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 3 × 3 tensor; it is given in coordinates by the Jacobian matrix of the acceleration vector ( g = [ g x g y g z ] T {\displaystyle g=[g_{x}g_{y}g_{z}]^{\text{T}}} ), totaling 9 scalar quantities: G = ∇ g = [ ∂ g x / ∂ x ∂ g x / ∂ y ∂ g x / ∂ z ∂ g y / ∂ x ∂ g y / ∂ y ∂ g y / ∂ z ∂ g z / ∂ x ∂ g z / ∂ y ∂ g z / ∂ z ] {\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).