An Efficient Algorithm for Solving the Inverse Problem of Locating the Interfaces Using the Frequency Sounding Data

We consider the inverse coefficient problem of locating the interface positions arising in frequency sounding of layered media. Such a problem is of particular interest in the exploration of geophysics, underwater acoustics and electromagnetics, optical sensing, and so forth. We found that a simplified algorithm can be constructed to determine the approximate positions of interfaces. Unlike the conventional nonlinear least squares, this algorithm does not require the time-consuming constrained optimisation. Instead, the predictor–corrector method is applied to solve numerically the auxiliary Cauchy problem for a Riccati equation. The feasibility of this algorithm is demonstrated in computational experiments with a model problem of electromagnetic frequency sounding of layered media.