrument’s output signal and divide it by the spatial interval, inmetres, between the two measurements. The calibration coefficient (the scale factor)must stay unchanged during the measurement time.

The above is summarized and illustrated by two examples below.1. A single static gravimeter (typically represented by a proof mass and a

spring) is moved from station A to station B, as depicted in figure 1.25.The result of measuring a difference ΔV of its output signal is as follows:

Δ = − = ΔΔ

=V k g g kLgZ

kLG( ) .ZZ2 1

2. Two identical static gravimeters are placed at stations A and B and movedalong the X-axis by a distance ΔX. Their output signals are subtracted in

Table 1.5. Some of the existing gravity gradiometers are broken down into ‘absolute’, ‘relative’ and ‘can becalibrated in absolute units’ categories.

Gradiometers Absolute RelativeCan be calibratedin absolute units

University of Maryland No Yes NoUWA & Rio Tinto (OQR) No Yes NoGravitec (static string) No Yes NoLockheed Martin (modulating) No No YesGravitec & UWA (modulating) No No YesMicro-g (free fall) Yes No


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order to cancel out kinematic disturbances that are not related to gravity.This results in the following:

δ δ δ δ δΔ − Δ = Δ − Δ = ΔΔ

=⎜ ⎟⎛⎝

⎞⎠V V k g g kL

gZ

kL G( ) ( ) .A B A B ZZ

This result is modified, as shown below, if the gravimeters are mounted on amoving platform with a constant speed v along the X-axis:

δ δ τ δ τφ

Δ − Δ = + − =

= ∂∂

∂∂

V t V t kL G t G t kL vG

Gx z

( ( ) ( )) ( ( ) ( ))

.A B ZZ ZZ XZZ

XZZg

2

2

Here τ is the measurement time and φg is the gravitational potential (section 4.2).

1.4 Gravity gradiometry applications1.4.1 Gravity gradiometry in oil, gas and mineral exploration

There are a number of important applications for gravity gradiometry in oil and gasexploration (Dransfield 2007, Golden 2017). Airborne gravity gradiometry canprovide significantly lower noise and higher resolution data than airborne gravim-etry and faster coverage with reduced access issues compared to surface gravimetry.In general, the major areas of application are those that provide extra informationwhen seismic data is limited or in mapping large areas in order to target an expensiveseismic survey effectively.

Gravity gradiometry has already proven itself in these fields. A report waspublished on the successful mapping of an Eocene channel in a Falcon™ gravitygradiometer survey over a portion of the Gippsland Basin, Australia’s majordomestic oil source (Rose et al 2006). Another report disclosed the successful

Figure 1.25. A simplified diagram of a single static gravimeter moved from station A to station B, or twoidentical gravimeters, positioned at stations A and B, are moved along the X-axis.


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use of FTG data in a three-dimensional (3D) inversion constrained by seismicinformation to calculate the base of the K2 salt body in the Gulf of Mexico down todepths of 20 000 feet (O’Brien et al 2005).

A successful airborne structural gravity gradient mapping in the Papua New Guineafold belt, a region where ‘jungle cover, rugged topography, and paucity of roads’makeexploration on the surface difficult and expensive, was reported in (Nelson et al 2004).In the Bonaparte Gulf off the north-western Australian coast, Nexus aicraft flew aFalcon™ survey to map salt diapirs (Dransfield and Walker 2005).

The enhancement of the data available to the petroleum industry was incrementalbut significant, but the real step change arising from gradiometrey was seen in on-shore mineral exploration. By October 2005, the Falcon systems had flown 1 millionline km of surveys, almost entirely for mineral exploration (see figure 1.26). Manymore km have been flown since then, on top of those flown by the Air-FTG andFTGe systems now in operation. It is clear that airborne gravity gradiometry hasbecome a major part of mineral exploration efforts. Suddenly, explorers were able togenerate prospect scale to regional scale high-resolution maps representing lateraland vertical changes in rock density. These maps were used as qualitative pseudo-geology maps showing geological units, faults and contacts. At the same time,computer advances enabled sophisticated numerical inversion programs that couldgenerate simulated geological models of the Earth. A few examples of the types of

Figure 1.26. A Falcon™ gravity gradiometer full assembly being prepared for a survey flight. Currently sixsuch systems are in operation: Einstein since October 1999, Newton since April 2000, Galileo since July 2002,Feynman since June 2005, Cavendish since August 2011 and Kepler since January 2016. Reproduced withpermission from CGG-Multiphysics.


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mineral exploration targets that are detectable using gravity data, and specificallygravity gradiometer data, are described below.

