Thesis (Ph. D.)--University of Pennsylvania, 1906.

Thesis (Ph. D.)--University of Pennsylvania, 1906.

Thèse : Astronomie : Paris, Faculté des sciences : 1842. / Titre provenant de l'écran-titre.

Thèse : Mécanique : Paris, Faculté des sciences : 1839. Thèse : Astronomie : Paris, Faculté des sciences : 1839. / Titre provenant de l'écran-titre.

Milton W.Y. Wan. / Title also in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf [37]

The perturbation method is applied to solve two numerical problems in the earth sciences, viz., (l)the computation of deep sea currents in the coastal region of the northeast Pacific and (2) the interpretation of D.C. conduction data in exploration geophysics. The perturbation method is largely equivalent to the method of successive approximation. The variational method is also used in the study of the dynamics of the deep sea currents. The deep sea currents in the coastal region of the northeast Pacific can be calculated approximately by solving the linearized equations for long waves in shallow basins. Both the perturbation and the variational methods are employed to solve these equations in the case of step shelf models approximating the shelf contours in the region. It is concluded that the perturbation method using the Fourier transform technique is to be preferred for the problem at hand. The results show that the topography of the continental shelf and the continental slope has only a minor effect on the deep sea currents in the abyssal plain region. In the case of the D.C. conduction exploration method, the perturbation method is applied both to the problem of computing the surface potential due to a given conductivity distribution and also to the inverse problem of interpreting given field data. The first case involves the solving of an ordinary second order differential equation by numerical methods followed by a numerical Hankel transformation. The inversion procedure involves, in particular, the numerical inversion of a Laplace transformation. The application of these methods to two- and three-layer cases is demonstrated by working out some examples. It is shown that the perturbation method can be applied with good results provided certain conditions are satisfied. The main practical difficulty is encountered in the numerical Laplace inversion which is an improperly posed problem. / Graduation date: 1974

For a wave system of three dimension, produced by the interactions betw een two progressive gravity wave trains on the free water surface in uniform water depth, a perturbation expansion method with chain rule has been applied to obtain the third order solution, including the resonant and non-resonant cases In the resonant case, the growth of the induced resonant wave motion with time and its propagating time distance is displayed in the form of mathematics and figure clearly, by applying the transmission of the energy flux. As for verifying the accuracy of this paper, the third order solution is valid when the wave system is degenerated into a progressive gravity wave train on the free water surface and the standing waves respectively. Furthermore, the experimental results of Longuet-Higgins & Smith (1966) and McGoldrick et al.(1966) are cited to compare, presenting the analytical results in this paper are great agreements.

Thesis (Ph. D.)--University of Pennsylvania. / "Biographical": p. 36.

Thesis (PH. D.)--University of Chicago, 1905. / Published also as Astronomiska iakttagelser och undersökningar, band 10, no. 1. Includes bibliographical references.

Thesis (PH. D.)--University of Chicago, 1905. / Published also as Astronomiska iakttagelser och undersökningar, band 10, no. 1. Includes bibliographical references. Also available on the Internet.