Of Poles and Zeros: Fundamentals of Digital Seismology

by F. Scherbaum

Overview

Digital signal processing has become an integral part of observational seismology. Seismic waveforms and the parameters commonly extracted from them are strongly influenced by the effects of numerous filters, both within the earth and within the recording system. With the advent of numerous software tools for the processing of digital seismograms, seismologists have unprecedented power in extracting information from seismic records. These tools are often based on sophisticated theoretical aspects of digital signal processing which, to be used properly, need to be understood. This book is aimed at observational seismologists and students in geophysics trying to obtain a basic understanding of those aspects of digital signal processing that are relevant to the interpretation of seismograms. It covers the basic theory of linear systems, the design and analysis of simple digital filters, the effect of sampling and A/D conversion, the calculation of ‘true ground motion', and the effects of seismic recording systems on parameters extracted from digital seismograms. It contains numerous examples and exercises together with their solutions.

Product Details

ISBN-13:	9780792340133
Publisher:	Springer Netherlands
Publication date:	05/31/1996
Series:	Modern Approaches in Geophysics , #15
Edition description:	Softcover reprint of the original 1st ed. 1996
Pages:	257
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

1 Introduction.- 2 RC Filter.- 2.1 The system diagram.- 2.2 The differential equation.- 2.3 The frequency response function and the Fourier transform.- 2.4 The transfer function and the Laplace transform.- 2.5 The impulse response function.- 2.6 The step response function.- 2.7 The frequency response function and the pole position.- 2.8 The difference equation.- 2.9 Review RC filter.- 3 General linear time invariant systems.- 3.1 Generalization of concepts.- 3.2 Graphical estimation of the frequency response function.- 3.3 The phase properties of general LTI system.- 3.4 The interpretation of the frequency response function.- 4 The seismometer.- 4.1 The solution for simple initial conditions.- 4.2 The determination of the damping constant.- 4.3 The frequency response function.- 5 The sampling process.- 5.1 The sampling of analog data.- 6 Analog-to-digital conversion.- 6.1 The principle of analog to digital conversion.- 6.2 Increasing dynamic range and resolution.- 7 From infinitely continuous to finite discrete.- 7.1 Fourier series for periodic continuous-time signals (CTFS).- 7.2 Fourier transform for aperiodic continuous-time signals (CTFT).- 7.3 Fourier transform of discrete-time signals.- 7.4 Fourier series for periodic discrete-time signals.- 7.5 The Discrete Fourier Transform (DFT).- 7.6 The z-transform and the discrete transfer function.- 7.7 The inverse z-transform.- 7.8 The z-transform and the Discrete Fourier Transform (DFT).- 7.9 The convolution of sequences.- 8 The digital anti-alias filter.- 8.1 Removing the maximum phase component of a FIR filter.- 9 Inverse and simulation filtering of digital seismograms.- 9.1 Stability problems.- 9.2 Implementation.- 9.3 Review inverse and simulation filtering.- 10 The measurement of wavelet parameters from digital seismograms.- 10.1 The determination of ground motion amplitudes.- 10.2 The properties of seismic onsets.- 10.3 Rise time and pulse duration.- 10.4 Signal moment.- References.- Appendix: Solution to problems.

Editorial Reviews

Based on a professional training course and a university course, introduces observational seismologists and students in geophysics to the principles and techniques of digital signal processing as it is increasingly being used to interpret seismograms. Covers the basic theory of linear systems, the design and analysis of simple digital filters, the effect of sampling and analog-digital conversion, calculating trueground motion, and the effects of seismic recording systems on parameters extracted from digital seismograms. Includes problems with their solutions. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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