It seems that the original motivation for using gravity gradiometers for mineralexploration was centred on diamond exploration. Kimberlite pipes intrude countryrocks and, if the erosion level is not too deep, a low-density portion of the pipe atshallow depths is preserved that is easily detectable and manifests itself as a negativegravity anomaly. These anomalies can be measured using conventional ground-based gravimeters, but BHP Billiton in the 1990s embarked on an exploration pushin remote and often wet and swampy regions of northern Canada. The airbornegravity gradiometry technology enabled kimberlite pipes to be detected in theseremote regions. Of course, the technology was soon applied in other regionsprospective for kimberlites in difficult terrain, but also in many more hospitablelocations where the speed and convenience of airborne acquisition was seen as acompetitive advantage for those with access to the technology.

Besides diamonds, some of the most sought-after deposits in the world are ironoxide copper gold (IOCG) deposits. The largest, Olympic Dam, is in WesternAustralia and is a major source of gold and uranium in a host of hematite that isalmost twice as dense as the surrounding host rock. The exploration and expansionof the Olympic Dam deposit was intimately associated with ground gravimetry.After BHP Billiton acquired the deposit, their Falcon airborne gravity gradiometerwas flown over the deposit and successfully reproduced the ground gravity results.Since then, several other similar deposits have been overflown with similar results,and the technology is still frequently used in the search for IOCG deposits on severalcontinents.

Massive sulphide nickel–copper deposits are another prime target for gravitygradiometry. They occur in dense host rocks and often consist of massive, very densesulphides that can create masses detectible by gravity. The ability of gradiometry tobe measured in an airborne platform makes the search for these nickel depositspossible in a variety of remote locations with difficult access.

Another type of very dense sulphide mineralisation occurs in volcanogenicmassive sulphide (VMS) copper and gold deposits. The first airborne gravitygradiometry survey ever flown was over part of the Bathurst Camp in Canada,host to several very large VMS deposits.

Iron ore exploration includes deposits consisting of massive haematite andbanded iron, both of which can be very dense compared with the host rocks inwhich they are emplaced. Gravity gradiometry is an appropriate tool for such ironexploration and has been carried out in Michigan (USA), South Australia, WesternAustralia, Brazil and elsewhere.

Lead and zinc also commonly occur as dense ore bodies hosted in relatively low-density sedimentary rocks and present excellent targets for gravity gradiometry. TheCannington silver–lead–zinc deposit in Australia showed up as a Falcon anomalyand there is reason to believe that other large deposits such as the Broken Hilllead–zinc mine would also be appropriate targets.

Low density will also result in an anomaly that can be detected by gravitationalmethods. Coal has a very low density with respect to surrounding lithologies, and


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gravity gradiometry has been employed in the search for coal, much as it has forpetroleum, in south-east Australia and elsewhere.

Palaeochannels can contain economic gold or hydrocarbon deposits as well asother detrital minerals that are the object of mineral exploration. These channelsalso present themselves as low-density features that are excellent targets for gravitygradiometry.

Lastly, gravity data can be an excellent tool to map geological features,particularly under cover. The ability to map faults, weathering profiles and lithologiescan be of very significant value, especially in remote areas and/or rugged topographywhere physical mapping can be difficult or impossible. Such mapping can add valueto any exploration project, in particular in examples such as the search for golddeposits in weathered areas of greenstone belts in Western Australia andWest Africa,as well as porphyry copper projects in regions such as Mongolia and the Andes.

In summary, many petroleum and mineral deposits exhibit characteristics thatinclude rocks of contrasting density that are detectable using gravity measurements.These measurements have been in common use on land for a century, but the adventof gravity gradiometry has enabled the technique to be employed rapidly over largeareas and, importantly, over water and in remote and rugged terrain.

Gravity gradiometry is an important tool, along with other geophysical, geologicaland geochemical techniques, for mineral and hydrocarbon exploration. Advances inthe technology that enable even better spatial frequencies, sensitives and noisecharacteristics will make the gravity gradiometry technique even more important.

CGG, the Canadian exploration giant, has been developing advanced airborneexploration methods based on a combined gravimetry and gravity gradiometrytechnologies. CGG-Multiphysics (Australia) has developed the world’s first com-mercial strapdown gravimeter, sGrav, which has achieved the same levels of dataquality at the long end of the gravity spatial spectrum content (i.e. wavelengths) asstabilized platform systems (van Galder and Dransfield 2016, Dransfield 2017).With a repeatability of ∼0.71 mGal at 300 s filtering, it is ideally suited to augmentthe long wavelength airborne gravity gradiometer data. The sGrav data isincorporated into the airborne gravity gradiometer processing stream by a modifiedconforming technique that first converts the gravity data to gravity gradients andthen merges the result with the gradients from the gravity gradiometer. Thisimproved process has advantages for conforming gravity gradiometer data to anyregional gravity data.

