Fig. 3: 2D numerical model of hydrothermal circulation.

a An example hydrothermal modeling with constant fault width and the permeability contrast between fault and background. In this case, the assumed fault width (d) is 400 m, and the permeability contrast (c = k_df/k_b) is 60 (k_df = 3 × 10⁻¹⁴ m², k_b = 5 × 10⁻¹⁶ m²). Temperature field distribution is at quasi-steady state, and the isotherms for 100, 200, 300, and 400 °C are shown in green and the simulated vent field with high temperature of 379 °C is shown by red triangle. b The temperature–pressure paths of fluid tracers in our 2D numerical model. The blue lines are the modeled possible circulation paths for the hydrothermal circulations. Dashed lines mark phase regions (filled in different colors) of seawater. c The comparison of the assumed fault width with the predicted venting temperature. c = k_df/k_b = 10–100, and the horizontal dashed line represent the observed highest temperature of Longqi-1 venting fluids.