Eotvos (unit)

In free space, the gravitational gradient tensor has trace 0 by Poisson's equation, so the sum of gravity gradient along any three perpendicular directions is 0.

Near the surface of earth, the equipotential surface is nearly spherical, following the near-spherical shape of earth. Thus, the gravity gradient tensor has its three principal directions: a tensile direction along the local vertical direction, and two compressive directions perpendicular to the local vertical direction. The vertical tensile component gradient is ≈3,080 E (an elevation increase of 1 m gives a decrease of gravity of about 0.3 mGal). For a perfectly spherical earth, this value is theoretically ${\displaystyle |\partial _{r}g|={\frac {2GM}{R^{3}}}\approx 3080~\mathrm {E} }$. Since the equipotential surface is nearly spherical, the two compressive gradients are roughly half of that, at ≈1,540 E. Gravity gradiometry usually measures the perturbation away from this ideal value.

The effect of Earth's rotation creates an acceleration value of ${\displaystyle \omega ^{2}R\cos \phi }$, where ${\displaystyle \omega }$ is its angular velocity, and ${\displaystyle \phi }$ is the latitude. This perturbs the measured gradient. The maximal perturbation is obtained at the equator, with a value of ${\displaystyle \omega ^{2}\approx 5~\mathrm {E} }$.

Geological formations can modify the gradient. A mountain range, or an underground formation with increased density, is a large amount of mass that increases the tensile component of the gradient, and tilts the direction of tensile component towards the mass. An underground formation of decreased density, such as a salt dome or an oil formation, has the opposite effect.

In general, the gradiometric perturbation of a structure falls off as ${\displaystyle d^{-3}}$, so a structure of characteristic size ${\displaystyle r}$ buried ${\displaystyle d}$ underground produces roughly the same amount of perturbation at the ground surface as a structure of characteristic size ${\displaystyle kr}$ buried ${\displaystyle kd}$, for any ${\displaystyle k>0}$.

The Eötvös torsion balance was used in the exploration for oil and gas reservoirs during the 1918–1940 period. It could achieve 1–3 E in accuracy, but requires up to 6 h per station.^[7] Modern (2013) airborne systems can reach 3–6 E in rms accuracy at integration time of ≈6 seconds. Such a system achieves higher spatial resolution on slower aircraft, so the gradiometry maps have higher spatial resolution on zeppelins and helicopters than on fixed-wing aircraft. Spatial resolution is also higher for lower-flying aircraft.^[8]

• Gravimetry