Applying full-waveform methods to image small-scale structures of geophysical interest buried within the Earth requires the computation of the seismic wavefield over large distances compared to the target wavelengths. This represents a considerable computational cost when using state-of-the-art numerical integration of the equations of motion in three-dimensional earth models. "Box Tomography" is a hybrid method that breaks up the wavefield computation into three parts, only one of which needs to be iterated for each model update, significantly saving computational time. To deploy this method in remote regions containing a fluid-solid boundary, one needs to construct artificial sources that confine the seismic wavefield within a small region that straddles this boundary. The difficulty arises from the need to combine the solid-fluid coupling with a hybrid numerical simulation in this region. Here, we report a reconciliation of different displacement potential expressions used for solving the acoustic wave equation and propose a unified framework for hybrid simulations. This represents a significant step towards applying 'Box Tomography' in arbitrary regions inside the Earth, achieving a thousand-fold computational cost reduction compared to standard approaches without compromising accuracy. We also present examples of benchmarks of the hybrid simulations in the case of target regions at the ocean floor and the core-mantle boundary.