An inverse scattering approach to imaging using Marchenko equations in the presence of a free surfac

The Green's function is the impulse response of a system and is used to infer the properties of the system from surface measurements. In exploration seismology, imaging algorithms use estimates of the Green's functions along with surface measurements to image the subsurface, i.e. locate the Earth's interfaces and its properties, so as to identify valuable energy resources. These conventional imaging algorithms only account for singly reflected waves (primaries) in the subsurface and hence, in the subsurface image, produce false interfaces in the presence of multiply reflected waves (internal and free-surface multiples).;Recent work has shown that we can retrieve the Green's function that accounts for primaries and internal multiples. Imaging with these Green's functions reduces the artifacts caused by internal multiples compared to conventional imaging algorithms. These Green's functions require the free-surface multiples to be removed from the surface measurements before retrieval and imaging.;I modify the retrieval of the Green's function to account for free-surface reflections and therefore no longer require the free-surface multiples to be removed from the surface measurements. Thus the Green's function, in the method I propose, includes not only primaries and internal multiples but also free-surface multiples. These Green's functions are constructed from an arbitrary point in the subsurface (no physical receiver is required at this location) to the surface..;The method I use to retrieve the Green's function does not specify the approach to image the subsurface. In this thesis I also analyze different imaging strategies using the retrieved Green's functions. Imaging with these Green's functions reduces the artifacts caused by multiply reflected waves compared to standard imaging algorithms. Significantly, the Green's function that I retrieve and use for imaging require the same inputs as conventional imaging algorithms: the surface measurements and a smooth version of the subsurface velocity.;I also extend the construction of the Green's function from the subsurface to the surface to any two arbitrary points in the subsurface (no physical source or physical receiver is required at either of these locations). This Green's function is called the virtual Green's function and includes all the primaries, internal and free-surface multiples. The virtual Green's function retrieval requires the same inputs as the previously mentioned Green's functions.