Loading...
On the inverse gravimetry problem with minimal data
Titi, Aseel
Titi, Aseel
Citations
Altmetric:
Files
Authors
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2021-07
Type
Dissertation
Genre
Keywords
Subjects (LCSH)
Electronic dissertations
Electronic dissertations
Electronic dissertations
Citation
Abstract
In this dissertation we considered the inverse source problem $\Delta u = \mu,$ where lim $u (x) = 0$ as |x| goes to $\infty$ and $\mu$ is zero outside a bounded domain $\Omega$. The inverse problem of gravime-
try is to find $\mu$ given $\Delta \mu$ on $\partial \Omega$. Due to nonuniqueness of $\mu$ we assumed that $\mu = \chi^{(D)}$ where D is unknown domain inside $\Omega$ We first studied the two-dimensional case where
we found that about five parameters of the unknown D can be stably determined given
data noise in practical situations. An ellipse is uniquely determined by five parameters. We
proved uniqueness and stability of recovering an ellipse for the inverse problem from minimal
amount of data which are the gravitational force at three boundary points. In the proofs
we derived and used simple systems of linear and non linear algebraic equations for natural
parameters of an ellipse. To illustrate the technique we used these equations in numerical
examples with various location of measurements points on $\partial \Omega$. We also handled the problem in three dimensions where we proved uniqueness for an ellipsoid in some particular cases.
Table of Contents
Description
Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
Publisher
Wichita State University
Journal
Book Title
Series
Digital Collection
Finding Aid URL
Use and Reproduction
© Copyright 2021 by Aseel Titi
All Rights Reserved