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Imaging deep targets underneath highly heterogeneous overburden using data from non-ideal acquisition is always challenging. In Block SC38, offshore Philippines, the seismic energy propagation is disrupted by a complex volcanic system in the overburden, leading to washed-out imaging beneath the volcano. The absence of diving waves further complicates velocity modeling, and heterogeneous velocity variations challenge depth imaging. An accurate velocity model and advanced migration approach are both crucial for deep target imaging in this area. This paper demonstrates how the combination of Dynamic-Resolution Time-lag Full-waveform Inversion (DR-TLFWI) and Least-squares PSDM (LS-PSDM) addresses these challenges. DR-TLFWI optimizes contributions from low- and high-wavenumber components, improving velocity model accuracy for deep targets beyond the reach of diving waves. With the improved velocity, Least-squares PSDM (LS-PSDM) further compensates for illumination loss and enhances amplitude fidelity in complex subsurface conditions. The results demonstrate improved event focusing and gather flatness in the target reservoir, highlighting the effectiveness of DR-TLFWI with LS-PSDM for sub-volcanic imaging.