The article deals with the inverse problem of determining the transient resistance of the main pipeline insulating coating. For this, UAV measurements of the magnetic induction vector modulus of the magnetic field excited by the system of electrochemical cathodic protection of pipelines are used. The solution method is based on Tikhonov's method for finding the extremal of the regularizing functional. The developed algorithm is implemented in software. The results of computational experiments are presented.
The authors consider the problem of the computational investigation of cathodic protection electric fields measured for an underground pipeline taking into account the anisotropic nature of soil specific electrical conductivity. A computational experimental method was used to compare the figures for anisotropic soils against the current distribution for a homogeneous half-space; the influence of anisotropy factors and the azimuth conductivity tensor rotation angle for pipeline-enclosing soil on the electrical parameters of cathodic protection of the pipeline were investigated. It was demonstrated that protective capacity can vary significantly for areas close to the drainage points of cathode stations and for defective segments. It was concluded that there is a need to take into account terrain structure (its electrical anisotropy) when there are prerequisites of soil lamination/fracturing, or if its specific electrical conductivity contrast in the lateral direction is in excess of 2–2.5 times.
A mathematical model is constructed and computational experiments are performed to study the effect of anisotropy of the specific electrical conductivity of the soil on the distribution of electric and magnetic fields generated by cathodic electrochemical corrosion protection stations of the underground main pipeline (MP). The variation of electric and magnetic fields depending on the azimuth angle of rotation of the specific electrical conductivity tensor of the soil containing the pipeline is analysed.
Теория сейсморазведки базируется на теории упругости, где одну из важных ролей
играют материальные уравнения -- закон Гука. В уравнения теории упругости входит плотность среды. В общем случае в каждой точке среды необходимо определить матрицу параметров размерностью 12$\times$12 элементов. Эти параметры могут
быть диспергирующими, т.е. зависеть от частоты. Для такого количества параметров решение обратной задачи с использованием стандартных процедур измерений
и вычислений является затруднительным.
Предложен новый подход к решению обратных задач, основанный на развитии идеи
М.В. Клибанова. Исходя из векторного представления уравнений теории упругости,
получен баланс упругой энергии и интегральные уравнения для исследования принципа взаимности. Выведены объeмные интегральные уравнения, на основе которых
получено решение обратной задачи теории упругости. Рассмотрены некоторые примеры численной реализации решения прямой и обратной задач теории упругости в
трехмерно-неоднородных анизотропных моделях геологической среды.
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