Seawater, being a highly conductive medium, generates induced electromagnetic fields in space when moving within the geomagnetic field. This phenomenon increases the difficulty of electromagnetic exploration for offshore oil, gas, and mineral resources. To quantitatively calculate the distribution of the wave-induced magnetic field generated by ocean waves at different sea depths, this study establishes a three-layer model (air layer, seawater layer, and seabed layer) based on marine electromagnetic theory, describing the wave motion system. By applying the boundary condition that the normal component of the magnetic field is continuous across interfaces, a model for the monochromatic wave-induced magnetic field in an ocean of arbitrary finite depth is derived. When the total ocean depth approaches infinity, the calculated results from this model coincide with those of Weaver's infinite-depth ocean wave model, demonstrating the model's validity. Utilizing this validated model, the influence of total ocean depth on the monochromatic wave-induced magnetic field is analyzed. Furthermore, building upon the monochromatic wave model, a wave spectrum is introduced to investigate polychromatic wave-induced magnetic fields. The distribution characteristics of these polychromatic fields, possessing identical total energy but varying frequency ranges, are computed. The results indicate that: (1) For monochromatic waves at different total ocean depths, the wave-induced magnetic field exhibits a maximum value as a function of depth within the water column, and the variation of the field with wave period is significantly affected by the total ocean depth; (2) The distribution characteristics of polychromatic wave-induced magnetic fields across different total ocean depths are similar to those of monochromatic waves but are markedly influenced by the frequency range of the wave spectrum. The modeling approach proposed in this study provides an effective means for predicting the distribution of wave-induced magnetic fields in oceans of varying total depths. This offers a reliable theoretical basis for advancing marine electromagnetic detection technology and enhancing the precision of marine resource exploration.