To solve the problems on the feasibility and techniques of resistive reservoir (e.g. hydrocarbon) exploration in offshore areas of China using MCSEM, this paper studies the frequency-domain electromagnetic responses of the 1D marine model excited by a horizontal electric source in the seawater with finite depth, establishing the theoretical base for 1D and 3D electromagnetic simulation. In the derivation of electromagnetic field formulas, the Lorentz-gauged potential in each layer is solved first, and then the Coulomb-gauged potential in each layer is derived from the solution of Lorentz-gauged potential in the corresponding layer by the relationship between these two kinds of potentials. Although the electromagnetic fields in all layers can be computed from either the Lorentz-gauged potentials or the Coulomb-gauged potentials, the Coulomb-gauged potentials are advantageous in finite-element computation. The electromagnetic fields and potentials of a long wire source can be obtained by integrating those for an electric dipole along the source length. The electromagnetic field formulas in seawater both for a horizontal electric dipole and for a long wire source are given in this paper and they are used to simulate the distribution of electric fields and magnetic fields over seafloor in underwater environments of varied depths. The effect of water depth on the electromagnetic anomalies of hydrocarbon reservoirs buried in seafloor is discussed in the end. The study results show that the intensity and shape of the electromagnetic anomalies markedly change with the decrease of water depth and only the Ex and Ez components reveal perceptible anomalies when seawater is very shallow, for example, 50 m. At last, the Ex anomalies for two known oil fields with different water depths are calculated, which show good prospect of the electric-source frequency-domain MCSEM in seafloor exploration, even in a shallow sea environment. The problems that need further study in the practical application of this method are also discussed.