Gravity Methods
2.4 Gravity meters
2.4.3 Marine and airborne gravity systems
Box 2.8 Determination of g using a vibrating string
Gravity= 4×string length2×frequency2×string mass suspended mass
g = 4L2f 2ms
M
quartz construction makes it much easier to reduce thermal effects.
Indeed, the whole assembly is housed in a glass vacuum flask and some models have an electrical thermostat. As the spring cannot be clamped, the Worden gravimeter is sensitive to vibration and has to be transported extremely carefully. The range of the instru- ment is about 20,000 g.u. (2000 mGal) with an accuracy to within 0.1–0.2 g.u. (0.01–0.02 mGal). However, quartz gravimeters such as the Worden can be quite difficult for inexperienced operators to read and a realistic accuracy may be more like 1 g.u. (0.1 mGal).
The Worden gravimeter has two auxiliary springs, one for coarse and the other for fine adjustments.
2.4.2.5 Vibrating string
The earliest vibrating string gravimeter was developed in the 1940s and consisted of a central element of flat beryllium-copper ribbon about 50 mm long, suspended in the field of a permanent magnet, with a 65 g mass at its lower end (Gilbert, 1949). More modern instruments have been based on one, two or three strings (Jones, 1999). If a mass is suspended on a fibre which is forced to oscil- late by an a.c. circuit, then the frequency of vibration, which can be measured electronically, will vary with changes in gravity. For a fibre of length L, and mass per unit length ms, from which a mass M is suspended, by measuring the frequency of vibration (f ), gravity can be determined (Box 2.8). However, the technology is not sufficiently developed to provide the same resolution and accu- racy as other gravimeters, but it does give the impression that even more compact and lightweight gravimeters may be forthcoming in the future. Vibrating string gravimeters have tended to be used on shipborne platforms in marine gravity surveys where gravity can be measured to an accuracy of better than 1 mGal in moderate sea conditions. However, such instruments are subject to erratic drift.
Such instruments are likely to be superseded by Full Tensor Gravity Gradiometers (TFGs) (see Section 2.4.3) in marine gravity surveys.
(B)
Stabilising fin
Glass flotation
Spherical pressure cases
Lifting bail
Adjustable pivot
Syntactic foam
Tow bridle
Beam clamp motor Gimbal clamp
Gravity sensor Gimbal
frame
Torque motor
Counter weight
Aft pressure case
Flotation
Pressure gauge
Power supplies Inverter
Gravity meter
interface Multi-task computer Compass
Tilt sensor
Internal pressure
Temp Forward pressure case
A/D converter
Telemetry Co-axial tether (A)
Figure 2.15 (A) A block diagram of the towed gravity meter and (B) a schematic illustration showing the major exterior components. The gravity meter used is a modified LaCoste & Romberg Model S. After Zumberge et al. (1997), by permission.
beam-type gravity meters. Its accuracy at sea is typically less than 1 mGal and has a range of 7000 mGal, and for airborne systems the range is 10,000 mGal. Like many other systems it also utilises the UltraSysTMplatform and sensor control functions.
Permanent magnet Coil Induced magnetic field Permanent magnetic field Permanent magnet Servo
loop DC
current
Figure 2.16 The principle of operation of the accelerometer unit of the Bell marine gravimeter. After Bell and Watts (1986), by permission.
In the last ten years some military technology has been declassi- fied for civilian purposes, enabling significant technological benefits to become available commercially. For example, a system developed by the USA government and Lockheed Martin Federal Systems as a stealth navigation system for Trident-class nuclear-powered sub- marines has been modified for use in exploration for hydrocarbons and minerals (Eaton, 2003). The instrument is a gravity gradiome- ter, typically weighing around 450 kg and costing several million dollars, and is usually mounted on the most stable part of an air- craft’s interior.
The instrument comprises four pairs of opposing accelerome- ters mounted on a rotating disc (Figure 2.17). When airborne and in motion, the linear inertial acceleration is cancelled out. The gravity gradient is measured in the plane of the rotating disc and represents the difference between values measured by two oppos- ing accelerometers. FALCON, the world’s first airborne gradiome- ter, began commercial production in 1999 following a decade-long
$30 million investment programme by BHP Billiton and Lockhead Martin. The system is being flown under contract from BHP Billiton by Fugro.
X axis
Y axis Z axis
Accelerometers
A2
B3 A3 B1 B4 A1
A4 B2
2r
Figure 2.17 Opposing pairs of accelerometers are mounted on a horizontal disc that rotates at a specified frequency. Another set of accelerometers (the B set) doubles the measured gradients.
After Eaton (2003), by permission.
