Geotherms

burnman.geotherm.brown_shankland(depths)

Geotherm from [BS81]. NOTE: Valid only above 270 km

Parameters:

depths : list of floats

The list of depths at which to evaluate the geotherm. \([m]\)

Returns:

temperature : list of floats

The list of temperatures for each of the pressures. \([K]\)

burnman.geotherm.anderson(depths)

Geotherm from [And82].

Parameters:

depths : list of floats

The list of depths at which to evaluate the geotherm. \([m]\)

Returns:

temperature : list of floats

The list of temperatures for each of the pressures. \([K]\)

burnman.geotherm.adiabatic(pressures, T0, rock)

This calculates a geotherm based on an anchor temperature and a rock, assuming that the rock’s temperature follows an adiabatic gradient with pressure. This amounts to integrating:

\[\frac{\partial T}{\partial P} = \frac{ \gamma T}{ K_s }\]

where \(\gamma\) is the Grueneisen parameter and \(K_s\) is the adiabatic bulk modulus.

Parameters:

pressures : list of floats

The list of pressures in \([Pa]\) at which to evaluate the geotherm.

T0 : float

An anchor temperature, corresponding to the temperature of the first pressure in the list. \([K]\)

rock : burnman.composite

Material for which we compute the adiabat. From this material we must compute average Grueneisen parameters and adiabatic bulk moduli for each pressure/temperature.

Returns:

temperature: list of floats

The list of temperatures for each pressure. \([K]\)

burnman.geotherm.dTdP(temperature, pressure, rock)

ODE to integrate temperature with depth for a composite material Assumes that the minerals exist at a common pressure (Reuss bound, should be good for slow deformations at high temperature), as well as an adiabatic process. This corresponds to conservation of enthalpy. First consider compression of the composite to a new pressure P+dP. They all heat up different amounts dT[i], according to their thermoelastic parameters. Then allow them to equilibrate to a constant temperature dT, conserving heat within the composite. This works out to the formula:

\[dT/dP = T*\frac{\Sigma_i(X[i]*C_{p}[i]*\gamma[i]/K[i])}{\Sigma(X[i]*C_{p}[i])}\]

Where \(X[i]\) is the molar fraction of phase \(i\), \(C_p\) is the specific heat at constant pressure, \(\gamma\) is the Gruneisen parameter and \(K\) is the bulk modulus. This function is called by burnman.geotherm.adiabatic(), and in general it will not be too useful in other contexts.

Parameters:

pressure : float

The pressure at which to evaluate dT/dP. \([Pa]\)

temperature : float

The temperature at which to evaluate dT/dP. \([K]\)

rock : burnman.composite

Material for which we compute dT/dP.

Returns:

dT/dP : float

Adiabatic temperature gradient for the composite at a given temperature and pressure. \([K/Pa]\)