Gravimeters are unable to distinguish kinematic accelerations from gravity, butthe kinematics can be supplied by other means. A proven option in this direction isto use Global Navigation Satellite System (GNSS, https://www.amsa.gov.au/navigation/resources/gnss/). The ability of GNSS to estimate aircraft accelerationis therefore crucial and it operates well for periods greater than 100 s. At typicalaircraft speed, this means that airborne gravimetry is useful at wavelengths above7 km. Gravity gradiometers do not have this limitation and routinely provideuseful information at wavelengths down to a few hundred metres. At wavelengthsabove 20 km, the gravity information from an airborne gravimeter is moreaccurate than that from an airborne gradiometer. This suggests that using a


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https://www.amsa.gov.au/navigation/resources/gnss/

https://www.amsa.gov.au/navigation/resources/gnss/

gravimeter and gradiometer in combination would be effective. However, the cost,weight and size of standard airborne gravimeters present challenges. It turns out thatstandard airborne gravimeters rely on being rotationally stabilised via a nested gimbalplatform in order to successfully resolve wavelengths down to ∼7 km. If one only caresabout wavelengths above 20 km, then a strapdown gravimeter is a possibility. Thiswould substantially reduce the cost, size and weight.

1.4.2 Borehole gravity gradiometry

To date no gravity gradiometry measurements have been made subsurface. With theexception of a classic theoretical paper (Nekut 1988), and a few similar publications(Krieger et al 2010, Rim and Li 2012), no case histories have been reported onwellbore gravity gradiometry. It is a virgin market niche and any discussions arebased on potential. Below is an attempt to analyse this potential and make someprediction in regard to an extremely challenging application of gravity gradiometry(Neill 2009a).

Surface gravity versus gravity gradiometry marketSurface gravity measurements (both gravimeter and gradiometer based) have beenwidely used in oil and gas exploration and are typically classified along withmagnetic measurements as potential field measurements. While there is someoverlap between surface and subsurface gravity measurements, there are funda-mental differences in terms of both the technology used and the interpretation of thedata acquired. Traditionally, surface gravity measurements are primarily focused onexploration and are a ‘macro’ measurement used to identify potential areas ofinterest prior to more detailed seismic measurements.

Within the larger oil companies, gravity and gravity gradiometry technology-exploring groups can often be found, but they are often at the margins. Outsidethese groups the level of knowledge and understanding of these technologies islimited. Seismic exploration dominates and seismic geophysicists are the keydecision makers. Gravity is often viewed as a niche technology and treated witha degree of scepticism. Typically, it is only when seismic techniques cannot deliversatisfactory results that alternative techniques such as gravity and/or gravitygradiometry be seriously looked at. The largest player in the gravity and magneticsmarket was Fugro Gravity and Magnetic Services, a part of the Fugro group (nowa part of CGG). It employed about 100 people globally and operated both in theoil and gas industry and, in a smaller proportion, in the mining industry. Theformer Fugro group used traditional gravity technology in land, marine andairborne applications. As this market has existed for decades it should be viewedas a niche, mature market.

With the development of surface gravity gradiometry by companies such asLockheed Martin and Bell Geospace, gravity gradiometry measurements have beenused to provide a higher level of detail than was possible with traditional gravity.Airborne gravity gradiometry is on the rise but has not yet demonstrated its fullpotential to establish itself as a mainstream oilfield exploration technology.


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Bell Geospace has been using the Lockheed Martin FTG gravity gradiometersystem for about 20 years, but its commercial operations are limited. Arkex, aformer UK technology company, was one of the recent FTG users that packaged theLockheed Martin FTG system with magnetics, LIDAR and video to market theirBlueQube surveying technology. It conducted some commercial FTG-based sur-veys, but is no longer present in this market niche.

Surface gravity and, more particularly, surface gravity gradiometry have a majorconstraint—depth of investigation. The depth of investigation is determined by themass anomaly of the event and the effective sensitivity of the sensor. Only largeanomalies will be detectable as one goes deeper, thus the ‘marco’ constraint of thetechnology. The effective sensitivity of the sensor will not only be determined by theinherent performance of the sensor, but also by the environmental conditions.Surface noise may be a limiting factor, but where the sensor is moving the accuracyof the ‘land elevation’ will also be critical.

