Homomorphic deconvolution: Application to gravitational and magnetic field waveforms

Abstract

The gravitational and magnetic field waveforms which represent potential fields of geologic structures can be expressed as the sum of overlapping, delayed replicas of a certain basic waveform. Such field waveforms, therefore, can be thought of as the outcome of a convolutional process. One way of separating signals which have been combined through convolution or multiplication is by using a set of systems called homomorphic systems. A particular feature of the process called homomorphic deconvolution is that no previous assumption of the character or nature of the basic waveform need be made. It is this feature of homomorphic deconvolution which makes it attractive for applications to gravitational and magnetic field waveforms.