Ray-based Q-estimation methods have serious drawbacks for complex depth-imaging problems. In the presence of complex wave propagation (i.e. multipathing and geometrical dispersion), ray-based migration methods often cannot produce high-quality images, while wavefield-continuation methods yield better images. Therefore, wave-equation MQA (WEMQA) is needed to avoid the well-known instability problems that rays encounter when the Q model is complex and has sharp boundaries. The objective function of this method minimizes the residual wavenumber shift (equation 23) in the angle/offset domain. The theory and numerical results for this method are a topic of ongoing study.