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We present a new methodology for local wave field simulation after model updates using exact boundary conditions (EBC’s). The finite-difference time-domain (FDTD) solver can be applied to models of arbitrary complexity. We apply the local wave field modelling algorithm to a subset of the Sigsbee 2B model. We demonstrate that the wave field can be correctly modelled on a truncated domain and includes all (long-range) interactions with the surrounding domain. The proposed method, which is extendable to 3D and is also applicable to multiple disconnected truncated domains, could be advantageous for applications based on targeted iterative wave field recomputations, such as full waveform inversion (FWI).