In the oil and gas industry there is a clear trend towards ‘deeper’, whether it bedeeper subsea or deeper below the surface/seabed. The easy or shallow oil and gashave generally been found. Gravity signals decay as a square of the distance from thesource. Gravity gradients decay as a cube of the distance from the source. Based onpublished data and industry discussions, in the majority of situations gravitygradiometry using existing mobile sensors will not provide useful data below 2000 m.Even at 2000 m it will require optimal scenarios such as large events and significantdensity differences. This is obviously a major generalization, but unless there is a changein true sensor performance, including the issues of noise and elevation, surface gravitygradiometry applications will be limited. The majority of today’s targets are at depthsgreater than 2000 m.

In deep water there would be significant benefits in deploying the sensor close tothe seabed and thus reducing the distance to the target. Many of the West Africandeepwater fields are relatively shallow in terms of depth below the seabed. Thereforethere may be an interesting market for deploying gravity gradiometers in an UAVfor surveying or permanently installing them on the seabed.

Downhole gravimeter versus gravity gradiometer marketThe LaCoste and Romberg gravimeter tool has existed since the 1980s, but themarket has never developed and today only three usable tools exist. The reasons whythe market has not developed are typically presented as follows.

• Only a limited number have ever been built.• The maximum deviation was limited to 15°.• The smallest OD was 4 1/8′, restricting the borehole size.• Stationary readings are taken with time intervals lasting up to 10 min.• The required accuracy of depth control between stations meant that stationsneeded to be far apart in order to reduce inaccuracies.

A new technology needs a compelling business case to succeed and, to date, nogravimeters have been able to deliver that case. If the case had existed, more toolswould have been built, R&D work would have been done to reduce the tool size, etc.


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Gravimeters give an average density all around the wellbore, and thus do not providethe detail required for useful interpretation. In addition, the vertical resolution islimited by depth control accuracy. The end result is that as a standalone tool it hasstruggled to showa compelling business case, except for use in niche applications. Thatsaid, Scintrex have recently developed the GRAVILOG technology so that a 1.9′ODtool exists that is reported to be capable of operating in deviations up to 60°. Micro-gand LaCoste reported a Bluecap™ tool that is designed for use in the petroleumindustry, with higher temperature and pressure ratings.

Gravity gradiometry brings two major advantages over gravimetry, and theseenable the creation of a compelling business case for downhole applications. Themeasurement is directional and there is no wire-line depth measurement accuracyconstraint. The other advantages, such as relative immunity to noise, higher spatialwavelength and the ability to operate horizontally are nice to have, but in themselveswill not deliver a compelling business case.

However, gravity gradiometry also has disadvantages compared to gravimetry. Itrequires asymmetry and therefore will not detect density boundaries in a perfectlysymmetrical environment, bulk density cannot be easily calculated from themeasurement as it is a second order function and the gravity gradient signal decaysas a cube function versus a square function for a gravimeter, thus reducing the depthof investigation for equivalent sensor performance. The ideal wellbore tool wouldprobably in the future incorporate both gravity gradiometry and a gravimeter. Threepotential subsurface applications or markets have been identified for a wellboregravity gradiometer.

• Reservoir fluid saturation monitoring.• Dipping bed determination.• Structural mapping.

Reservoir fluid saturation marketIn fluid saturation monitoring the gravity gradients are used to determine therelative percentages of water, gas and oil in the matrix remotely from the wellbore.The ability to ‘see’ deeper into the reservoir from the wellbore compared totraditional measurements and in a directional manner is the unique selling pointand, we hope, the compelling business case. The client niches are the reservoirengineering departments within oil companies.

Thermal decay tools (TDT) or carbon–oxygen tools are currently the primarysaturation monitoring tools available to reservoir engineers. They are run on electriclines and have a very shallow depth of investigation, typically a few centimetres. Theglobal market for TDT/CO tools is estimated to be worth $100 million per annum,with the major geographical markets being the North Sea and the Middle East.Production logging tools are used to determine flow rates and relative fluidpercentages in the wellbore. This is an aligned market with an estimated globalsize of $400 million per annum.

The ability to monitor saturation changes remotely from the wellbore has longbeen on oil companies’ technology wish lists. Casing resistivity has been developed


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in an attempt to address this, as have deep reading electromagnetic (EM) tools.However, these are constrained by the laws of physics governing current paths andin reality achieve depths of investigation of a maximum of 5 m.

The other major tools used by reservoir engineers for reservoir monitoring are:• pressure/temperature surveys;• four-dimensional (4D) seismic techniques.

In high-value wells pressure and temperature sensors will typically be perma-nently installed with a cable back to the surface. This gives nothing more than thepressure at the bottom of the well. The majority of subsea and offshore wells willhave this instrumentation installed and it is estimated to be a market worth $500million per annum. On land, where the access is easier and the well value is lower, itis more typical to run intermittent surveys on slick-line.

