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In the supplemental information, the analytical formula for the gravitational attraction of a rectangular prism is presented. They are necessary to calculate the gravity parts of the design matrix (equation 3.7) and the gravitational attraction by the topography (Δg _terrain in equation 3.5).

The analytical integration of equation 3.7 is complicated. The problem is rather simplified by assuming that the observer is located at the origin of the Cartesian coordinate system (Figure S3.1). Equation 3.7 then is reduced to the form

(S3.1)

The analytical solution is provided by many authors (e.g., Nagy, 1966; Plouff, 1977). Especially among them, Plouff’s solution is rather simple:

(S3.2)

where and s = s _i s _j s _k with s ₁ = −1 and s ₂ = +1. This formula provides the gravity kernel written in equation 3.7. When the elevation model is provided in a rectangular grid, the gravitational attraction of the topography is calculated easily just by summing up all the gravitational contributions of prisms in each grid.

Figure S3.1 Geometry of a rectangular prism and its gravitational attraction.