Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Νούτσης Βασίλειος
Supervisors info:
Μ. Μητρούλη Αναπλ. Καθηγ.(Επιβλέπουσα), Β Δουγαλής Καθηγ., Σ. Νοτάρης Αναπλ. Καθηγ.
Original Title:
Μελέτη του κανονικοποιημένου προβλήματος ελαχίστων τετραγώνων με υπό συνθήκη λύση και εφαρμογή του στη Βαρυτική Μέθοδο
Summary:
In many applications we end up with a linear system of the form Ax=b. In this
paper we discuss the interpretation of geophysical data (gravitational
measurements), interpretation which leads to the solution of the linear
system Ax=g, where by g we denote the measured gravity values , with x
the unknown densities of rocks in the subsurface of investigation area and A
is a matrix resulting from geometry of the selected model. Two problems arise:
We want a constrainted solution because the densities of rocks are ranging
between 2-3kg /dm^3
The condition number of matrix A is 10^13, which leads us to the use of
numerical analysis methods.
We will see:
The gravitational method (from Newton’s law to its application to geophysics),
The Brezinski’s type of error for the quantity ||x-x*|| where x* is any one
solution,
The convertion of two oldest methods for iterative solution of linear system
(Levenberg-Marquardt and Kaczmarz) to constrained solution,
The Tikhonov regularization with constrained solution of the system.
In the end we will see the results of geophysical research, the geological
interpretation.
Keywords:
Geophysical interpretation, Ill conditioned matrix, Tichonov regularization, Constrained solution, Brezinski's error formula
