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We study the effectiveness of velocity-only time-domain waveform inversion for inverting synthetic data modeled with both velocity and density contrasts. We present a detailed review of the Born approximation for the constant-density acoustic wave equation and its application to the inversion of velocity models for seismic reflection data. We create synthetic models with both constant and variable density and compare the effectiveness of velocity-only waveform inversion in each case. Results from this simple test suggest that density contrasts can hamper the reconstruction of velocity perturbations.