Authors: D.Yu. Sirota

Title of the article: Restore the shape of the cross section of the cylindrical Current source as the solution of the inverse problem Of geoelectrics

Year: 2016, Issue: 5, Pages: 60-66

Branch of knowledge: Electrical engineering

Index UDK: 622.822.2: 622.271: 519.6

DOI: -

Abstract: The urgency of the discussed issue. One of the many purposes of the interpretation of geophysical data is the recovery of the natural source (electrical, thermal, magnetic, gravitational) fields of land. As is known, this problem can be reduced to solution of integral equations of Uryson 1-St kind. Unlike linear (fredholmian) integral equations of the 1st kind (based on the method of regularization A. N. Tikhonov) at present there is no complete theory for solving this kind of equations. Therefore, a review of various numerical options and attempts of application of the method A. N. Tikhonov such integral equations is undoubtedly interesting and relevant. The main aim of study. Development of numerical algorithm and its software implementation to solve the inverse problem of restoring the shape of the cross section of the cylindrical source of the electric field on the measured values of the potential on the surface. The methods used in the study Methods of mathematical physics for the formulation of the problem of restoring the shape of the source as ill-posed problems solutions of integral equations of the 1st kind. Methods of mathematical programming – to generate the numerical calculation scheme of approximate sequential restoration of the shape of the field source. The results. The calculation of the magnitude of the electric field potential generated by the test area of cylindrical shape with an elliptical cross section. suggested in a three-layer environment. Using the obtained values, the reverse is not solved-posed problems of restoring the shape of the cross section of the source electric field as the solution of integral equations of Fredholm – Uryson 1-St kind. Conducted a comparative analysis of the form and results of the calculation of the direct problem from precisely specified and blajenno found region.

Key words: ill-posed nonlinear inverse problem integral equation of Uryson-1 of the first kind the method of regularization A N Tikhonov interpretation of geophysical data

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