An elongated cylinder, modelled as a polyhedron with polygonal ends and elongated rectangular side facets, leads to a growing numerical instability in the computed magnetic gradient anomaly as the curved surface is discretized more faithfully with increasing numbers of such facets. We exhibit this effect in model calculations, and demonstrate that our stabilized algorithm can mitigate the growth in numerical error. This study suggests that increasingly refined polyhedral target approximations come with a penalty: either the calculations are subject to increased destructive numerical noise, or there is increased computational burden from the use of stabilized numerical methods


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  1. Holstein, H. and Ketteridge, B.
    [1996] Gravimetric analysis of uniform polyhedra. Geophysics, 61, 357–364.
    [Google Scholar]
  2. Holstein, H., Schürholz, P., Starr, A. and Chakraborty, M.
    [1999] Comparison of gravimetric formulas for uniform polyhedra. Geophysics, 64, 1438–1446.
    [Google Scholar]
  3. Holstein, H., Sherratt, E. and Reid, A.
    [2007] Gravimagnetic field tensor gradiometry formulas for uniform polyhedra. Proceedings of the 77th Annual Meeting of the Society of Exploration Geophysicists (San Antonio, Texas).
    [Google Scholar]
  4. Strakhov, V., Lapina, M. and Yefimov, A.
    [1986] A solution to forward problems in gravity and magnetism with new analytical expressions for the field elements of standard approximating bodies I. Izvestiya, Earth Sciences, 22, 471–482.
    [Google Scholar]

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