Adaptive approaches to signal enhancement and deconvolution (with particular reference to reflection seismology)

Abstract

Deconvolution and signal enhancement are important aspects of digital
signal processing. Many techniques have been developed to achieve these
twin aims, the vast majority however were designed to deal with stationary
signals. However, many practically occurring signals are significantly
non-stationary and these techniques are rendered at least partially
ineffective.

This thesis is devoted to the study of adaptive techniques, these form a
class of methods which are specifically designed to give the flexibility
to deal with non-stationarity. The thesis demonstrates the value of
adaptive approaches to problems of deconvolution and signal enhancement,
particularly in reflection seismology. Adaptive processes are divided
into two classes - modelled and empirical. The power of both these
approaches is demonstrated by concentrating primarily on one algorithm of
each class. In the case of the modelled approach the technique chosen is
a recent approach to deconvolution based on the methods of optimal control.
The method is redeveloped in discrete-time, the theory is extended to
include the important problem of noise reduction in deconvolution, and for
the first time, the method is applied to physical problems. The principal
application is to the deconvolution of seismic data incorporating both
stationary and non-stationary models. A second application is to the
deconvolution of data derived from a velocity meter.

The empirical approach to adaptive processing is illustrated by the so-called
LMS (least mean-square) algorithm. The theory of this method is
rationalised and extended both for broadband inputs, particularly for the
important area of non-stationary random processes, and for narrowband inputs.
Two new configurations of the LMS algorithm are introduced for signal
enhancement. One, dubbed the generalised comb filter is designed for the
enhancement of signals which may be considered to consist of a series of
slowly time-varying wavelets of unknown form, recurring at roughly constant
intervals and embedded in random noise with unknown properties. The theory
of this method is developed and the technique is applied to the enhancement
of voiced speech and to the enhancement of seismic signals. This seismic
enhancement has two forms - one for highly reverberant single-channel
seismic data, and the other for enhancing multi-channel data. The second
novel configuration of the LMS is in the form of a sparse adaptive filter,
that is one with relatively few coefficients in relation to its length,
with the objective of signal enhancement by cancellation of multiple
interfering sinusoids. This technique is also applied to the problem of
speech enhancement.

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