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
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/29262 |
| Date | 16 August 1973 |
| Creators | Lu, Richard Shih-Ming |
| Contributors | Bodvarsson, Gunnar |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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