We develop a theory that relates gas hydrate saturation in marine sediments to the depth of the sulfate-methane transition (SMT) zone below the seafloor using steady state, analytical expressions. These expressions are valid for systems in which all methane transported into the gas hydrate stability zone (GHSZ) comes from deeper external sources (i.e., advective systems). This advective constraint causes anaerobic oxidation of methane to be the only sulfate sink, allowing us to link SMT depth to net methane flux. We also develop analytical expressions that define the gas hydrate saturation profile based on SMT depth and site-specific parameters such as sedimentation rate, methane solubility, and porosity. We evaluate our analytical model at four drill sites along the Cascadia Margin where methane sources from depth dominate. With our model, we calculate average gas hydrate saturations across GHSZ and the top occurrence of gas hydrate at these sites as 0.4% and 120 mbsf (Site 889), 1.9% and 70 mbsf (Site U1325), 4.7% and 40 mbsf (Site U1326), and 0% (Site U1329), mbsf being meters below seafloor. These values compare favorably with average saturations and top occurrences computed from resistivity log and chloride data. The analytical expressions thus provide a fast and convenient method to calculate gas hydrate saturation and first-order occurrence at a given geologic setting where vertically upward advection dominates the methane flux.