Underground Gas Storage (UGS) facilities in depleted hydrocarbon reservoirs have garnered significant attention due to their inherent advantages of low operational risk, substantial storage capacity, and cost-effectiveness. However, the precise characterization of internal gas migration distribution patterns within such UGS systems continues to present a substantial scientific and technical challenge. This study analyzes the feasibility of applying the wide-field electromagnetic method(WFEM) to UGS gas-water migration monitoring by using coupled field finite element. Firstly,we established the correlation mechanism between the gas-water distribution state in UGS and formation electrical properties through effective medium theory, thereby obtaining an electromagnetic field coupled three-dimensional geological model containing the two-dimensional equivalent anomaly structure of UGS. We use Finite Element Method (FEM) to solve the electromagneic model, thereby quantifying the impacts of gas migration on the reservoir's electrical properties. Subsequently, electromagnetic forward modeling was conducted to generate the WFEM apparent resistivity distribution response. Subsequently, two distinct WFEM apparent resistivity parameters were computed for UGS models under diverse gas injection schemes. We systematically investigated the response characteristics of injection rate, injection duration, and gas migration direction on both apparent resistivity distributions, while rigorously evaluating the sensitivity of WFEM apparent resistivity to fluid distribution variations. The results show that two types of apparent resistivity changes can effectively track the state of gas migration in UGS,and the apparent resistivity calculated using the electric field component is consistent with the distribution of gas-water saturation in the UGS. This result demonstrates the potential ability of the WFEM to be applied to on-site monitoring of UGS gas status. This study aims to deliver a robust technical methodology for the refined operational management of large-scale, long-cycle UGS facilities.