Переводная версия статьи
Александров П. Н., Кризский В. Н. Решение нелинейной коэффициентной обратной задачи геофизики на основе интегральных уравнений / Физика Земли, № 2, 2022. С 136 - 143 .
Abstract—One of the promising modern trends in the development of the theory of solving inverse problems is the approach based on the idea of M.V. Klibanov (Beilina and Klibanov, 2012). In the cited work, the authors considered an inverse problem of identifying the objects with different dielectric properties using ground-penetrating radar method, which led to studying a nonlinear differential equation. This paper develops the idea of this approach leading to a linear matrix first-order partial differential equation. The solution of the linear inverse problem is presented for the case when the calculation formula for the field in the direct problem is the formula for the volumetric integral representation. The algorithm of this solution can be used to reconstruct physical properties of heterogeneous and anisotropic media for various geophysical methods. The results of computational experiments on the development of observation systems that simulate some practical cases are demonstrated. Keywords: linear coefficient inverse problem of geophysics, controlled sources, anisotropic, bianisotropic, elastic media DOI: 10.1134/S106935132202001X