Hydrothermal Update Steps

For each marker $m$ in drainage basin $k$ do:

  1. Check if Hydrothermal Cooling Criteria are satisfied.
  2. If criteria are met, update Effective Thermal Conductivity.

Hydrothermal Cooling Criteria

[1] Marker composition $C_m$ is normal or fractionated gabbro, normal or fractionated gabbroic emplaced magma, basalt, mantle or continental crust.

[2] There is a water column above the marker indicated by $y_{ml} > y_{sl}$ where $y_{ml}$ is the y-coordinate of the mudline at the x-coordinate $x_m$ of the marker and $y_{sl}$ is y-coordinate of sea level.

[3] The marker is below sea level as indicated by $y_m > y_{sl}$ where $y_m$ is the y-coordinate of the marker.

[4] Sediment thickness at the x-coordinate of the marker $d_{sed,x_m}$ is below a threshold of 2500 m.

Effective Thermal Conductivity

[1] Calculate the x-limits of the molten zone $x_{molten}^{min}$ and $x_{molten}^{max}$ using equation eq:x-molten-limits with the x-coordinate of the mid-point of the gabbroic molten zone $x_{molten,k}$ and the width of the gabbroic molten zone $W_{molten,k}$ where $k$ is the drainage basin index.

[2] Calculate the distance from the molten zone $D_{molten}$ using equation eq:distance-from-molten-zone with $x_{molten}^{min}$, $x_{molten}^{max}$ and the x-coordinate of the marker $x_m$.

[3] Calculate the hydrothermal distance factor $f_{hydro}$ using equation eq:hydrothermal-distance-factor with $D_{molten}$.

[4] Calculate the distance-based Nusselt number $Nu_{dist}$ using equation eq:distance-based-nusselt with $f_{hydro}$.

[5] Calculate the effective Nusselt number $Nu_{eff}$ using equation eq:effective-nusselt with $Nu_{dist}$, the plastic strain rate $\dot \epsilon_{plastic,m}$ and plastic strain $\epsilon_{plastic(m)}$ of the marker $m$.

[6] Update marker thermal conductivity $k_m$ using equation eq:hydrothermal-k with the current thermal conductivity $k_m$ as the unmodified thermal conductivity of the marker, marker x-coordinate $x_m$, marker y-coordinate $y_m$, marker temperature $T_m$, the submud depth of the marker $d_{sm,m}$, sediment thickness at x-coordinate of marker $d_{sed,x_m}$, y-coordinate of mudline at the x-coordinate of marker $y_{ml}$ and the effective Nusselt number $Nu_{eff}$.