Monitoring a time-lapse geophysical anomaly due to variation in the pore-fluid contents of a subsurface reservoir is critical for further development and management. However, it may be difficult to detect the changes in P-wave responses beyond a certain level of saturation. A comprehensive 3D finite-difference time domain (FDTD) forward modeling, based on idealized subsurface resistivity structures, demonstrates the possibility of marine controlled-source electromagnetic (CSEM) surveying to monitor the movement of subsurface storage. We focused on CSEM sensitivity studies with respect to variations in geometry and/or saturation of storage, evaluation of the effects of reservoir depths and lithology, and detection of leakage from the main storage. A 100% lateral expansion from the initial diameter (1500 m) of a typical plume with thickness and resistivity of 100 m and 80 Ωm, respectively, at 850 m below seafloor, results in 41% electric field (E-field) magnitude increase at 2500 m source-receiver offset for 0.5 Hz source frequency. In comparison, a 300% vertical expansion of a 50 m thick plume with diameter and resistivity of 2500 m and 80 Ωm, respectively, gives only a 7% E-field magnitude anomaly. An increase of the aspect ratio of a plume with diameter and thickness of 1750 and 130 m, respectively, by 110%, without volumetric change, results in a 20% E-field magnitude increase. The E-field magnitude differences due to saturation change by 20% in clay-rich (10% clay) and clean reservoirs are almost identical; thus, a time-lapse anomaly in a clay-rich reservoir might be detectable. A gradual inverse variation of offset and frequency can differentiate the responses of a 50 m thick shallow accumulation, 200 m below the seafloor, from the main plume at 850 m below the seafloor and allow for early warning of leakage.