Geophysics

Methods in Computational Physics, Volume 13: Geophysics is a 10-chapter text that focuses with the theoretical solid-earth geophysics. This volume specifically covers the general topics of terrestrial magnetism and electricity, the Earth's gravity field, tidal deformations, dynamics of global spin, spin processing, and convective models for the deep interior.
This volume surveys first the construction of mathematical models, such as the representation of the geomagnetic field by assuming arrangements of multipole sources in the core and the fast computer evaluation of two- and three-dimensional gravity models, which revolutionized their use in mineral prospecting and in studies of the crust. These topics are followed by a presentation of geophysical modeling and the uncertainties involved in quantitative convection studies of mantle flow. Other chapters explore the construction of numerical geophysical models related intimately to the inverse problem whereby maximum likelihood estimates of the required parameters must be determined along with calculation of confidence limits, including density, conductivity, and viscosity. The remaining chapters are devoted to the importance of harmonic analysis in geophysics, particularly spherical harmonic analysis, which has seen many refinements and applications.
Physicists, geoscientists, and mathematicians will find this book invaluable.

Contenu

Contributors
Preface
Errata
Signal Processing and Frequency-Wavenumber Spectrum Analysis for a Large Aperture Seismic Array
I. Introduction
II. Optimum Detector for Seismic Arrays
III. Signal Estimation Procedures
IV. Frequency-Wavenumber Power Spectrum
V. Estimation of Frequency-Wavenumber Power Spectrum
VI. Signal-to-Noise Ratio Improvement Results at LASA
VII. Characteristics of Background Microseismic Noise
VIII. Analysis of Rayleigh-Wave Multipath Propagation at LASA
IX. Detection of Interfering Rayleigh Waves at LASA
X. Conclusions
References
Models of the Sources of the Earth's Magnetic Field
I. Introduction
II. The Spherical Harmonic Analysis
III. The Radial Dipole Model
IV. The Magnetohydrodynamic Models
V. Modeling Archival Data
References
Computations with Spherical Harmonics and Fourier Series in Geomagnetism
I. Introduction
II. Recurrence Relations for Spherical Harmonics
III. Analysis of Cartesian Components of the Geomagnetic Field
IV. Eccentric Geomagnetic Dipoles
V. Wigner 3-j Coefficients
VI. Transformation of Spherical Harmonics under Rotation
VII. Applications of Wigner 3-j Coefficients
VIII. Fourier Analysis of Geomagnetic Hourly Mean Values
IX. Numerical Procedure
References
Inverse Methods in the Interpretation of Magnetic and Gravity Anomalies
I. Formulation of Problem
II. The Linear Inverse Method
III. Nonlinear Inverse Methods
References
Analysis of Geoelectromagnetic Data
I. Introduction
II. The Forward Problem
III. The Inverse Problem
References
Nonlinear Spherical Harmonic Analysis of Paleomagnetic Data
I. Introduction
II. Technique of Analysis
III. Synthetic Paleomagnetic Fields
IV. The Quaternary Field
References
Harmonic Analysis Of Earth Tides
I. Special Aspects of the Earth Tides Problem
II. Tidal Analysis
III. Some Recent Results of Earth Tide Analysis
References
Computer Usage in the Computation of Gravity Anomalies
I. Introduction
II. Notation, Coordinate System and Gravitational Effect of Simple Bodies
III. Gravitational Effect of Two-Dimensional Bodies of Arbitrary Shape
IV. Gravitational Effect of Three-Dimensional Bodies of Arbitrary Shape
V. Terrain Correction on a Flat Earth
VI. Computational Problems on a Spherical Earth
References
Analysis of Irregularities in the Earth's Rotation
I. Introduction
II. Theory and Measurements
III. Irregularities in the Rotation of the Earth as Time Series
IV. Examples of the Analysis of Measurements
V. Discussion
References
Convection in the Earth's Mantle
I. Introduction
II. Surface Displacements
III. Properties of the Mantle
IV. Applicable Equations
V. Numerical Method
VI. Results
VII. Summary
References
Author Index
Subject Index
Contents of Previous Volumes