Gravity gradiometry is the study and measurement of variations in the acceleration due to gravity. The gravity gradient is the spatial rate of change of gravitational acceleration.

Gravity gradiometry is used by oil, gas and mining companies to measure the density of the subsurface, effectively the rate of change of rock properties. From this information it is possible to build a picture of subsurface anomalies which can then be used to more accurately target oil, gas and mineral deposits. It is also used to image water column density, when locating submerged objects, or determining water depth (bathymetry).

Gravity gradiometers measure the spatial derivatives of the gravity vector. The most frequently used and intuitive component is the vertical gravity gradient, Gzz, which represents the rate of change of vertical gravity (gz) with height (z). It can be deduced by differencing the value of gravity at two points separated by a small vertical distance, l, and dividing by this distance. $G_{zz} = {\partial g_z\over \partial z} \approx {g_z \left (z + \tfrac{l}{2} \right ) - g_z \left (z - \tfrac{l}{2} \right )\over l}$

The two gravity measurements are provided by accelerometers which are matched and aligned to a high level of accuracy.

### Units

The unit of gravity gradient is the Eotvos, which is equivalent to 10-9 s-2 (or 10-4 mGal/m). A person walking past at a distance of 2 metres would provide a gravity gradient signal approximately one Eotvos. Mountains can give signals of several hundred Eotvos.

Full tensor gradiometers measure the rate of change of the gravity vector in all three perpendicular directions giving rise to a gravity gradient tensor (Fig 1).

Fig 1. Conventional gravity measures ONE component of the gravity field in the vertical direction Gz (LHS), Full tensor gravity gradiometry measures ALL components of the gravity field (RHS)

### Comparison to gravity

Being the derivatives of gravity, the spectral power of gravity gradient signals is pushed to higher frequencies. This generally makes the gravity gradient anomaly more localised to the source than the gravity anomaly. The table (below) and graph (Fig 2) compare the gz and Gzz responses from a point source,

Signal $${GM\,z \over \left ( r^2 + z^2 \right ) ^{3/2}} \times 10^5 \; \left [ \text{mGal} \right ]$$ $${GM \left (r^2 - 2z^2 \right ) \over \left ( r^2 + z^2 \right ) ^ {5/2}} \times 10^9 \; \left [ \text{E} \right ]$$
Peak signal (r = 0) $${GM \over z^2} \times 10^5$$ $${2GM \over z^3} \times 10^9$$
Full width at half maximum $$1.53 \, z$$ $$\approx z$$
Wavelength (λ) $$3.07 \, z$$ $$2 \, z$$
Fig 2. Vertical gravity and gravity gradient signals from a point source buried at 1 km depth

Conversely, gravity measurements have more signal power at low frequency therefore making them more sensitive to regional signals and deeper sources.

## Dynamic survey environments (airborne and marine)

The derivative measurement sacrifices the overall energy in the signal, but significantly reduces the noise due to motional disturbance. On a moving platform, the acceleration disturbance measured by the two accelerometers is the same so that when forming the difference, it cancels in the gravity gradient measurement. This is the principle reason for deploying gradiometers in airborne/marine surveys where the acceleration levels are orders of magnitude greater than the signals of interest. The signal to noise ratio benefits most at high frequency (above 0.01 Hz), where the airborne acceleration noise is largest.

## Applications

Gravity gradiometry has predominately been used to image subsurface geology to aid hydrocarbon and mineral exploration. Over 2.5 million line km has now been surveyed using the technique.[1] The surveys highlight gravity anomalies that can be related to geological features such as Salt diapirs, Fault systems, Reef structures, Kimberlite pipes, etc. Other applications include tunnel and bunker detection[2] and the recent GOCE mission that aim to improve the knowledge of ocean circulation.

The Lockheed Martin gravity gradiometer is based on a classified system originally developed by the US Defence Department[3] and deployed on US Navy Ohio Class Trident submarines designed to aid covert navigation. The existence of the gravity gradiometer was famously exposed in the film “The Hunt for Red October”. The system was declassified and in 1994 and adapted for mineral exploration.

There are two types of Lockheed Martin gravity gradiometers currently in operation: the 3D FTG, (Full Tensor Gravity Gradiometer, deployed in either a fixed wing aircraft or a ship) and the FALCON gradiometer (a partial tensor system with 8 accelerometers and deployed in a fixed wing aircraft or a helicopter). The 3D FTG system contains three Gravity Gradiometry Instruments (GGI’s), each consisting of two opposing pairs of accelerometers arranged on a spinning disc with measurement direction in the spin direction.

Electrostatic Gravity Gradiometer This is the gravity gradiometer deployed on the European Space Agency’s GOCE mission. It is a three-axis diagonal gradiometer based on three pairs of electrostatic servo-controlled accelerometers.

Superconductive Gravity Gradiometer An evolution of technology originally developed for the afore mentioned European Space Agency mission, the EGG, (Exploration Gravity Gradiometer), developed by ARKeX, uses two key principles of Super Conductivity to deliver its performance: the “Meissner_effect”, which provides levitation of the EGG proof masses and “flux quantization”, which gives the EGG its inherent stability. The EGG has been specifically designed for high dynamic survey environments.

Ribbon Sensor Gradiometer The Gravitec gravity gradiometer sensor consists of a single sensing element (a ribbon) that responds to gravity gradient forces. It is designed for borehole applications.

UWA Gravity Gradiometer The UWA Gravity Gradiometer uses an orthogonal quadrupole responder (OQR) design based on pairs of micro-flexure supported balance beams.

## References

1. Gravity Gradiometry Today and Tomorrow, South African Geophysical Association, retrieved 2011-06-27
2. Using Gravity to Detect Underground Threats, Lockheed Martin, retrieved 2011-06-27
3. Gravity gradiometry developments at Lockheed Martin, European Union of Geosciences, retrieved 2011-06-27