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Seismic modelling and inversion often require the calculation of many closely related forward problems. If model perturbations are restricted to a small subvolume, a local wave solver can be an efficient alternative to a wave simulation performed on the entire model. We present a method for immersive wave simulation which, unlike previous methods, does not require explicit knowledge of reflectors in the background medium outside the simulated target area. The information about the background medium is contained in Green's functions which provide the interactions of the wave simulation with its surrounding background. These Green's functions are derived with the Marchenko scheme, using surface reflection data, a smooth velocity model and density information of the simulated area. Once they are available we can introduce arbitrary perturbations in the target area. This allows for an efficient simulation of a suite of models that differ in the target area, but are unchanged elsewhere. The wave simulation is fully coupled with its surroundings, including all orders of multiple scattering, but we assume preferential vertical wave propagation when using the Marchenko scheme. We can further use the Marchenko-derived overburden transmission response to calculate reflection responses measured at the acquisition surface with the perturbed target area. This calculation however requires availability of additional amplitude information. [ABSTRACT FROM AUTHOR]