Terrace-function inversion for three-dimensional modelling of potential-field data

Abstract

A recursive operator based on evaluation of the sense of local curvature, named the 'terracing operator', transforms smoothly varying potential-field data into a step function, consisting of steeps and flats. The terraced function, rescaled to units of physical property, provides a first approximation for data inversion from which a satisfactory final solution is quickly derived. The method is directly applicable to gravity data and can be applied to aeromagnetic data that have been transformed to pseudo-gravity. The objectives of the method are somewhat akin to those of susceptibility mapping, but differ in that the terraced function, like a geologic map, favours uniform physical property domains with sharp domain boundaries. It suppresses both ringing at the boundaries due to Gibbs' phenomenon (an advantage) and gradational physical property variation (possibly a disadvantage).