The Lockheed Martin gradiometer has also spawned another offspring to compete with the FALCON. In February 2003, Bell Geospace announced its commercialisation of its Air-FTGTMsystem which is based upon Bell Geospace’s Full Tensor Gradient (3-D FTG) acquisition system. The 3-D FTG system measures three gravity vec- tors (in x, y and z directions) and three tensors for each vector – each vector has three coordinate components (Gx, Gyand Gz; Fig- ure 2.18). By measuring the rate of change of the three components of the gravity vector, the tensor gradient is obtained (Box 2.9). This produces nine measured components. However, of the nine, five gradients are independent and four are redundant. The x-direction measures east–west gradients, the y-direction north–south. The
x direction
y direction Three components
of gravity vector
Gyx
Gzx
Gxz
Gyz
Gzy Gxy
z direction
Gx Gy
Gz
Figure 2.18 Description of the relationship between gravity vectors and the tensor components. After Hammond and Murphy (2003), by permission.
Box 2.9 Tensor gravity gradients (see Figure 2.18)
A nine-component symmetric tensor that defines the rate of change of the three components of the gravity gradient is given by:
Ti,j=
⎡
⎣Txx Txy Txz
Tyx Tyy Tyz
Tzx Tzy Tzz
⎤
⎦
The independent gradients are shown in bold; the redundant tensor gradients are:
Txy=Tyx
Txz=Tzx
Tyz=Tzy
Tzz= −(Txx+Tyy) (From Hammond and Murphy, 2003)
z-direction is vertical and most closely represents geological struc- tures. Bell’s shipborne 3-D FTG system was first used in commercial surveys in 1999. Physically the acquisition system comprises three rotating disks (gravity gradiometer instruments, GGIs) each con- taining two pairs of orthogonally mounted accelerometers (Figure 2.19). Each GGI is rotated at a set frequency to avoid bias in the measurement in the direction of the primary components. The dif- ference in the gravity field sensed by each pair of accelerometers is used to compensate for most of the turbulence experienced by the aircraft. This also helps to retain the high frequency signal that is essential to provide the high quality of data required for mineral ex- ploration. The FTG system is normally positioned near to the centre of pitch, roll and yaw of the aircraft (currently a Cessna Grand Car- avan 208B), thus minimising rotational accelerations. Survey flying heights as low as 80 m and line spacings in the range of 50 m to 2000 m are usual, depending upon the type of target and the style of survey being undertaken.
12 Accelerometers, 3 Disks
y axis
Spin axis
x axis
a2 a4
a3 a1
Figure 2.19 Bell Geospace’s 3-D FTG systems consists of three gravity gradiometer instruments (GGIs). Internal to each GGI is a rotating disk with four accelerometers. After Hammond and Murphy (2003), by permission.
The Lockheed Martin gradiometer system has also generated an- other new entry to the airborne gravity gradiometry arena in the form of a modified FTG system based upon a levitated supercon- ducting proof mass. The principle of the system relies upon the fact that a superconducting proof mass can be levitated by passing currents through coils close to its surface in a module operated at
−269◦C. The motion of the levitated mass can then be monitored and controlled without the complications of physical attachments required to constrain the motions of a physical spring. The advan- tage of this system is that it should have unprecedented sensitivity, resolution and stability, postulated by its developers to be almost an order of magnitude more sensitive than current systems. The Ex- ploration Gravity Gradiometer (EGG), as it is known, entered into commercial service in the first quarter of 2006 operated by Fugro Airborne Surveys on behalf of its developers ARKex, Cambridge, UK. For more details of this system, see the paper by Lumley et al.
(2008, accessible from www.arkex.com).
Airborne gravimetry has been used extensively since 1977, ini- tiated by the Soviets (Aleshkova et al., 2000), in investigating the subglacial environment in polar regions. During the 1990s more than 275,000 km of data were collected by USA researchers using a DHC-6 Twin Otter aircraft using either a Bell Aerospace BGM-3 marine gravimeter or a LaCoste & Romberg S-gravimeter modified by ZLS Corporation (Blankenship et al., 2001). Similarly, European and Australian researchers (Jones et al., 2002; McLean and Reitmayr, 2005) have used LaCoste & Romberg air/sea gravimeters and a ZLS Ultra-Sys LaCoste & Romberg air/sea gravimeter, respectively. In 2007 tests were undertaken to compare different airborne gravime- ter systems with the potential of producing higher resolution data in polar regions whilst improving flight efficiency (Studinger et al., 2008). Studinger and colleagues tested an AIRGrav system (Sander Geophysics Ltd) and a Canadian Micro Gravity (CMG) GT-1A sys- tem (based on Russian Federation technology) on a DHC-6 Twin Otter, flying both systems side by side.
The CMG GT-1A system comprises an airborne, single-sensor, vertical scalar gravimeter with a Schuler-tuned three-axis inertial platform (Gabell et al., 2004). The Sanders AIRGrav system con- sisted of a three-axis stabilised inertial platform using three orthog- onal accelerometers and two two-degrees-of-freedom gyroscopes (Sander et al., 2004). It was found that both systems would allow broader potential applications for polar use compared with the pre- viously used BGM-3 and LaCoste & Romberg gravimeters. Of the two instruments tested against each other, the AIRGrav system was found to have a lower noise level and greater accuracy and to be less sensitive to changing flight conditions than the GT-1A system.