In this paper, phase correction and amplitude compensation are introduced to a previously developed mixed domain method (MDM), which is only accurate for modeling wave propagation in weakly heterogeneous media. Multiple reflections are also incorporated with the one-way model to improve the accuracy. The resulting model is denoted as the modified mixed-domain method (MMDM) and is numerically evaluated for its accuracy and efficiency using two distinct cases: a layered medium and a human skull. It is found that the MMDM is significantly more accurate than the MDM for strongly heterogeneous media, especially when the phase aberrating layer is roughly perpendicular to the acoustic beam. Additionally, convergence study suggests that the second-order reflection is sufficient for wave modeling in lossy biological media. The method developed in this work could be used to facilitate therapeutic ultrasound for treating brain-related diseases and disorders.
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