Solving the inverse problem of GPR for linearly continuous quasi-homogeneous layers

The solution of the GPR inverse problem is considered in application to the context of linearly continuous quasi-homogeneous layers. A new implementation of the solution of Fredholm equation is proposed, allowing to extend the scope of the GPR method for evaluating the complex dielectric permittivity of a medium. The analytical and numerical methods based on Tikhonov regularization theory are developed for solving the Fredholm integral equation of the first kind (convolution) with respect to the required amplitude reflection coefficient. An algorithm is proposed to allocate the boundaries between linearly continuous quasi homogeneous ground layers. Theoretical calculations were performed in the approximation of non-polarized electromagnetic radiation. The quality of developed algorithm was tested by solving the inverse GPR problem for the model of three consecutive transparent non-absorbing layers and its solution is in good agreement with pre-known results.