Elastic full-waveform inversion requires the capability to efficiently do accurate forward seismic<br>simulations based upon an earth model. The rotated staggered grid (Saenger, 2000) has been<br>a great advance for accurate elastic wave simulation in isotropic and anisotropic media but has<br>requirements that complicate source insertion too close to a free surface boundary. Coarse-grid<br>simulations limited to lower-frequency components in the data are frequently used to accelerate<br>early stages of waveform inversion both for computational efficiency and to better condition the<br>inversion (Bunks et al., 1995). This works better for acoustic waveform inversion than in the<br>elastic case. In the elastic case, the free-surface boundary requires a fine spatial grid both for<br>accurate computation of surface waves and for accurate source insertion. These requirements<br>offset part of the multi-grid advantage, especially for typical seismic acquisition geometries with<br>sources and receivers located somewhere near the surface of the earth.


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