Advances in Geophysics

by Dmowska; Saltzman

• ISBN13: 9780120188406
• ISBN10: 0120188406
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-06-14
• Publisher: Elsevier Science

Summary

Advances in Geophysics, Vol. 40 systematically compares many of the currently used statistical approaches to time series analysis and modeling to evaluate each method's robustness and application to geophysical datasets. This volume tackles the age-old problem of how to evaluate the relative roles of deterministic versus stochastic processes (signal vs noise) in their observations. The book introduces the fundamentals in sections titled "1.2 What is a Time Series? " and "1.3 How is a Time Series Quantified?", before diving into Spectral Analysis, Semivariograms, Rescaled-Range Analysis and Wavelet Analysis. The second half of the book applies their self-affine analysis to a number of geophysical time series (historical temperature records, drought hazard assessment, sedimentation in the context of hydrocarbon bearing strata, variability of the Earth's magnetic field). This volume explores in detail one of the main components of noise, that of long-range persistence or memory. The first chapter is a broad summary of theory and techniques of long-range persistence in time series; the second chapter is the application of long-range persistence to a variety of geophysical time series.

Table of Contents

Contributors	vii
Preface	ix
Self-Affine Time Series: I. Generation and Analyses
Bruce D. Malamud
Donald L. Turcotte
Introduction	1	(18)
Brief Overview of Article	1	(1)
What Is a Time Series?	2	(1)
How Is a Time Series Quantified?	3	(3)
Autocorrelations and Semivariograms	6	(4)
Self-Affine Fractals	10	(3)
Gaussian White Noises and Brownian Motions	13	(6)
Spectral Analysis	19	(16)
The Fourier Transform	19	(3)
The Power-Spectral Density	22	(6)
The Relation of β, Ha, and D	28	(3)
Weak vs Strong Persistence	31	(1)
Spectral Variance and Leakage	32	(3)
Synthetic Fractional Noises and Motions	35	(16)
What Are They?	35	(1)
Spectral Analysis	35	(8)
Method of Successive Random Additions	43	(4)
Semivariograms	47	(4)
Log-Normal Noises and Motions	51	(7)
Log-Normal Distributions	51	(2)
Fractional Log-Normal Noises and Motions	53	(1)
Spectral Analysis	53	(3)
Semivariograms	56	(2)
Rescaled-Range (R/S) Analysis	58	(6)
The Method	58	(4)
Applications to Fractional Gaussian Noises and Motions	62	(2)
Applications to Fractional Log-Normal Noises and Motions	64	(1)
Average Extreme-Value Analysis	64	(7)
The Method	64	(2)
Applications to Fractional Gaussian Noises and Motions	66	(4)
Applications to Fractional Log-Normal Noises and Motions	70	(1)
Wavelet Analysis	71	(8)
The Method	71	(1)
Applications to Fractional Gaussian Noises and Motions	72	(3)
Applications to Fractional Log-Normal Noises and Motions	75	(4)
Summary	79	(12)
Acknowledgments	83	(1)
Appendix	83	(4)
References	87	(4)
Self-Affine Time Series: II. Applications and Models
Jon D. Pelletier
Donald L. Turcotte
Introduction	91	(1)
Natural Variability of Climate	92	(25)
Temperature Spectra	92	(6)
River-Discharge and Tree-Ring Spectra	98	(2)
Stochastic Diffusion Model	100	(14)
Variations in Solar Luminosity	114	(1)
Drought Hazard Assessment	115	(2)
Variations in Sedimentation	117	(23)
Introduction	117	(1)
Stochastic Diffusion Model	118	(6)
Observations	124	(7)
Completeness of the Sedimentary Record	131	(5)
Bed Thicknesses	136	(4)
Variability of the Earth's Magnetic Field	140	(15)
Variations of the Dipole Moment	140	(2)
Reversal Record	142	(6)
Inclination and Declination Data	148	(4)
Model for Geomagnetic Variations	152	(3)
Other Applications	155	(2)
Conclusions	157	(10)
Acknowledgments	160	(1)
References	160	(7)
Index	167