4D seismic was introduced as a time-lapse reservoir monitoring technique in thelate 1990s. Today the majority of 4D seismic is run in the North Sea, but it is gainingacceptance globally in offshore environments. Over 140 fields have had 4D surveysrun on them. Most surveys are towed arrays as per traditional 3D surveys, but thereis a small market for seabed deployed geophone arrays.

4D is estimated to be 5% of the overall seismic market ($15 billion), resulting in amarket size of $750 million. While 4D seismic has established itself as the tool ofchoice for monitoring saturation changes on a field scale it has limitations:

a) difficult to do on land;b) expensive;c) long turnaround time;d) lacks resolution at the reservoir level;e) does not work in all situations (e.g. Saudi Arabian carbonates).

There is no direct comparison to wellbore gravity gradiometry, however, if onewere to define the existing competition for wellbore gravity gradiometry as 4Dseismic, TDT/CO logging, deep reading electrical/EM and a fraction of theproduction logging and permanent monitoring markets (PMD), it is possible tosay that the present market for reservoir saturation monitoring is worth $1 billionper annum.

There are clearly unmet needs within this market and, therefore, new technologyhas the potential to grow this market further. Active management of reservoirs iscontinuing to grow in importance globally as oil companies strive to improve overallrecovery factors from the reservoir.

What percentage of this $1 billion market is market potential for GDI dependsheavily on the performance of the sensor and the accessibility of the wells.Accessibility is an issue as the cost of re-entering a subsea well can run intomillions of dollars and therefore electric line surveys are unlikely to be runroutinely, and as a result wire-line deployed time-lapse surveys are not practical.This can be resolved by permanently installing the sensor or an array of sensors in asimilar manner to PMD gauges. This has the added benefit that time averaging can


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be used to significantly improve the resolution of the sensor and thus the depth ofinvestigation.

With a sensor that has a usable resolution in the order of 20 eotvos one wouldprobably be competing with the TDT/CO technology and in a market worth$100 million. The better the performance of the sensor, the deeper it will readinto the formation, and the larger the slice of the $1 billion market the technologywill be able to compete in. Developing a sensor that can deliver sub-5 eotvosperformance in wire-line or permanently deployed forms will greatly increase boththe portion of market accessible to GDI and also the market size. It is worthremembering that (assuming that the non-mitigated noise is white) a 100 s stationwill provide an effective performance that is 10 times better than that for a 1 smeasurement. Therefore a 50 Eo/√Hz sensor will produce an effective resolutionof 5 eotvos for a 100 s station (wire-line application) or 0.5 eotvos for a 2.8 hmeasurement (PMD application).

The PMD application is interesting, as when it is combined with an intelligentwell it has the potential to revolutionize reservoir management. Today flow controldevices in intelligent wells are operated once water or gas has reached the wellbore.This is of benefit, but does not seem to be really intelligent. The ability to monitorthe movement of fluids distant from the wellbore would allow zones to be chokedback in order to actively manage the reservoir and thus improve overall recoveryfactors. For example, in a long horizontal well sensors could be used to monitorconing as it happens, either water up or gas down, and then alter the flow controldevice settings in order to prevent breakthrough at the wellbore. The ability to dothis would clearly differentiate a completion company from its competitors andprovide a game changing advantage.

A subset of the reservoir monitoring market is CO2 sequestration (Neill 2009b).CO2 sequestration is a hot topic for governments around the world. Capturing CO2

and injecting it subsurface represents a potentially viable means of managing theworld’s greenhouse gas issues. As such, multiple government-funded researchprojects are running on the subject. One of the critical issues with CO2 sequestrationis monitoring, measurement and verification (MMV). This means monitoring thespread of the CO2 plume within the reservoir and verifying that there are no leaksout of the reservoir. Permanently installed gravity gradiometers could be well suitedto this. While presently a limited science project, CO2 sequestration could become ahuge market. All the major service companies have now established CO2 initiatives,as have most of the major oil companies.

In order to understand the reservoir monitoring market better, modelling work isrequired. To date, only very basic modelling has been done and even time-lapsemode interpretation is unlikely to be straightforward. With the exception of largehomogeneous formations, the movement of water or gas through the reservoir israrely uniform. For example, varying permeability layers or stingers will createpreferential flow paths. The residual saturations will need to be assumed. There willstill be multiple variables and only one measurement leading to a solution that isnot fully constrained. At present there is no clear understanding regarding theseissues.


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In addition to understanding the market potential, it is critical to recognise themarket adoption factors. The oil industry is notoriously conservative in the adoptionof new technology and unfortunately a time-lapse technique would only make thatworse.

