THESIS
2014
xv, 140 pages : illustrations ; 30 cm
Abstract
In this thesis, we study the computation of high frequency wave and the related
inverse problems based on eikonal equations. Particularly this thesis focuses
on the first arrival transmission traveltime tomography, the joint transmission-reflection traveltime tomography and the multi-valued solutions of eikonal equations. We propose Eulerian methods on these subjects, which adopt Cartesian
coordinates and yield uniformly distributed solutions.
For the first arrival transmission traveltime tomography, we propose a level set
adjoint state method to solve the problems where the underlying slowness is
piecewise continuous. The level set method is incorporated to implicitly represent
the discontinuity in the slowness. Then this level set adjoint state method is
extended to study the...[
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In this thesis, we study the computation of high frequency wave and the related
inverse problems based on eikonal equations. Particularly this thesis focuses
on the first arrival transmission traveltime tomography, the joint transmission-reflection traveltime tomography and the multi-valued solutions of eikonal equations. We propose Eulerian methods on these subjects, which adopt Cartesian
coordinates and yield uniformly distributed solutions.
For the first arrival transmission traveltime tomography, we propose a level set
adjoint state method to solve the problems where the underlying slowness is
piecewise continuous. The level set method is incorporated to implicitly represent
the discontinuity in the slowness. Then this level set adjoint state method is
extended to study the joint transmission-reflection traveltime tomography, where
the reflection part is carefully handled in the algorithm; also we introduce an
easily computed quantity which can quantify the reliability of our reconstruction.
In addition, we propose an Eulerian labeling method to compute the multi-valued
solutions of eikonal equations. Our method is based on the idea of the shock
splitting method and we improve the solutions in inhomogeneous medium.
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