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Computing the optimal transversely isotropic approximation of a general elastic tensor

Joe Dellinger
Computing the optimal transversely isotropic approximation of a general elastic tensor
Geophysics (October 2005) 70 (5): I1-I10

Abstract

Mathematically, 21 stiffnesses arranged in a 6 X 6 symmetric matrix completely describe the elastic properties of any homogeneous anisotropic medium, regardless of symmetry system and orientation. However, it can be difficult in practice to characterize an anisotropic medium's properties merely from casual inspection of its (often experimentally measured) stiffness matrix. For characterization purposes, it is better to decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic (TI) medium (whose properties can be readily understood) plus a generally anisotropic perturbation (representing the medium's deviation from perfect symmetry), followed by a rotation (giving the relationship between the medium's natural coordinate system and the measurement coordinate system). To accomplish this decomposition, we must find the rotated symmetric medium that best approximates a given stiffness matrix. An analytical formula exists for calculating the distance between the elastic properties of two anisotropic media. Starting from this formula, I show how to analytically calculate the TI medium with a z symmetry axis that is nearest to a given set of 21 stiffness constants. There is no known analytical result if the symmetry axis is not fixed beforehand. I therefore present a simple search algorithm that scans all possible orientations of the nearest TI medium's symmetry axis. The grid is iteratively refined to optimize the solution. The algorithm is simple and robust and works well in practice, but it is not guaranteed to always find the optimal global answer if there are secondary minima that provide almost as good a fit as the optimal one.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 70
Serial Issue: 5
Title: Computing the optimal transversely isotropic approximation of a general elastic tensor
Author(s): Dellinger, Joe
Affiliation: British Petroleum, Houston, TX, United States
Pages: I1-I10
Published: 200510
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 13
Accession Number: 2007-051989
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Annotation: Includes appendices
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 200728
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