Geophysical Journal | 2009 volume 31 3

Solution of Fredholm equation of the first kind of convolution for induction logging problems

© Myrontsov M.L.

The possibility to use efficiently the non-iteration method permitting to find a solution of Fredholm equation of the first kind with the kern of convolution type based on the convolution theorem and find the sought function in a limited domain in the form of a Fourier series was considered. It is demonstrated by the examples that the given method has an accuracy, which exceeds considerably the present-day requirements to a solution accuracy for induction logging problems and exceeding considerably an accuracy of methods applied practically in the present time based on "an accounting of shoulder effects".

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