Direct and inverse problems in electromagnetic sounding of three-dimensional heterogeneous medium

The structure and features of a software package for 3D inversion of geophysical data are considered. The presented software package is focused on solving direct and inverse problems of electrical exploration and engineering geophysics. In addition to the parameters that determine physical properties of the medium, the software package allows you to restore the geometry parameters of the geophysical model, namely layer reliefs and boundaries of three-dimensional inclusions. The inclusions can be in the form of arbitrary hexagons or prisms with a polygonal base. The software package consists of four main subsystems: an interface, subsystems for solving direct and inverse problems, and a client-server part for performing calculations on remote computing nodes. The graphical interface consists of geophysicist-oriented pre- and postprocessor modules that allow you to describe the problem and present the results of its solution in user-friendly terms. To solve direct problems, the finite element method and the technology for dividing the field into normal and anomalous components are used. At the same time, special methods of discretization of the computational domain are used, which make it possible to take into account both the complex three-dimensional structure of the environment and the presence of man-made objects (wells) in the computational domain. To increase the efficiency of solving direct problems, nonconforming grids with cells in the form of arbitrary hexahedrons are used. Methods for efficient calculation of derivatives (with respect to these parameters) necessary for solving inverse problems by the Gauss-Newton method are also described for the geometry parameters. The main idea for efficient derivatives computation is to identify the effect of changing the value of the parameter (used to compute the value of the generalized derivative) on the problem. The main actions performed by the subsystem for solving inverse problems and the features associated with the processing of geometry parameters are described.

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Mathematical Modeling of Direct and Inverse Problems of Dynamics of Thick Elastic Layer. Part I. Mathematical Modeling of the Field of Transverse Dynamic Displacements of Layer

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v48.i7.60 ◽

2016 ◽

Vol 48 (7) ◽

pp. 55-64

Author(s):

Vladimir Antonovich Stoyan ◽

Konstantin V. Dvirnychuk

Keyword(s):

Mathematical Modeling ◽

Inverse Problems ◽

Elastic Layer ◽

Direct And Inverse Problems ◽

Transverse Dynamic ◽

Inverse Problems Of Dynamics

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Identification of the string boundary conditions using natural frequencies

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2016.1.007 ◽

2016 ◽

Vol 11 (1) ◽

pp. 38-52

Author(s):

I.M. Utyashev ◽

A.M. Akhtyamov

Keyword(s):

Inverse Problems ◽

Power Series ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Natural Frequencies ◽

Boundary Value ◽

External Environment ◽

Direct And Inverse Problems ◽

Symmetric Potential ◽

Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

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