This is a true cross-section, not a flattened 3D scene: the seafloor is walked outward from the shelf break as a chain of independent columns, each one x metres further down-slope with its own water depth
WD(x) = WD₀ + x·sin β
Every column solves the same hydrate phase-equilibrium root as a standalone problem — ambient pressure from a hydrostatic column crossing the Clausius–Clapeyron hydrate curve:
P_eq(T) = exp(33.818 − 8987.6 / T) [MPa, T in K]
P(z) = 0.101 + 0.0101·(WD(x)+z) [MPa]
T(z) = T_bw + grad·z/100 [°C]
Because water gets deeper going down-slope, ambient pressure rises with x even at constant temperature, so the GHSZ base is genuinely deeper at the foot of the slope than at its top — a spatial gradient the 3D single-column view cannot show. Where a column's base has retreated from its pre-warming depth, it sources excess pore pressure that then obeys a real 1D diffusion equation along the slope:
∂p/∂t = D·∂²p/∂x² + source(x) − decay·p
so pressure generated at one dissociating patch spreads into its neighbours before it dissipates — exactly the lateral pore-pressure coupling invoked in retrogressive submarine slope failures. Each column then gets its own infinite-slope factor of safety from its local depth and local pore pressure:
FS(x) = [c' + (σ'v·cos²β − Δu(x))·tanφ'] / (γ_sat·D(x)·sinβ·cosβ)
When a column's FS drops below 1 it fails and dumps a surcharge load onto the next column down-slope — the retrogressive mechanism that lets one weak patch drag its downhill neighbours into failure in sequence, as seen at slides like Storegga.
- Bottom-water temperature — warms every column, shrinking the GHSZ from below.
- Water depth at slope top — sets the pressure baseline the whole profile is built from.
- Geothermal gradient — how fast each column warms with sediment depth.
- Slope angle β — steepens both the bathymetry (how fast WD(x) grows) and lowers baseline FS.