Marchenko equations for acoustic Green's function retrieval and imaging in dissipative media

We present a scheme for Marchenko imaging in a dissipative heterogeneous medium. The scheme requires measured reflection and transmission data at two sides of the dissipative medium. The effectual medium is the same as the dissipative medium, but with negative dissipation. We show how the measured double-sided data can be combined to obtain the single-sided reflection response of the effectual medium. Two sets of single-sided Marchenko equations follow that are used to compute to the focusing wavefield and the Green functions. Each uses single-sided reflection responses of the dissipative and effectual medium. To start the solution for these equations an initial estimate of the dissipation is required in addition to the estimate of the travel time of the first arrival. Avoiding the estimate of dissipation of the first arrival in a low-loss medium does not have a detrimental effects on the image quality. The numerical example shows the effectiveness of this strategy.