Gravity gradiometry

Gravity gradiometry is the study of variations (anomalies) in the Earth's gravity field via measurements of the spatial gradient of gravitational acceleration. The gravity gradient tensor is a 3x3 tensor representing the partial derivatives, along each coordinate axis, of each of the three components of the acceleration vector (${\displaystyle g=[g_{x}g_{y}g_{z}]^{T}}$), totaling 9 scalar quantities:

${\displaystyle G=\nabla g={\begin{bmatrix}\partial {g_{x}}/\partial {x}&\partial {g_{x}}/\partial {y}&\partial {g_{x}}/\partial {z}\\\partial {g_{y}}/\partial {x}&\partial {g_{y}}/\partial {y}&\partial {g_{y}}/\partial {z}\\\partial {g_{z}}/\partial {x}&\partial {g_{z}}/\partial {y}&\partial {g_{z}}/\partial {z}\end{bmatrix}}}$

It has dimension of square reciprocal time, in units of s^-2 (or m ⋅ m^-1 ⋅ s^-2).

Gravity gradiometry is used by oil and mineral prospectors to measure the density of the subsurface, effectively by measuring the rate of change of gravitational acceleration due to underlying 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). Physical scientists use gravimeters to determine the exact size and shape of the earth and they contribute to the gravity compensations applied to inertial navigation systems.