Gravity anomaly

A difference between observed gravity and a specified reference field after stated reductions. Free-air, Bouguer and isostatic anomalies remove different modeled effects; they are not interchangeable raw measurements.

The absolute density difference between a subsurface body and the material it replaces, commonly in $\mathrm{kg}{\mathrm{m}}^{-3}$. It is the source term in local gravity inversion, unlike the dimensionless relative density contrast used in cosmology.

The correction to moving-platform gravity for the change in apparent vertical acceleration caused by motion over the rotating Earth. Eastward motion generally lowers apparent gravity and requires a positive correction; latitude and platform speed enter the full expression.

A regional planetary mass concentration producing a gravity anomaly; lunar examples are associated with large impact basins.

A spectral transfer estimate $Z(k)=⟨g_k{h}_k^{\ast }⟩/⟨|h_k{|}^2⟩$. Its wavelength dependence constrains compensation, density structure and support, but one transfer curve does not uniquely determine them.

The narrow volcanic ridge loads the lithosphere and generates a regional flexural response, while the broad swell involves deeper support. The observed positive ridge anomaly, negative flanks, outer positive belt, and long-wavelength positive swell anomaly probe distinct spatial scales.^[ref]

The Hawaiian swell is the broad elevation of the seafloor on which the narrower Hawaiian volcanic ridge sits. These are different spatial scales: the volcanic load bends the lithosphere through lithospheric flexure, while the broad elevation requires an explanation for deeper or more distributed support.

Ship and submarine gravity measurements show a long-wavelength positive anomaly correlated with the swell, distinct from the larger local ridge and flanking anomalies. The original analysis found that ridge crustal structure alone was unlikely to explain the long-wavelength signal and discussed compensation associated with flow beneath the lithosphere.^[ref] Combining gravity-topography admittance with other observations helps test support models; topography alone does not uniquely identify a deep mass density distribution.

For cross-spectrum $S_{gh}$ and autospectra $S_{gg},S_{hh}$, squared coherence is $|S_{gh}{|}^2/(S_{gg}{S}_{hh})$. It measures the fraction of spectral association between gravity and topography. Low coherence can signal uncorrelated internal loading, noise or shortcomings of a simple surface-load model; interpreting it as elastic thickness requires a loading model.

For a surface load above a uniform-density crust over a denser substrate, a simple lithospheric flexure model gives the indicated gravity-topography admittance, with ${\ell }_f^4=D/[g({\rho }_m-{\rho }_c)]$. The surface mass contributes positive gravity; downward displacement of the density interface contributes a compensating negative signal attenuated by $e^{-kt}$. Hence $Z\to 0$ at long wavelength and $Z\to 2\pi G{\rho }_c$ at short wavelength. Here $t$ is the interface depth, not automatically the effective elastic thickness.

A gravity anomaly after removing an approximate topographic mass contribution, often an infinite slab $2\pi G\rho h$, in addition to free-air reduction. Terrain and spherical-curvature corrections refine the slab model.

An ideal laterally infinite horizontal slab, whose vertical gravity anomaly is proportional to its thickness $h$ and geophysical density contrast $\Delta \rho$ with replaced material. A negative geophysical density contrast gives a negative anomaly in a downward-positive convention. The slab's field above it does not specify burial depth; applying it to finite bodies is an approximation.

A correction for the difference between real surrounding relief and the assumed simple topographic slab. Its computation needs terrain geometry and an assumed density, and can matter in rough surface topography.

gravity reduced to a reference elevation while retaining the gravitational contribution of the intervening topographic mass. The local elevation correction is approximately $2gh/R$ for a spherical reference, with sign chosen to undo the measured decrease with height.

The adjustment for measurement elevation without adding or removing the attraction of intervening terrain. Near sea level a station $h$ metres above a datum receives an approximate $+0.3086h\mathrm{mGal}$ correction when reduced to that datum.