During the last 15 years, more attention has been paid to derive analytic formulae for the
gravitational potential and field of polyhedral mass bodies with complicated polynomial
density contrasts, because such formulae can be more suitable to approximate the true
mass density variations of the earth (eg, sedimentary basins and bedrock topography) than
methods that use finer volume discretization and constant density contrasts. In this study, we
derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with …

ABSTRACT A new singularity-free analytical formula has been developed for the gravity
field of arbitrary 3D polyhedral mass bodies with horizontally and vertically varying density
contrast using third-order polynomial functions. First, the observation sites are moved to the
origin of the coordinate system. Then, the volume and surface integral theorems are invoked
successively to transform the volume integrals into surface integrals over polygonal faces
and into line integrals over the edges of the polyhedral mass bodies. Furthermore …