Graduate Thesis Or Dissertation
 

Perturbation methods in geophysics and oceanography

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  • 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.
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