Three-dimensional first arrival traveltimes and amplitudes via eikonal and transport finite difference solvers

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dc.contributor.advisorSymes, William W.en_US
dc.creatorAbd El-Mageed, Maissa A.en_US
dc.date.accessioned2009-06-04T08:25:56Zen_US
dc.date.available2009-06-04T08:25:56Zen_US
dc.date.issued1997en_US
dc.description.abstractFirst arrival traveltimes and associated amplitudes are essential components in Kirchhoff migration and modeling. Traditionally they have been determined by ray tracing. However ray tracing does not give traveltimes on a regular grid, and is not guaranteed to produce the minimum traveltime. Seismic traveltimes in three dimensions can be computed efficiently and accurately on a regular grid using an essentially nonoscillatory ("ENO") Hamilton-Jacobi (HJ) second order scheme. The scheme can be implemented in fully vectorizable form. Several examples illustrate the effectiveness of this approach to traveltime computation. A similar accurate scheme is required to solve the transport equation for the amplitudes associated with the first arrival traveltimes. A second-order Runge-Kutta upwind finite difference scheme is constructed for this purpose. The transport equation involves the traveltime gradient and Laplacian which must be evaluated using the output of the eikonal scheme $\tau.$ The error in $\tau$ is second order accurate, hence the approximation to the traveltime Laplacian is zeroth order accurate, and there is no reason to expect the traveltime Laplacian, hence the amplitude, to converge. One remedy to ensure that the traveltime Laplacian is sufficiently accurate to guarantee convergence, is to use a higher order scheme, say third order ENO upwind scheme to solve the eikonal equation. Preliminary numerical results are presented to demonstrate the third-order accuracy of the HJ-ENO numerical flux in spatial directions (x and y) and of TVD (total variation diminishing) Runge-Kutta method in z-direction.en_US
dc.format.extent69 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 1997 ABD EL-MAGEEDen_US
dc.identifier.citationAbd El-Mageed, Maissa A.. "Three-dimensional first arrival traveltimes and amplitudes via eikonal and transport finite difference solvers." (1997) Diss., Rice University. <a href="https://hdl.handle.net/1911/19123">https://hdl.handle.net/1911/19123</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19123en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectGeophysicsen_US
dc.subjectMathematicsen_US
dc.titleThree-dimensional first arrival traveltimes and amplitudes via eikonal and transport finite difference solversen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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