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Geophysical Interpretation and Integral Equations (Hardcover)
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Geophysical Interpretation and Integral Equations (Hardcover)
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The development of numerical methods, together with the advent of
fast digital computers, have facilitated the application of
integral equations in geophysical modelling. This is also due to
the successful derivation of integral equations that are applicable
to the modelling of complex structures and efficient numerical
algorithms for their solution. The purpose of this work is to give
the principles by which boundary value problems describing
geophysical models can be converted into integral equations.
"Geophysical Interpretation and Integral Equations" introduces
Fredholm integral equations that are well suited to the numerical
solution of boundary value problems representing the electrical,
magnetic, electromagnetic and seismic models of geophysics. These
methods form a most efficient class of techniques for the numerical
modelling of geophysical phenomena. The geophysical methods are
briefly described, their mathematical expressions are given in the
form of boundary value problems and, by applying the Green's
functions, these boundary value problems are then converted into
integral equations that can then be solved by standard numerical
methematics. The end results are integral formulae and integral
equations that form the theoretical framework for model
calculations associated with practical geophysical interpretation.
The approach is physical rather than mathematical, ie the physical
phenomenon is represented by the integral formulae explained in
detail, with the mathematical analysis confined to a minimum.
Numerical algorithms for solving the integral equations are
discussed in connection with some illustrative examples involving
numerical modelling results. This work seeks to provide a reference
source for all geophysicists and engineers concerned with
geophysical phenomenon.
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