An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

Handle URI:
http://hdl.handle.net/10754/621948
Title:
An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis
Authors:
Hao, Qi; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 )
Abstract:
Seismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter υS0 in Thomsen's notation and the S-wave attenuation coefficient AS0 in Zhu and Tsvankin's notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the proposed eikonal equation to realistic attenuating media, an alternative perturbation solution to the proposed eikonal equation, and the feasibility of applying the proposed nonhyperbolic equation for the imaginary part of the complex-valued traveltime to invert for interval attenuation parameters. © 2017 Society of Exploration Geophysicists.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Hao Q, Alkhalifah T (2016) An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis. GEOPHYSICS 82: C9–C20. Available: http://dx.doi.org/10.1190/geo2016-0160.1.
Publisher:
Society of Exploration Geophysicists
Journal:
GEOPHYSICS
Issue Date:
21-Nov-2016
DOI:
10.1190/geo2016-0160.1
Type:
Article
ISSN:
0016-8033; 1942-2156
Sponsors:
Q. Hao thanks the Rock and Seismic (ROSE) project for support and A. Stovas for helpful discussion on attenuation anisotropy. T. Alkhalifah thanks KAUST for its support. We also thank the assistant editor J. Etgen, associate editor Y. Liu, and three anonymous reviewers for many valuable suggestions.
Additional Links:
http://library.seg.org/doi/10.1190/geo2016-0160.1
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHao, Qien
dc.contributor.authorAlkhalifah, Tariq Alien
dc.date.accessioned2016-12-06T08:40:06Z-
dc.date.available2016-12-06T08:40:06Z-
dc.date.issued2016-11-21en
dc.identifier.citationHao Q, Alkhalifah T (2016) An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis. GEOPHYSICS 82: C9–C20. Available: http://dx.doi.org/10.1190/geo2016-0160.1.en
dc.identifier.issn0016-8033en
dc.identifier.issn1942-2156en
dc.identifier.doi10.1190/geo2016-0160.1en
dc.identifier.urihttp://hdl.handle.net/10754/621948-
dc.description.abstractSeismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter υS0 in Thomsen's notation and the S-wave attenuation coefficient AS0 in Zhu and Tsvankin's notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the proposed eikonal equation to realistic attenuating media, an alternative perturbation solution to the proposed eikonal equation, and the feasibility of applying the proposed nonhyperbolic equation for the imaginary part of the complex-valued traveltime to invert for interval attenuation parameters. © 2017 Society of Exploration Geophysicists.en
dc.description.sponsorshipQ. Hao thanks the Rock and Seismic (ROSE) project for support and A. Stovas for helpful discussion on attenuation anisotropy. T. Alkhalifah thanks KAUST for its support. We also thank the assistant editor J. Etgen, associate editor Y. Liu, and three anonymous reviewers for many valuable suggestions.en
dc.publisherSociety of Exploration Geophysicistsen
dc.relation.urlhttp://library.seg.org/doi/10.1190/geo2016-0160.1en
dc.rightsArchived with thanks to Geophysicsen
dc.subjectAcousticen
dc.subjectAnisotropyen
dc.subjectAttenuationen
dc.subjectP-waveen
dc.subjectTraveltimeen
dc.titleAn acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axisen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalGEOPHYSICSen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionNorwegian University of Science and Technology (NTNU), Department of Petroleum Engineering and Applied Geophysics, Trondheim, Norwayen
kaust.authorAlkhalifah, Tariq Alien
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