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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 5, Pages 867–880 (Mi zvmmf11756)

Mathematical physics

On the simultaneous determination of the distribution density of sources equivalent in the external field and the spectrum of the useful signal

I. È. Stepanovaa, D. V. Lukyanenkob, I. I. Kolotovb, A. V. Shchepetilovb, A. G. Yagolab, I. A. Kerimova, A. N. Levashovb

a Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, 123242, Moscow, Russia
b Lomonosov Moscow State University, 119991, Moscow, Russia

Abstract: The article examines the possibility of simultaneous reconstruction of sources equivalent in the external field and spectral characteristics of the useful signal. Examples of variational formulations are given for various versions of the method of linear integral representations, and the problem is formulated of finding the distribution density of gravitating or magnetic masses on several horizontal planes and the Fourier transform of an anomalous field element from the values of a disturbed signal known at points of a certain observation network.

Key words: systems of linear algebraic equations, integral representations, Poisson summation formula.

UDC: 519.6

Received: 28.06.2023
Revised: 28.06.2023
Accepted: 14.01.2024

DOI: 10.31857/S0044466924050147


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:5, 1089–1102

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© Steklov Math. Inst. of RAS, 2026