“…In this case, Equation (A22) is a convolution equation with respect to transversal coordinates, and it is possible to obtain the transversal spectrum of the scattered field in the form of a one-dimensional integral with respect to the depth coordinate z that includes the product of the transverse spectrum of inhomogeneity and the integral form of the corresponding transverse spectra of the Green functions: where the exact formulas for the Green functions were obtained in [ 19 ] for inhomogeneity in layered media. Substituting (A23) in (A2) gives a one-dimensional integral equation obtained in [ 19 ], which was also used in the multifrequency method in cases of frequency-independent permittivity [ 20 , 21 ]: From (A24) and (A1), one has the integral equation for the spectrum of the real-valued pulse: As is seen, Equation (A26) is, in general, an underdetermined equation that cannot be used directly in pulse diagnostics. However, in the case of the real-valued , (A24) is reduced to the integral equation: with the kernel Based on Equation (A24) with the kernel (A25), it is possible to propose various schemes of the tomography method based on data of the single-frequency measurements with the variable parameters of the source-receiver offset (base) similar to the method that was proposed and studied by the authors in [ 25 ].…”