Data-driven inversion of GPR surface reflection data for lossless layered media

Two wavefields can be retrieved from the measured reflection response at the surface. One is the Green´s function at a chosen virtual receiver depth level in a layered model generated by a source at the surface. The other wavefield consists of the upgoing and downgoing parts of a wavefield that focuses at the virtual receiver depth level. From the upgoing part of the focusing wavefield an image can be computed at one-way vertical travel time and with correct amplitudes of the local reflection coefficients as a function of incidence angle. These reflection coefficient values can be used to invert for electric permittivity and magnetic permeability. From these values and the known image times the layer thickness values can be obtained for each layer. This method renders the full waveform inversion problem for horizontally layered media a linear problem.