OPTIMIZATION APPROACH FOR SOLVING THE CONTINUATION PROBLEM IN FREQUENCY DOMAIN

The paper presents analytical expressions for solving the problem of continuation of the electromagnetic field in the frequency domain for a horizontally layered medium. The numerical solution algorithm uses layerwise recalculation of the required quantities, for which analytical expressions are presented in a form that allows calculations and layerwise recalculation without the accumulation of rounding errors. The solution to the continuation problem is obtained as a solution to the cost functional minimization problem. The strong convexity of the functional is proven, which implies the existence of a unique solution to the problem posed. Before solving the continuation problem, it is proposed to apply the Butterworth filter to smooth the radargrams and the Hilbert transform technique to clarify the coordinates of the discontinuity points of the medium.