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Weak-anisotropy approximation of P-wave geometric spreading in horizontally layered anisotropic media of arbitrary symmetry; tilted transversely isotropic specification

Veronique Farra and Ivan Psencik
Weak-anisotropy approximation of P-wave geometric spreading in horizontally layered anisotropic media of arbitrary symmetry; tilted transversely isotropic specification
Geophysics (August 2021) 86 (4): C119-C132

Abstract

Understanding the role of geometric spreading and estimating its effects on seismic wave propagation play an important role in several techniques used in seismic exploration. The spreading can be estimated through dynamic ray tracing or determined from reflection traveltime derivatives. In the latter case, derivatives of nonhyperbolic moveout approximations are often used. We offer an alternative approach based on the weak-anisotropy approximation. The resulting formula is applicable to P-waves reflected from the bottom of a stack of horizontal layers, in which each layer can be of arbitrary anisotropy. At an arbitrary surface point, the formula depends, in each layer, on the thickness of the layer, on the P-wave reference velocity used for the construction of reference rays, and on nine P-wave weak-anisotropy (WA) parameters specifying the layer anisotropy. Along an arbitrary surface profile, the number of WA parameters reduces to five parameters related to the profile. WA parameters represent an alternative to the elastic moduli and, as such, can be used for the description of any anisotropy. The relative error of the approximate formula for a multilayered structure consisting of layers of anisotropy between 8% and 20% is, at most, 10%. For models including layers of anisotropy stronger than 20%, the relative errors may reach, locally, even 30%. For any offset, relative errors remain under a finite limit, which varies with the anisotropy strength.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 86
Serial Issue: 4
Title: Weak-anisotropy approximation of P-wave geometric spreading in horizontally layered anisotropic media of arbitrary symmetry; tilted transversely isotropic specification
Affiliation: Universite de Paris, Institut de Physique du Globe, Paris, France
Pages: C119-C132
Published: 202108
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 25
Accession Number: 2021-049217
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Secondary Affiliation: Academy of Sciences of the Czech Republic, Prague, CZE, Czech Republic
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2021, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 2021
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