A simulation of the synthetic aperture radar (SAR) observation of a complex sea scene is proposed. The observed sea patch consists of sea clutter and a metallic, steady object. The simulation process is based on a local, discrete calculation using the finite difference method in the time domain. This approach turns out to be relevant when considering precise, complex scenes such as depicted in the study, despite a few drawbacks that are enlightened in the article. Antenna synthesis is performed upon a series of simulations using finite differences, and leads to the formation of a SAR image of the studied scene.