文档介绍：
ᎏᎏ
ADVANCES IN
GEOPHYSICS
VOLUME 40
This
Page
Intentionally
Left
Blank
ᎏᎏ
Advances in
GEOPHYSICS
Long-Range Persistence in
Geophysical Time Series
Edited by
RENATA DMOWSKA
Division of Applied Sciences
Harvard University
Cambridge, Massachusetts
BARRY SALTZMAN
Department of Geology and Geophysics
Yale University
New Haven, Connecticut
VOLUME 40
ACADEMIC PRESS
San Diego London Boston New York
Sydney Tokyo Toronto
This
Page
Intentionally
Left
Blank
ᎏᎏ
CONTENTS
CONTRIBUTORS ...................................... vii
PREFACE .......................................... ix
Self-Affine Time Series: I. Generation and Analyses
BRUCE D. MALAMUD AND DONALD L. TURCOTTE
1. Introduction ..................................... 1
Brief Overview of Article .......................... 1
What Is a Time Series? ........................... 2
How Is a Time Series Quantified? ..................... 3
Autocorrelations and Semivariograms ................... 6
Self-Affine Fractals .............................. 10
Gaussian White Noises and Brownian Motions ............. 13
2. Spectral Analysis .................................. 19
The Fourier Transform ........................... 19
The Power-Spectral Density ......................... 22
The Relation of , Ha, and D ....................... 28
Weak vs Strong Persistence ......................... 31
Spectral Variance and Leakage ....................... 32
3. Synthetic Fractional Noises and Motions .................... 35
What Are They? ................................ 35
Spectral Analysis ............................... 35
Method of essive Random Additions ................. 43
Semivariograms ................................ 47
4. Log-Normal Noises and Motions ......................... 51
Log-Normal Distributions .......................... 51
Fractional Log-Normal Noises and Motions .