In the time-lapse mode a baseline survey is run and then a further survey isperformed some time later. The changes in gravity response can then be attributed tosaturation changes in the reservoir, as all other factors should stay the same. Onewould need compelling field examples in order to convince the majority adopters ofthe performance of the technology and, due to the time-lapse approach, this will takemore time than a single-run technology. Excitement over the size of the potentialmarket should be tempered by a recognition of the need to push the performance ofthe sensor below 5 eotvos and ideally towards 1 eotvos, and the likely slow adoptionof the technology for reservoir monitoring until a permanently deployed sensor isdeveloped.

Dipping bed determination marketWhile time-lapse saturation monitoring is likely to be the prime driver, there areother applications that may help adoption of the technology and add to the overallmarket potential. Initial modelling has shown that it should be possible to identifydipping beds and also the angle of dip from wellbore gravity gradients. At presentdipping beds are either identified at the micro level by electric line dip-meters orformation micro-scanners or on a field level by surface seismic. There is nomeasurement between these. The dip-meter will only see dipping beds as they crossthe wellbore and therefore is a limited ‘snapshot’. Interpretation of surface seismicinvolves iterative processes to best fit dipping beds. A structural dipping bedmeasurement that could be fed back into the surface seismic interpretation couldadd significant value in reducing the uncertainty of the seismic interpretation.

Apart from the initial modelling study and some discussions with clients, no workhas been done on this potential market. The dip-meter/formation micro-scannermarket is estimated to be worth $200 million per annum. Gravity gradienttechnology could only take a fraction of this, but it does represent another potentialmarket.

This market would be an open hole or exploration market. In a very similarmanner one could see the gravity gradiometer being run in open hole on explorationwells to determine whether there are any gravity anomalies or ‘sweet spots’ in thewellbore that would suggest a sidetrack should be drilled. For example, if the well isthe wrong side of a fault or there is a gas cap nearby. Again, no detailed work hasbeen done to determine whether this is a viable application.

Structural mapping marketClosely aligned with the dipping bed determination application is the structuralmapping application. This is where wellbore gravity gradiometry is used inconjunction with surface seismic and/or wellbore seismic to improve the mappingof features such as salt domes or in areas where surface seismic is of poor quality,such as sub-basalt fields.


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Other similar applications could be improving mapping sub-basalt structures insome plausible areas, mapping the edges of salt diapers and determining the edge ofthe salt for gas storage wells. These applications would comprise open-hole electric-line deployment, possibly in conjunction with a vertical seismic profile (VSP). TheVSP market is estimated to be worth $70 million per annum. The potential marketsize for gravity gradiometry is heavily dependent on the performance of the sensor.A 5 eotvos sensor could improve the definition of the base of the salt for 1500 maround the well. Improving this beyond 5 eotvos would obviously open up a largermarket.

1.4.3 Global positioning system (GPS)-free navigation

Passive navigation is a desirable tool for precise position determination in a situationwhere GPS-based standard navigation systems are no longer available. In themodern world, almost every moving carrier depends on GPS for position updates.A network of navigation satellites generates the GPS signals in a UHF band that arereceived on Earth by GPS receivers. The latter, in turn, convert the signals intoposition information, such as latitude, longitude, elevation above see level, speed,etc. However, one can imagine a number of situations in which GPS cannot work ifthe satellite signals are not available, say, due to a natural disaster or physicaljamming.

A GPS-free inertial navigation system (INS) that is totally independent of anyexternal conditions can be realised by using a gravity gradiometer that is capable ofbeing deployed in a strapdown mode, i.e. bolted down tightly to a moving carrier.The strapdown gravity gradiometer is still a ‘holy grail’ of passive navigation. Thechallengies associated with such a system are overhelming and, currently, there arenot any practical candidates among existing gravity gradiometers that can playthat role.

The first passive navigation system, which used gravity gradient map matchingtechniques, was discussed by Clive Affleck and Albert Jircitano of Bell AerospaceTextron (USA) (Affleck and Jircitano 1990). The system required no externalinformation, and was intended to be non-emanating and non-jammable. At theheart of the system was the Bell Airspace all-accelerometer rotating gravitygradiometer described in section 1.2. The basic principle is simply a real-timecomparison between measured gravity gradients and those stored in a ‘harddrive’.

David Gleason of the Air Force Phillips Laboratory (USA) published a detailedanalysys studying the integration of an INS and a gravity gradiometer for passive,purely autonomous navigation and terrain avoidance (Gleason 1995). In such aninertial gradiometer-aided system, navigation errors are bounded by passive updatesconsisting of real-time matches between the single flight-path profile of measuredgravity gradients and stored, constant-altitude grids of estimated gradients based onall available ground gravity, terrain elevation and mass density data.

