Mohapatra, S. and McMechan, G.A., 2021. Wavenumber recovery by FWI from slowness-limited, and source-frequency-limited elastic seismic data. Journal of Seismic Exploration, 30: 577-600. Any feature in an elastic model can be extracted by full wavefield inversion (FWI) only if its physical wavenumbers (k) are also present in the illuminating and recorded wavefields. The effective incident wavenumbers contain the combined information in the incident wavefront directions (in the slownesses p) and in the frequencies o (in the source time function). The fundamental relationship is k = wp. Thus, the wavenumber spectral aperture of surface data can be increased by increasing the effective slowness aperture (e.g., by increasing the offset, or adding data from borehole recorders) and/or by increasing the frequency bandwidth of the source wavelet. For a given k, w and p are not unique; an infinite number of (@, p) pairs can provide the same k, but only if both are present. Because the acquisition geometry and the source spectral bandwidth are both discrete and finite, the wavenumber spectra of the inverted parameters of any target model can never be fully recovered by FWI; FWI images are always a bandlimited version of the complete solution. A prerequisite for minimizing cycle skipping in FWI is that the temporal and spatial sampling of the data and the model must be unaliased, and therefore satisfy the half-wavelength condition as the frequency is progressively increased during the FWI iterations. The phase of the data provides stronger constraints than the amplitude; thus velocities are better, fitted than densities. Image correlation, and calculation of the correlation coefficient (R° ) of model images quantify the behavior of decreasing model misfits as iterations proceed. Synthetic elastic examples for models containing finite bandwidths illustrate how the ability to recover wavenumbers is limited by the wavenumber information that is contained in the illuminating wavefield, and by the sampling of the data in both time and space.