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Full waveform inversion (FWI) is a powerful tool to quantify Earth properties of the subsurface from seismic data, and has become a major area of research. Because of very high computational cost, FWI has so far been used for either 2D full elastic or 3D acoustic media. Here we propose an efficient way to perform time-lapse elastic FWI in 3D using grid injection method, which allows for efficient calculation of synthetic seismograms after model alterations within a localized area. The technique allows for significant reductions in computational time and memory requirements without noticeable losses in accuracy.