Another self-contained, passive, jam-proof gravity gradiometer aided inertialnavigation system was proposed in Richeson and Pines (2007). The sensitivities of


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the system to variations in inertial measurement unit (IMU) quality, gravity field,noise, update rate and sensor type were investigated in detail along with a baselineINS/GPS system. A projected future gravity gradiometer system was shown to boundroot-mean-square (RMS) position error at 0.336 m, velocity errors at 0.0069 m s−1,and attitude errors at 0.00977°, which are comparable to an INS/GPS system with a10 s update rate.

Among the predictive-only multiple research papers published on this matter, onemay have a look at Zorn (2002), (Jekeli (2006) and Zhou et al (2016). There are notyet any published reports on testing a real alternative to INS/GPS aboard a movingcarrier, based on a fast-operating and sufficiently sensitive gravity gradiometer.

1.4.4 Underground tunnels and void detection

Shallow underground structures, such as empty cavities (bunkers), tunnels andvoids, are perfect targets for gravity gradiometers, as they create large negative massdensity contrasts, which, in turn, result in large gravity gradient anomalies abovethem.

A comparison of different gravimetric techniques, including gravity gradiometry,for measuring subsurface void signatures was published in Romaides et al (2001).The potential of gravity gradiometry in the detection of underground structures orvoids was demonstrated by conducting an experiment at an underground missilelaunch facility at Vandenberg Air Force Base, California (USA). Gravity data werecollected using a LaCoste–Romberg model G gravimeter and gravity gradientmeasurements were made using a vertical spin-axis Lockheed Martin-developedarms control verification gravity gradiometer (see figure 1.27).

Figure 1.27. A Lockheed Martin vertical spin-axis all-accelerometer gravity gradiometer for ground-basedapplications. Reproduced with permission from the Lockheed Martin Corporation.


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After performing all necessary corrections, the data were compared to modelledsignatures of the launch facility. Peak gravity and gravity gradient anomalies ofapproximately −75 μGal (1 μGal = 10−8 m s−1) and 30 eotvos, respectively, weremeasured over the centreline of the largest capsule. The presence of the buriedlaunch facility was apparent in the observed gravity and gravity gradient data. Thegravity gradients were unambiguous in resolving the underground facility’s signa-ture and thus revealing its location. In contrast, identifying the launch complexsolely from the gravity anomaly data would have proven difficult due to a strongregional trend across the target area.

A detailed theoretical analysis and modelling of gravity gradiometry data inrelation to subterranean void detection was published in Lockerbie (2014). Twogeneric types of gravitational source are analysed in detail, and compared: a cubicalsubterranean void, and a subterranean tunnel. A vectorial targeting method wasshown to work well with both types of finite target, picking out the centre of mass ofthe cubical source and the axis of the tunnel. Some unusual results were reported inconnection with the apparent length of the tunnel target, and limitations on theinformation that may be gleaned from the gravity gradient signals arising from bothtypes of target were discussed.

1.4.5 Cargo hidden masses detection

Gravity gradiometry can be used at ports and airports for static density signaturemonitoring of container cargo imports (to detect hazardous substances such asexplosives).

A stationary ground-based gravity gradiometer could be used in portal perimetermonitoring to detect gravitational effects produced by mass distributions ofshrouded containers or the contents of railcars and trucks moving through theportals, or in observations of missiles to determine the number of warheads theycarry or whether extraordinary shielding had been employed to block telltaleemissions of nuclear radiation. It could also be used in some circumstances todistinguish non-nuclear cruise missiles from cruise missiles carrying nuclear weaponsif measurements that used neutron or gamma-ray irradiation were considered toointrusive (Parmentala 1990).

A detailed consideration of using gravity gradiometry for imaging cargo contain-ers was given in Kirkendall et al (2007). The analysis was focused on developing thenecessary numerical algorithms and carrying out feasibility studies without beingconcerned with engineering, instrumentation and application issues. To obtainrealistic images with sharp boundaries, robust estimators were applied to the modelobjective function of the inversion operator and coupled with a Huber norm (Huber1964) to provide stable numerical computation. It was shown that it is possible toidentify high-density materials with a minimum volume of 15 cm3. In addition, therecovered density threshold to suggest the presence of high-density materials from anarbitrary recovered density model and two examples of recovering concealed fissilematerial from a cargo container were presented.


