A lossless earth Green's function representation between any two subsurface points from surface reflection GPR data

Abstract

We present a three-dimensional scheme that can be used to compute the electromagnetic impulse response between any two subsurface points from surface reflection data measured at a single surface of a lossless medium. The scheme first computes a virtual vertical radar profile using the Marchenko scheme from which focusing wavefields are computed. With the aid of the Green's functions of the virtual vertical radar profiles these focusing wavefields are then used to compute the Green's function between any two points in the subsurface. One point is a virtual receiver and the other point is a virtual source. Virtual radar images can be created as well as the whole time evolution of the radar wave field throughout the subsurface generated by any subsurface virtual source. We show with a numerical example that the method works well in a one-dimensional configuration.