A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Doctor of Philosophy / Inverse theory provides an important tool that the geophysicist can use to explore the structure of the Earth. This thesis examines several new approaches to the inverse problem, and suggests ways of improving the conventional least-squares technique. Non least-squares inversion was applied to borehole temperature data from South Africa, and when the norm of the inversion was controlled by the statistics of the misfit, It reduced by over 50% the number of iterations required for the inversion to converge upon a solution. Various damping schemes were also examined, and the use of the misfit in controlling the damping is shown to provide the best solution of those studied (Cooper and Jones, in press). Improvements to the efficiency of the inverse process were also achieved by the fitting of parabolic forms to portions of the misfit surface, using both the misfit value and the gradient of the surface. for gravity data. The presence of nearby minima other than the one that the inversion has just converged to can also be detected in this manner. The set of initial models that converged to a particular solution using leastsquares inversion was studied for magnetic data, and it was noted to have a fractal nature. The fractal dimension of the set was found to be inversely proportional to the damping of the inverse problem. The inverse process was pushed into a chaotic state by the modification of the least-squares inversion equation. The chaotic state was studied, and exploited to / AC2017

Geophysical measurements can often be described in terms of multichannel, autoregressive data models from which one can directly derive measures of the harmonic composition of the underlying geophysical process and its inherent self-predictability. / We explore methods for and uses of multichannel autoregressive data modelling in a geophysical context. / Autoregressive data modelling using the least-squares linear prediction method is generalized to multichannel time series. A recursive algorithm is obtained for the formation of the system of multichannel normal equations which determine the least-squares solution of the multichannel linear prediction problem. Solution of these multichannel normal equations is accomplished by the Cholesky factorization method. / The corresponding multichannel Maximum Entropy spectra derived from these least-squares estimates of the autoregressive model parameters are compared to that obtained using those parameters estimated by a multichannel generalization of Burg's algorithm. Numerical experiments have shown that the multichannel spectra obtained using the least-squares method provides for more accurate frequency determination for truncated sinusoids in the presence of additive white noise.

No description available.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1979. / Microfiche copy available in Archives and Science. / Bibliography: leaves 86-88. / by Dawna Lisa Paton. / M.S.

Orientadores: Joerg Schleicher, Amelia Novais / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T21:47:51Z (GMT). No. of bitstreams: 1 Silva_MariaGabrielaMelo_M.pdf: 824279 bytes, checksum: 86fc870083d29ff7d1c834bea8c9f983 (MD5) Previous issue date: 2006 / Resumo: Em meios homogêneos, o operador diferencial da equação da onda cheia pode ser substituído pelo produto de dois operadores diferenciais. Cada um destes operadores gera uma equação da onda de sentido único. As soluções destas equações descrevem a propagação de uma onda para baixo e uma para cima, respectivamente. Estas soluções possuem os mesmos tempos de trânsito e amplitudes que a onda cheia, uma vez que satisfazem as mesmas equações iconal e de transporte. No entanto, em meios heterogêneos, estas ondas de sentido único satisfazem somente a mesma equação iconal que a onda cheia. Zhang et al. (2003) mostraram como obter equações da onda de sentido único de amplitude verdadeira de modo que estas possuam tanto os mesmos tempos de trânsito como as mesmas amplitudes da onda cheia. Com base nestas equações, desenvolveram uma migração da equação da onda de amplitude verdadeira para seções de fonte comum. Nosso objetivo neste trabalho é modificar a migração de Gazdag (1980), de tal maneira que esta passe a utilizar as equações da onda de sentido único de amplitude verdadeira ao invés das equações de sentido único padrão, para realizar uma migração da equação da onda em amplitude verdadeira para seções de afastamento nulo / Abstract: In homogeneous media, the two-way wave operator can be substituted by the product of two one-way wave operators each of which generates a one-way wave equation. One of these equations has a downgoing wave and the other has an upgoing wave as a solution. Those oneway waves have the same travei time and amplitudes as the full wave since they satisfy the same eikonal and transport equation. However, in heterogeneous media, the standard one-way waves satisfy only the same eikonal equation as the full wave. Thus, in this case, the amplitudes of the migrated section obtained through a migration method based on the standard wave equations are incorrect. Zhang et al. (2003) described how to modify the standard one-way waves in order to produce the true amplitude one-way waves, which not only have the same travei times but also the same amplitudes as the full wave. They use these true amplitudes one-way wave equations to preserve the amplitudes in common-shot wave-equation migration. Our goal is to modify Gazdag migration (Gazdag, 1980) in such a way that it uses the true amplitude one-way wave equations instead of the standard ones, in order to realize a true amplitude wave equation migration for zero-offset data / Mestrado / Geofisica / Mestre em Matemática Aplicada

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1980. / Microfiche copy available in Archives and Science. / Bibliography: leaves 156-158. / by Ronald Mark Errico. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Meteorology; and, (B.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / Microfiche copy available in Archives and Science. / Thesis (B.S.)--M.I.T., Dept. of Mathematics, 1979. / Includes bibliographical references. / by Norman R. Guivens, Jr. / M.S.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1980. / Microfiche copy available in Archives and Science. / Bibliography: leaves 152-159. / by Long Sang Chiu. / Sc.D.

No description available.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Meteorology and Physical Oceanography, 1981. / Microfiche copy available in Archives and Science. / Bibliography: leaves 63-65. / by Steven John Ghan. / M.S.