Methane hydrate is stable only where ambient pressure exceeds the hydrate equilibrium pressure for the local temperature. The equilibrium curve is fit to the Clausius–Clapeyron form:
P_eq(T) = exp(33.818 − 8987.6 / T) [MPa, T in kelvin]
Ambient sediment conditions come from a hydrostatic pressure column and a linear geotherm below the seafloor:
P(z) = 0.101 + 0.0101·z [MPa, z = total depth below sea surface, m]
T(z_s) = T_bw + grad·z_s/100 [°C, z_s = depth below seafloor, m]
The base of the gas hydrate stability zone (GHSZ) is the sediment depth z_s where P(z_total) = P_eq(T(z_s)) — found here by bisection. Warmer bottom water or a steeper geotherm raises T(z_s) faster than pressure grows, so the crossing point moves shallower: the GHSZ thins from below, dissociating hydrate into free gas that migrates upward through a gas "chimney" toward the seafloor — the bubble stream you see.
Dissociation converts solid hydrate to gas + water faster than it can drain, building excess pore pressure Δu that lowers the effective stress on the slope. The infinite-slope factor of safety follows:
FS = [c' + (σ'v·cos²β − Δu)·tanφ'] / (γ_sat·D·sinβ·cosβ)
where D is the failure-plane depth (taken at the GHSZ base), β the slope angle, and Δu is scaled by how far the GHSZ has retreated from its pre-warming reference position — the same mechanism proposed for hydrate-related submarine slope failures such as those inferred on the Storegga and Cape Fear slides.
- Bottom-water temperature — the main driver of ocean-warming-induced dissociation.
- Water depth — sets hydrostatic pressure; shallower water needs colder bottom water to keep hydrate stable.
- Geothermal gradient — how fast sediment warms with depth; a steeper gradient shrinks the GHSZ from below even without ocean warming.
- Slope angle β — steeper slopes have lower baseline FS and fail at a smaller excess-pressure trigger.