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SUPPLEMENTAL INFORMATION
S3.1. ANALYTICAL FORMULA FOR THE GRAVITATIONAL EFFECT
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)