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1.4.6 Space missions

Gravity gradiometers desined for extraterrestrial applications have been underconsideration since 1964, when a final report on a study of specific methods formeasuring lunar gravity was released (Levenstein et al 1964). Interestingly enough, avibrating string gravity gradiometer had been considered to be the appropriatecandidate for space missions on the Moon. However, unlike Gravitec’s stringgravity gradiometer (see section 1.2.4), it contained two localised proof massesattached to a flexible string fixed at both ends. Further, permanent magnets wereused to create a feedback force upon the string provided there was an electric currentpassing through the string’s sections adjasent to the magnets. Similar to well-knownvibrating string gravimeters, with just a single test mass attached to a string, thevibrating string design based on two test masses was shown to be sensitive to thedifferential force acting on the masses. Therefore, the string’s natural vibrationfrequency was a function of a gravity gradient along the string’s length. This design,however, had never been implemented in a real spaceborne gravity gradiometersystem.

The first successful extraterrestrial gravity gradiometer mission, called GravityField and Ocean Circulation Explorer (GOCE), was launched in 2009 by theEuropean Space Agency. The GOCE spaceborne gravity gradiometer mission was aresult of many years of research and development carried out at ONERA, theFrench Aeronautics, Space and Defence Research Laboratory (Touboul 2003,Touboul et al 2004). The ONERA-developed electrostatic gravity gradiometer(EGG) consists of matched pairs of electrostatically suspended gold proof masses.Three orthogonal pairs of EGG accelerometers and a capacitive read-out system aremounted on the ultra-stable carbon–carbon honeycomb support structure (seetable 1.6).

Table 1.6. A summary of the performance parameters of the electrostatic gravity gradiometer used in theGOCE. Courtesy of eoPortal.

Type

Three-axis diagonal gradiometerBased on threepairs of electrostatic servo-controlled

accelerometers

Design bandwidth 5 × 10−3 to 10−1 HzBaseline length (distance between

accelerometers)0.5 m

Sensitivity (detection noise) measurementbandwidth (MBW) extended bandwidth(10−5 to 1 Hz)

<10−12 m s−2 Hz−1/2

<10−10 m s−2 Hz−1/2

Resolution of accelerometer measurements <2.0 × 10−12 m s−2 Hz−1/2

Proof-mass positioning error 6 × 10−8 m Hz−1/2

Absolute/relative scale factorsAbsolute/relative misalignment 10−3 rad/10−5 rad


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The principle of operation of these accelerometers is as follows. A proof mass iskept levitated in the centre of a slightly larger cage by electrostatic forces, i.e. byapplying so-called control voltages between the (eight) electrode pairs embedded inthe cage and the different faces of the square cuboid proof mass. These voltages arerepresentative of the accelerations seen by the proof mass and are the initial input toan elaborate chain of processing steps that ultimately lead to a fully fledged model ofthe gravity field. The requirements for the gradiometer are severe and stringent.

The accelerations measured by each accelerometer within a band-limited fre-quency range of 5–100 mHz can be as small as one part in 1013 of the gravitationalattraction experienced on Earth.

A special GOCE drag-free satellite has been designed by the European SpaceAgency in order to fulfil the extremely stringent requirements for its design andaccommodate the EGG (see figure 1.28). After launch, the GOCE satellite achievedan extremely accurate injection altitude of 283.5 km. It then began free-falling at arate of 150–200 m a day and continued to do so until it entered the drag-free mode atan altitude of 273 km. At this altitude, the satellite started to actively compensate forthe effect of air drag and its payload went through a further six weeks ofcommissioning and calibration. The GOCE mission had begun.

In 2013, after nearly tripling its planned lifetime, the GOCE completed its missionand reentered the Earth’s atmosphere. With a sleek, aerodynamic design—responsiblefor it being dubbed the ‘Ferrari of space’—GOCE has mapped variations in Earth’sgravity with extreme detail. Scientists further exploited these data to create the firstglobal high-resolution map of the boundary between Earth’s crust and mantle—calledthe Moho. The detection of sound waves from the massive earthquake that hit Japanon 11 March 2011 is among the results obtained. In mid-October 2013, the missioncame to a natural end when it ran out of fuel and the satellite began its descenttowards Earth from a height of about 224 km.

Figure 1.28. An ESA image showing the GOCE satellite cross-section and its payload. Reproduced withpermission from ESA.


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‘GOCE data, models, and applications: a review’ provides a review of the resultspresented at the GOCE Solid Earth workshop at the University of Twente (theNetherlands), where an overview was given of the present status of the data modelsand applications in relation to the one-of-its-kind GOCE mission (van der Meijdeet al 2015).

A new concept of gravity gradiometer, the GREMLIT, which uses the sametechnology as that developed for the GOCE satellite gravity mission, was proposedin Douch et al (2014). It is a scaled-down adaptation of the ONERA electrostaticplanar accelerometer technique, intended for airborne goophysical surveys.However, no reports supporting this proposal have been published.

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