Geophysical Interpretation and Integral Equations

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.