The digital revolution has replaced traditional recording in the form of graphs on paper with numbers written to some form of magnetic or optical recording. Digital data can be processed to emphasise some aspect of the signal, an enormous advantage over paper records. For the student, the digital revolution has meant learning a whole host of new techniques, most of them based on quite advanced mathematics. The main purpose of this book is to provide the student of geophysics with an introduction to these techniques and an understanding of the underlying philosophy and mathematical theory.

The book is based on two courses taught to Bachelors and Masters students at Leeds over the past 10 years, one on Time Series in the second undergraduate year and one on Inversion in the third. The 3-year degree programme in the UK presents a problem: the techniques must be learnt in the second year if they are to be applied in the third. Time series analysis relies heavily on Fourier analysis, and although second year students have met Fourier series they have not met the Fourier integral theorem. This book makes a virtue of necessity by avoiding the Fourier integral transform and using only the discrete transform, for which we only need the sum of a geometrical series. I have come to see this as an advantage because modern data come in a discrete form, rather than as continuous functions, and are finite in duration, rather than going on forever.