The phrase "stability zone" refers to a state or condition in which things are calm, steady, and remain unchanged for a period of time. It suggests a sense of security, balance, and predictability. Full definition
The black contour shows the limits of the methane hydrate stability zone. (geosci.uchicago.edu)
One theory is that upward migration of fluid carries with it heat, preventing the methane from freezing as it travels through the nominal stability zone. (realclimate.org)
The hydrate stability zone will get thinner with an increase in the sediment column temperature. (realclimate.org)