A Discussion of the Bouguer Correction

The Bouguer correction of the gravity data of a thin-layered material is a classic topic of research that has been extensively investigated in the field of geodesy. In the case of a flat Earth model, the Bouguer slab formula $$2\pi G h$$ is often utilized, where $$h$$ denotes the height, $$\rho$$ denotes the density of the thin layer, and $$G$$ denotes the gravitational constant. In the case of a spherical thin layer, the effect of gravity is usually expressed by $$4\pi G\rho h$$ . Another Bouguer correction formula also exists, expressed by the spherical harmonics for an arbitrary inhomogeneous layer on the Earth’s surface, i.e., $$2\pi G\rho \sum [1 + 1/\left( {2n + 1} \right)]h_{{nm}} Y_{{nm}}$$ , where the thickness is expressed by spherical harmonic series $$Y_{{nm}}$$ with coefficient $$h_{{nm}}$$ . This implies that the geometric character of the thin layer exerts a significant influence on the Bouguer correction. To investigate the relationship between the three cases, we review and re-derive the three Bouguer correction formulae in detail using Newton's formula and the “Love numbers” mathematical framework, and thoroughly discuss the differences and relations between them from a mathematical and geodetic point of view. After that, we use different formulae and discuss three applications case by case. Finally, we give some suggestions for the use of the Bouguer correction formula in general.