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The quantitative study of how subsurface reflectivity coefficients vary with reflection angle, generally known as amplitude-versus-angle (AVA) analysis, is widely established as a hydrocarbon indicator. AVA analysis is typically performed on fully processed data and uses 1D assumptions to derive its underlying equations. Elastic full-waveform inversion (FWI) offers an opportunity to bypass conventional AVA analysis, with its attendant simplifications and requirement for processed data, by directly inverting for Earth model parameters such as p- and s-wave velocities, and density. These parameters can give a complete description of the subsurface, including AVA information. However, despite recent progress on elastic FWI, full-bandwidth updates are still very difficult due to various technical and computational challenges. Recent work shows that AVA information can be extracted from acoustic FWI of data partitioned into different reflection angle ranges. We describe an alternative strategy for extracting AVA using acoustic FWI, based on an angle-dependent density. Our approach is more efficient than the data-partitioning method as it considers all angles in a single FWI simultaneously, and improves the angle estimate by computing it directly from the wavefield. We demonstrate this new approach using two synthetic data sets, with further validation on field data from the Barents Sea.