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| FOUNDATIONS OF ANISOTROPY FOR EXPLORATION SEISMICS
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 Buy online with a credit card in the Elsevier Science & Technology Bookstore:  http://books.elsevier.com/elsevier/?isbn=0080372244
By
K. Helbig, Rijksuniversity of Utrecht and Free University of Amsterdam, The Netherlands
Included in series
Handbook of Geophysical Exploration: Seismic Exploration, 22
Description
Over the last few years, anisotropy has become a "hot topic" in seismic exploration and seismology. It is now recognised that geological
media deviate more or less from isotropy. This has consequences for acquisition, processing and interpretation of seismic data and also
helps determine the cause of anisotropy and adds to our knowledge concerning the structure of the medium at scales beyond the resolution
of the seismic method.
This volume addresses the theoretical foundations of wave propagation in anisotropic media at an easily accessible
level. The treatment is not restricted to exploration seismology. The book commences with fundamental material and covers the description
of wave propagation in anisotropic conditions by means of slowness and wave surfaces. It continues to explore the theory of elasticity,
the interaction of elasticity and material symmetry and conditions imposed by the stability of the medium. Wave propagation in general
anisotropic solids are discussed referring in particular to singular and longitudinal directions. Slowness and wave surfaces in transversely
isotropic media and in the planes of symmetry of orthorhombic media is presented and then moves on to wave propagation in orthorhombic
media by means of "squared slowness surfaces". The latter part of the book deals with layer-induced anisotropy showing how a particular
internal structure of a medium leads to anisotropy and how much of this structure can be recovered by "inversion" of the modelling algorithm.
A few fundamental aspects of exploration seismology are also discussed.
The final chapter discusses how concepts which were developed
by Kelvin, but only recently understood, can be utilised to determine the symmetry class and orientation of an elastic medium.
Audience
For researchers in exploration geophysics, seismologists and those working in material sciences and solid acoustics.
Contents
Chapter headings and selected contents:
Fundamentals.
What is homogeneity? What is anisotropy? What is dispersion? What
causes anisotropy of wave propagation. Appendix 1A: Analytical derivation of the relation between anisotropy and dispersion.
Tools
for the Description of Wave Propagation under Piecewise Homogeneous Anisotropic Conditions.
Ray velocity and normal velocity. The
ray-slowness surface; slowness and wave surface as polar reciprocals. Snell's Law. Appendix 2A: Formal description of the transformations
used in this chapter. Analytic expression for inversion (reflection in a circle). Analytic derivation of the tangent curve from the footpoint
curve. Analytic description of polar reciprocity.
Elasticity.
Tensors and vectors. Infinitesimal strain. Basic symmetries of the
elastic tensor and the contracted notation. The elastic constants and material symmetry. Appendix 3A: The relation between elastic constants
and rotational symmetry. Reduction of an arbitrary rotation to a sequence of rotations about one axis each. Tensors of rank two under
rotation of the coordinate system. Appendix 3B: Invariants of the elastic tensor. Contraction of the elastic tensor on itself. Appendix
3C: FORTRAN subroutines for operations on elastic tensors in four- and two- subscript notation.
Elastic Waves - The Dispersion Relation
and some Generalities about Slowness and Wave Surfaces.
The wave equation. Elements of inflection of the slowness surface. Slowness,
polarization and symmetry. Singular directions. Appendix 4A: Orthogonality of polarization vectors. Appendix 4B: Explicit versions of
the characteristic equation. Appendix 4C: Subroutines for the Kelvin-Christoffel matrix.
Stability Constraints.
The general stability
condition. Stability conditions for isotropic, hexagonal, cubic, strong tetragonal and orthorhombic media.
One-Parameter Expressions
for the Slowness Surfaces of Transversely Isotropic Media and the Slowness Curves in the Planes of Symmetry of Orthorhombic Media.
Decoupling of the across-plane polarization and a parameter expression for the "coupled" slowness curves. The "basic curves", the separating
ellipse and the general shape of the "coupled" slowness curves. The associate parameter, the representing point, and a geometric construction
for the polarization. A nomogram for the in-plane polarization. Appendix 6A: Closed explicit expressions for the coupled slowness curves
in the symmetry planes of orthorhombic media.
One-Parameter Expressions for the Wave Curves in the Symmetry Planes of Orthorhombic
Media.
Expressions for the wave surface in Cartesian and polar coordinates. Cusps. A measure of anisotropy.
Squared Slowness Surfaces
and Squared Slowness Curves.
Phenomenology of slowness surfaces in the squared domain. The "framework" in the planes of symmetry.
Deviations from the "framework" in the planes of symmetry. Appendix 8A: Determination of the type of the squared slowness curve. Appendix
8B: Properties of the square transformation. Coordinate grids. Straight lines. Symmetrically centered conics with aligned axes. General
centered conics. Appendix 8C: Geometric tools for the conversion of a squared slowness curve to the ordinary domain. Geometric determination
of curvature.
Causes of Anisotropy: Periodic Fine Layering.
Simple quasi-static strain modelling. Constraints on layer-induced
anisotropy. Inversion of the compound stiffnesses to constituent stiffnesses. A nomogram for the determination of layer parameters. Appendix
9A: Generalized averages.
Anisotropy and Seismic Exploration.
Elliptical anisotropy. An equivalence theorem for surface-to-surface
seismics. Some aspects of reflection seismics.
Eigentensors of the Elastic Tensor and their Relationship with Material Symmetry.
Rudimentary definition of a tensor space. Strain tensors and wave propagation. Coordinate-free representation of "wave-compatibility".
Eigentensors and symmetry. Eigensystems of specific symmetries. Determination of the symmetry class. Appendix 11A: Construction of media
with particular eigentensors. Reconstruction of an elastic tensor from its eigensystem. Construction of an eigensystem with particular
eigenvectors. References. Index.
220 line drawings, 195 lit. refs.
Bibliographic & ordering Information
Hardbound, 502 pages, publication date: JAN-1994
ISBN-13: 978-0-08-037224-2
ISBN-10: 0-08-037224-4
Imprint: PERGAMON
Price: Order form
GBP 102
USD 153.95
EUR 153
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Last update: 10 Jun 2008
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