Modelling the gravitational effects of random underground density variations

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A mathematical model for small-scale spatial variations in gravity above the Earth’s surface is presented. Gravity variations are treated as a Gaussian random process arising from underground density variations which are assumed to be a Gaussian random process. Expressions for two-point spatial statistics are calculated for both the vertical component of gravity and the vertical gradient of the vertical component. Results are given for two models of density variations: a delta correlated model and a fractal model. The effect of an outer scale in the fractal model is investigated. It is shown how the results can be used to numerically generate realisations of gravity variations with fractal properties. Such numerical modelling could be useful for investigating the feasibility of using gravity surveys to locate and characterise underground structures; this is explored through the simple example of a tunnel detection scenario.
Original languageEnglish
JournalMathematical Geosciences
Early online date9 Oct 2019
Publication statusE-pub ahead of print - 9 Oct 2019


  • Gravity sensing
  • Near-surface geophysics
  • Gravity gradiometry
  • Fractal gravity
  • Random density variations
  • Forward modelling


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