Linearized quantities in transversely isotropic media

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doi: 10.1139/e04-005
Authors:Daley, P. F.; Lines, L. R.
Author Affiliations:Primary:
University of Calgary, Department of Geology and Geophysics, Calgary, AB, Canada
Volume Title:Canadian Journal of Earth Sciences Revue Canadienne des Sciences de la Terre
Source:Canadian Journal of Earth Sciences = Revue Canadienne des Sciences de la Terre, 41(3), p.349-354. Publisher: National Research Council of Canada, Ottawa, ON, Canada. ISSN: 0008-4077
Publication Date:2004
Note:In English with French summary. Includes appendix. 18 refs.; illus.
Summary:This paper advocates a modified parameterization for transversely isotropic (TI) media in seismology. Transversely isotropic media may be parameterized by the reference quasi-compressional (qP) and quasi-shear (qSV) velocities, α and β, together with the two parameters, ε and δ. These last two variables account for the deviation of the coupled qP and qSV modes of wave propagation from the isotropic case. The dimensionless quantity ε is a measure of the ellipticity of the qP wavefront. The "strange" parameter δ has been employed as a measure of deviation of the qP wavefront or slowness surface from an ellipsoid of revolution and also of the qSV wavefront or slowness surface from a sphere. As the parameter δ has been described as "conceptually inaccessible"; it is logical to determine an alternative characterization in physically realizable quantities. As in the earlier literature, the defining parameter for the degree of ellipticity of the qP slowness or energy surface in a TI medium is chosen here to be ε. In addition, the deviation of both the qP and qSV surfaces from the degenerate ellipsoidal case will be specified here as σ. An examination of the linearized phase (wavefront normal) velocities, and the linearized PP and SVSV reflection coefficients at an interface between two TI media is undertaken to emphasize the merits of this modified parameterization. All formulae used here have appeared in one form or another in the cited literature. In this paper, a reformulation of existing equations as functions of the two independent variables, (ε, σ), is presented. This results in a more physically realizable context for the linearized formulae.
Sections:Physical properties of rocks and minerals
Subjects:Anisotropic materials; AVO methods; Body waves; Elastic waves; Geophysical methods; Linear distortion; P-waves; Phase velocity; Propagation; S-waves; Seismic methods; Seismic migration; Seismic waves; Theoretical studies; Transverse isotropy
Abstract Numbers:04M/2161
Record ID:2004054181
Copyright Information:GeoRef, Copyright 2019 American Geosciences Institute.
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040 |a ViAlAGI  |c ViAlAGI 
041 |a eng  |b fre 
072 7 |a 20  |2 georeft 
100 1 |a Daley, P. F.  |e analytic author  |u University of Calgary, Department of Geology and Geophysics, Calgary, AB 
245 1 0 |a Linearized quantities in transversely isotropic media 
300 |a p. 349-354 
500 |a In English with French summary. Includes appendix. 18 refs. 
500 |a Abstract number: 04M/2161 
500 |a Category Section: Physical properties of rocks and minerals 
500 |a Affiliation: University of Calgary, Department of Geology and Geophysics; Calgary, AB; CAN; Canada 
500 |a Key title: Canadian Journal of Earth Sciences = Revue Canadienne des Sciences de la Terre 
500 |a Source note: Canadian Journal of Earth Sciences = Revue Canadienne des Sciences de la Terre, 41(3), p.349-354. Publisher: National Research Council of Canada, Ottawa, ON, Canada. ISSN: 0008-4077 
500 |a Publication type: journal article 
504 |b 18 refs. 
510 3 |a GeoRef, Copyright 2019 American Geosciences Institute. 
520 |a This paper advocates a modified parameterization for transversely isotropic (TI) media in seismology. Transversely isotropic media may be parameterized by the reference quasi-compressional (qP) and quasi-shear (qS<V`) velocities, α and β, together with the two parameters, ε and δ. These last two variables account for the deviation of the coupled qP and qSV modes of wave propagation from the isotropic case. The dimensionless quantity ε is a measure of the ellipticity of the qP wavefront. The "strange" parameter δ has been employed as a measure of deviation of the qP wavefront or slowness surface from an ellipsoid of revolution and also of the qS<V` wavefront or slowness surface from a sphere. As the parameter δ has been described as "conceptually inaccessible"; it is logical to determine an alternative characterization in physically realizable quantities. As in the earlier literature, the defining parameter for the degree of ellipticity of the qP slowness or energy surface in a TI medium is chosen here to be ε. In addition, the deviation of both the qP and qS<V` surfaces from the degenerate ellipsoidal case will be specified here as σ. An examination of the linearized phase (wavefront normal) velocities, and the linearized PP and S<V`S<V` reflection coefficients at an interface between two TI media is undertaken to emphasize the merits of this modified parameterization. All formulae used here have appeared in one form or another in the cited literature. In this paper, a reformulation of existing equations as functions of the two independent variables, (ε, σ), is presented. This results in a more physically realizable context for the linearized formulae. 
650 7 |a Anisotropic materials  |2 georeft 
650 7 |a AVO methods  |2 georeft 
650 7 |a Body waves  |2 georeft 
650 7 |a Elastic waves  |2 georeft 
650 7 |a Geophysical methods  |2 georeft 
650 7 |a Linear distortion  |2 georeft 
650 7 |a P-waves  |2 georeft 
650 7 |a Phase velocity  |2 georeft 
650 7 |a Propagation  |2 georeft 
650 7 |a S-waves  |2 georeft 
650 7 |a Seismic methods  |2 georeft 
650 7 |a Seismic migration  |2 georeft 
650 7 |a Seismic waves  |2 georeft 
650 7 |a Theoretical studies  |2 georeft 
650 7 |a Transverse isotropy  |2 georeft 
700 1 |a Lines, L. R.,  |e analytic author 
773 0 |t Canadian Journal of Earth Sciences Revue Canadienne des Sciences de la Terre  |d Ottawa, ON : National Research Council of Canada, Mar. 2004  |x 0008-4077  |y CJESAP  |n Canadian Journal of Earth Sciences = Revue Canadienne des Sciences de la Terre, 41(3), p.349-354. Publisher: National Research Council of Canada, Ottawa, ON, Canada. ISSN: 0008-4077 Publication type: journal article  |g Vol. 41, no. 3  |h illus. 
856 |u urn:doi: 10.1139/e04-005