Electromagnetic Marchenko imaging in 1D

We present a one-dimensional lossless scheme to compute an image of a dissipative medium from two single-sided reflection responses. One reflection response is measured at or above the top reflector of a dissipative medium and the other reflection response is computed as if measured at or above the top reflector of a medium with negative dissipation which we call the effectual medium. These two reflection responses together can be used to construct the approximate reflection data of the corresponding lossless medium by multiplying and taking the square root in time domain. The corresponding lossless medium has the same reflectors as the dissipative medium. Then the constructed reflection data can be used to compute the focusing wavefield which focuses at the chosen location in subsurface of the dissipative medium. From the focusing function and constructed reflection response the Green’s function for a virtual receiver can be obtained. Because the up- and downgoing parts of the Green’s function are retrieved separately, these are used to compute the image. We show with an example that the method works well for a sample in a synthesized waveguide that could be used for measurements in a laboratory.