Abstract

A signal in a non-dispersive reverberent environment can generally be represented as the sum of overlapping delayed replicas of a basic wave form. This convolutional data model has long been employed in seismic analysis and can be usefully extended for the analysis of gravity and magnetic potential field data along with a host of other geophysical measurements. The deconvolution of gravity or magnetic data requires the separation of two basic components of the potential fields: one component represents a basic irreducible wave form or signature of the potential field, and the other represents the position and scale or distribution of this wave form throughout the area of measurement. The basic wave form often derives from the process of geophysical measurement (e.g., the upward-continuation operator) but may also be due to an inherent, common character of the geological structure of an area.Oppenheim obtained the formalism for a generalized theory of superposition that allows for a description of the deconvolution process in terms of non-linear homomorphic transformations. These methods have already found application in the geophysical analysis of seismic data; it now provides a useful tool for the deconvolution of geophysical potential field data.

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