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On gravity response over vertical cylinder: some notes

Roy Indrajit Ghosh

Acta Geophysica

2023

Vol. 71, no. 6

2663--2673

The aspects of gravity modelling with a semi-infinite vertical line of mass as an approximation to the model of semi-infinite vertical cylinder is critically reviewed. The brief outline of the derivations of gravity response due to both type of models, such as the semi-infinite vertical line of mass and vertical right circular cylinder, is given. The model of semi-infinite vertical right circular cylinder provides no closed form formula to compute gravity response on a free horizontal surface, and the ensuing formulation is comprised of elliptic integrals of the first and second kinds. On the other hand, there exists closed form formula of computing gravity response due to semi-infinite vertical line of mass that approximates closely to the semi-infinite vertical thin rod. Assessment on the limitation of replacing vertical cylinder model by vertical line of mass both by rigorous theoretical discourse and numerical tests is made. It is shown via numerical experiment that if the radius of cross section of the vertical right circular cylinder is one-tenth of its depth of burial, then the approximation of line of mass model would provide reasonably accurate results in the order of 10-4.