Rock Property Update Steps

[1] Update density $\rho_m$ for each marker $m$ using equation eq:density with thermal expansion coefficient $\alpha_m$, compressibility $\beta_m$, temperature $T_m$, pressure $P_m$, and reference density $\rho_{ref,m}$.

[2] Update heat capacity $C_{p,m}$ for each marker $m$ using equation eq:heat-capacity with heat capacity at $20^\circ C$ $C_{p20,m}$ and marker temperature in degrees Celsius $T_{^{\circ}C,m}$.

[3] Update marker thermal conductivity $k_m$ for each marker $m$ using equation eq:thermal-conductivity with reference thermal conductivity $k_{20^\circ C,m}$ and temperature $T_m$.

[4] Update marker adiabatic coefficient $c_{adi,m}$ using equation eq:adiabatic-coefficient with thermal expansion coefficient $\alpha_{m}$ and marker temperature $T_m$.

[5] Update sediment rock properties $\rho_m$, $k_m$ and $C_{p,m}$ for each marker $m$ to account for sediment porosity $\phi_m$ if marker composition $C_m$ is sediment using equations eq:sediment-rock-props with matrix properties for density, thermal conductivity and heat capacity equal to the current marker properties $\rho_m$, $k_m$ and $C_{p,m}$, respectively.

[6] Update $\rho_m$ and $k_m$ for each marker $m$ to account for serpentinization using equations eq:density-serpentinization and eq:thermal-conductivity-serpentinization with serpentinization ratio $R_{serp,m}$ and current marker properties $\rho_m$ and $k_m$ to define properties prior to update step.

[7] Update marker density $\rho_m$ for each marker $m$ to account for depletion of rock matrix due to partial melting using equation eq:density-melt-depletion with extracted melt fraction $M_{extracted,m}$ and current marker density $\rho_m$ used to define density prior to this update step.

[8] Update marker density $\rho_m$ for each marker $m$ to account for partial melt in pore space using equation eq:density-melt-pore-space with pressure $P_m$, extractable melt fraction $M_{extractable,m}$ and the current marker density $\rho_m$ to define density prior to this update step.