Knowledge of permafrost structure, with accumulations of free natural gas and gas hydrates, is indispensable for coping with spontaneous gas emission and other problems related to exploration and production drilling in Arctic petroleum provinces. The existing geophysical methods have different potentialities for imaging the permafrost base and geometry, vertical fluid conduits (permeable zones), taliks, gas pockets, and gas hydrate accumulations in the continental Arctic areas. The synthesis of data on cryological and geological conditions was the basis for a geophysical–geological model of northern West Siberia to a depth of 400 m, which includes modern permafrost, lenses of relict permafrost with hypothetical gas hydrates, and a permeable zone that may be a path for the migration of gas–water fluids. The model was used to model synthetic seismic, electrical resistivity tomography (ERT), and transient electromagnetic (TEM) data, thus testing the advantages and drawbacks of the three methods. Electrical resistivity tomography has insufficient penetration to resolve all features and can run only in the summer season. Seismic surveys have limitations in mapping fluid conduits, though they can image a horizontally layered structure in any season. Shallow transient electromagnetic (sTEM) soundings can image any type of features included into the geological model and work all year round. Thus, the best strategy is to use TEM surveys as the main method, combined with seismic and ERT data. Each specific method is chosen proceeding from economic viability and feasibility in the specific physiographic conditions of mountain and river systems.