Controlled-source electromagnetic (CSEM) field surveys offer a geophysical method to discriminate between high and low hydrocarbon saturations in a potential reservoir. However, the same geological processes that create the possible hydrocarbon reservoir may also create topography and near-surface variations of resistivity (e.g., shallow gas or hydrates) that can complicate the interpretation of CSEM data. In this paper, we discuss the interpretation of such data over a thrust belt prospect in deepwater Sabah, Malaysia. We show that detailed modeling of the key scenarios can help us understand the contributions of topography, near-surface hydrates, and possible hydrocarbons at reservoir depth. Complexity at the surface and at depth requires a 3D electromagnetic modeling code that can handle realistic ten-million-cell models. This has been achieved by using an iterative solver based on a multigrid preconditioner, finite-difference approach with frequency-dependent grid adaptation.