Abstract
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.
Highlights
This paper is concerned with gravitational clutter in gravity surveys
Results are given for both the vertical component of gravity and the vertical gradient of the vertical component, with particular emphasis on the latter because of its relevance to the recent development of new, highly sensitive gradiometers based on cold-atom technology (Sorrentino et al 2014)
The theoretical results predict the statistical properties of the gravity signals from the statistical properties of the underground density variations
Summary
This paper is concerned with gravitational clutter in gravity surveys. Gravity surveys measure small variations in the Earth’s gravity, and these variations can provide information about the nature and structure of the Earth and the underground environment. Results are given for both the vertical component of gravity and the vertical gradient of the vertical component, with particular emphasis on the latter because of its relevance to the recent development of new, highly sensitive gradiometers based on cold-atom technology (Sorrentino et al 2014) These new instruments may find application in near-surface geophysical monitoring. The task is twofold: first, to relate the autocorrelation function of the gravity variations to the autocorrelation function of the underground density variations, and second, to produce a computer model which can generate Gaussian-distributed gravity data having the prescribed autocorrelation function.
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