This paper is of survey and methodological nature. A brief overview of the most common methods of active marine electrical prospecting is given. The problems of effective numerical and analytical solution of Maxwell's equations in the frequency domain are considered for the electrical prospecting on the basis of the classical 1D multilayer model of the medium. The electromagnetic field response in the form of Hankel integrals is received using the approach proposed by K. Key. The effective numerical calculation of integrals by extraction of exponential asymptotics, and separate calculation of terms with different speed of convergence is considered. In this case, the approach of the 'additive scheme' developed by the author is used, in which the solution for a multilayer medium is represented as a sum of solutions for 2-, 3-layer, etc. media. This not only speeds up calculations and improves their accuracy, but is also convenient for parallelization. The analytical solution for the most poorly convergent case of two-layer air-water medium including 'air wave' is constructed. As an example, the results of calculations for the different frequencies, depths of the hydrocarbon layer and thicknesses of the water layer are presented.

electrical prospecting, Hankel integrals, numerical calculation of integrals, air wave

Mathematical modelling in actual problems of science and technics

Popov Sergey Borisovich,  ,  orcid.org/0000-0002-1608-6393,  KIAM RAS