Integral characteristics in the inverse problem of magnetotelluric sounding

This article examines some aspects of the one-dimensional inverse problem of magnetotelluric sounding. A uniqueness theorem is proved in the presence ofS-surfaces. A numerical algorithm based on transformation formulas is proposed. This research was partially supported by Russian Foundation for Basic Research (grant No. 96-01-00410) and by the State Scientific-Technical Program “Future Information Technologies” (grant No. 0201.06.010). Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 53–66, 1998.     

Linearization method in two-dimensional inverse problem of magnetotelluric sounding

An algorithm is described for the two-dimensional inverse problem of magnetotelluric sounding with E-polarization, based on minimization of the Tikhonov smoothing functional by the Newton—Kantorovich method (linearization method). The method of integral equations is used in the algorithm to solve the direct problem of magnetotelluric sounding. An iterative method is constructed for the solution of the integral equation in the direct problem and a rate of convergence bound is derived for this method.Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 199–215, 1986.     

Quasi-one-dimensional method for the two-dimensional magnetotelluric sounding inverse problem

The two-dimensional magnetotelluric sounding inverse problem is solved by a quasi-one-dimensional method. A linearization method is proposed for one-dimensional inverse problems. The appearance of false conducting structures in the solution of the inverse problem is considered and some counter-measures are suggested. The quasi-one-dimensional method is applicable to many-dimensional magnetotelluric sounding inverse problems if the electrical conductivity is a priori known to vary slowly along the Earth’s surface. __________ Translated from Prikladnaya Matematika i Informatika, No. 22, pp. 5–11, 2005.     

The inverse problem of electromagnetic frequency sounding of stratified media

A solution method is proposed for the inverse problem of electromagnetic sounding of a stratified medium with a field excited by an electrical source. The numerical solution of the problem is analyzed using a one-dimensional model of the medium with piecewise-constant variation of the geoelectrical parameters.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 159–165, 1985.     

Unique solvability of the inverse problem of impulse electromagnetic sounding

The article considers the inverse problem of impulse electromagnetic sounding with a field source in the form of a powerful one-time pulse. Unique solvability is proved for the inverse problem involving simultaneous determination of both the equation coefficient and the boundary condition in the boundary-value problem for an equation of parabolic type.Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach. Matematicheskoi Fiziki, pp. 18–21, 1993.     

Quasi-one-dimensional method for the two-dimensional inverse problem of magnetotelluric sounding

The article presents a quasi-one-dimensional method for solving the inverse problem of electromagnetic sounding. The quasi-one-dimensional method is an iteration process that in each iteration solves a parametric one-dimensional inverse problem and a two-dimensional direct problem. The solution results of these problems are applied to update the input values for the parametric one-dimensional inverse problem in the next iteration. The method has been implemented for a two-dimensional inverse problem of magnetotelluric sounding in a quasi-layered medium.     

A solution method for the inverse problem of magnetotelluric sounding

We consider the inverse problem of magnetotelluric sounding for integral conductivity. The problem is proved to be stable to changes in input data.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 165–174, 1985.     

Unique solvability of the inverse two-dimensional problem of magnetotelluric sounding forH-polarization

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 86–94, 1994.     

An inverse spectral problem

In this article an infinite periodic Jacobi matrix is under consideration. It is shown that the spectrum of the matrix consists of a single finite interval if and only if the period of the matrix is equal to unity.     

Spectral approach to quasi-3D inverse problem of vertical electric sounding

A method for solving the inverse problem of vertical electric sounding is proposed and investigated. The method uses the anomalous apparent resistivity spectrum. Translated from Prikladnaya Matematika i Informatika, No. 1, pp. 68–77, 1999.     

An inverse problem of Hamiltonian dynamics

We study the question of whether for a natural Hamiltonian system on a two-dimensional compact configuration manifold, a single trajectory of sufficiently high energy is almost surely enough to reconstruct a real analytic potential.

     

Spectral method for the inverse vertical electrical sounding problem in two-dimensional quasi-layered media

The spectral method is considered for solving the direct and inverse problems of vertical electrical sounding (VES) in two-dimensional quasi-layered media. The behavior of the anomalous potential spectrum is analyzed. An example is presented applying the spectral method to solve the inverse VES problem. Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 34–43, 1999.     

Uniqueness of the solution of the inverse problem of magnetotelluric sounding for two-dimensional media

Uniqueness of the solution of the inverse problem of magnetotelluric sounding in two-dimensional media is proved under certain assumptions on conductivity.Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 231–242, 1986.