High Frequency Asymptotic Methods for Traveltimes and Anisotropy Parameter Estimation in Azimuthally Varying Media

Handle URI:
http://hdl.handle.net/10754/317235
Title:
High Frequency Asymptotic Methods for Traveltimes and Anisotropy Parameter Estimation in Azimuthally Varying Media
Authors:
Masmoudi, Nabil
Abstract:
Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the anellipticity parameter and the symmetry axis azimuth in inhomogeneous background media. Specifically, our expansion assumes an inhomogeneous elliptically anisotropic background medium, which may be obtained from well information and stacking velocity analysis in HTI media. This formulation has advantages on two fronts: on one hand, it alleviates the computational complexity associated with solving the HTI eikonal equation, and on the other hand, it provides a mechanism to scan for the best fitting parameters without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameters.
Advisors:
Alkhalifah, Tariq
Committee Member:
Hoteit, Ibrahim ( 0000-0002-3751-4393 ) ; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Program:
Earth Sciences and Engineering
Issue Date:
May-2014
Type:
Thesis
Appears in Collections:
Theses; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.advisorAlkhalifah, Tariqen
dc.contributor.authorMasmoudi, Nabilen
dc.date.accessioned2014-05-21T08:45:20Z-
dc.date.available2014-05-21T08:45:20Z-
dc.date.issued2014-05en
dc.identifier.urihttp://hdl.handle.net/10754/317235en
dc.description.abstractTraveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the anellipticity parameter and the symmetry axis azimuth in inhomogeneous background media. Specifically, our expansion assumes an inhomogeneous elliptically anisotropic background medium, which may be obtained from well information and stacking velocity analysis in HTI media. This formulation has advantages on two fronts: on one hand, it alleviates the computational complexity associated with solving the HTI eikonal equation, and on the other hand, it provides a mechanism to scan for the best fitting parameters without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameters.en
dc.language.isoenen
dc.subjectTraveltimesen
dc.subjectAnisotropyen
dc.subjectRay Tracingen
dc.subjecteikonalen
dc.subjectAzimuthen
dc.subjectEstimationen
dc.titleHigh Frequency Asymptotic Methods for Traveltimes and Anisotropy Parameter Estimation in Azimuthally Varying Mediaen
dc.typeThesisen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberHoteit, Ibrahimen
dc.contributor.committeememberLaleg-Kirati, Taous-Meriemen
thesis.degree.disciplineEarth Sciences and Engineeringen
thesis.degree.nameMaster of Scienceen
dc.person.id124836en
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