Physical properties
TerraTools provides tools that facilitate the creation of TERRA-readable tables of material properties.
Elastic properties
PerpleX
One common way to calculate material properties as a function of composition, pressure and temperature is using the software package PerpleX [Connolly, 2009].
TerraTools comes packaged with three functions to interface directly with PerpleX. The first is properties.perplex.make_build_files, that creates a very specific type of input file; specifically one designed to tell PerpleX's vertex program to compute the stable equilibrium assemblages at a fixed bulk composition over a 2D grid of pressures and temperatures. The function allows the user to split up the problem into many smaller grids, helping ease memory constraints.
The second PerpleX helper function in TerraTools is properties.perplex.run_build_files, that runs PerpleX's vertex and pssect software on all the build files created by properties.perplex.make_build_files.
Finally, the third PerpleX helper function in TerraTools is properties.perplex.perplex_to_grid, that creates a 3D numpy array of all the properties that TERRA needs, over the pressures and temperatures of interest.
Anelastic properties
The properties output by PerpleX are (for the most-part) properties at infinite frequency. The seismic velocities are therefore the purely elastic ones. To convert these seismic velocities to anelastic velocities, TerraTools provides access to attenuation models. At present, the module includes three variations on a simple but flexible attenuation model [Goes et al., 2004;Maguire et al., 2016], packaged in the class properties.attenuation.AttenuationModelGoes. The effects of anelasticity on shear wave velocity are incorporated using a model for the S-wave quality factor \(Q_S\) that varies with pressure \(P\) and temperature \(T\) as $$ Q_S(\omega,z,T) = Q_0 \omega \alpha \exp \left(\alpha g \frac{T_m(z)}{T} \right) $$ where \(\omega\) is frequency, \(\alpha\) is exponential frequency dependence, \(g\) is a scaling factor and \(T_m\) is the dry solidus melting temperature.
\(Q_K\) is chosen to be temperature independent.
The anelastic seismic velocities are calculated as follows: $$ \lambda = \frac{4}{3} \left(\frac{V_{\text{S,el}}}{V_{\text{P,el}}}\right)^2 $$ $$ {Q_P}^{-1} = {(1 - \lambda)}{Q_K}^{-1} + {\lambda}{Q_S}^{-1} $$ If \({Q_P}^{-1}\) is negative, it is set to 0.
The properties.attenuation.AttenuationModelGoes models are constructed from three parts:
- A model for the solidus temperature \(T_m\) as a function of pressure, given by the function properties.profiles.peridotite_solidus designed as part of the TerraTools project to capture available experimental data [Hirschmann, 2000;Herzberg et al., 2000;Fiquet et al., 2010].
- A highly simplified model for the mineralogy of the mantle, split into upper mantle, transition zone and lower mantle. The proportions of each zone as a function of pressure and temperature are provided by the function properties.attenuation.mantle_domain_fractions.
- Parameters for the attenuation model for each mantle mineralogy. Three model parameterisations are provided with different temperature dependencies on attenuation: Q4Goes (weak temperature dependence), Q6Goes (strong temperature dependence), and Q7Goes (moderate temperature dependence). The favoured model is Q7Goes, which produces a good agreement with published studies on attenuation [Matas and Bukowinski, 2007].
| Model | Layer | \(Q_0\) | \(g\) | \(\alpha\) | \(Q_K\) |
|---|---|---|---|---|---|
| Q4 | upper mantle | 0.1 | 38.0 | 0.15 | 1000.0 |
| transition zone | 3.5 | 20.0 | 0.15 | 1000.0 | |
| lower mantle | 35.0 | 10.0 | 0.15 | 1000.0 | |
| Q6 | upper mantle | 0.1 | 38.0 | 0.15 | 1000.0 |
| transition zone | 0.5 | 30.0 | 0.15 | 1000.0 | |
| lower mantle | 3.5 | 20.0 | 0.15 | 1000.0 | |
| Q7 | upper mantle | 0.1 | 38.0 | 0.15 | 1000.0 |
| transition zone | 0.5 | 30.0 | 0.15 | 1000.0 | |
| lower mantle | 1.5 | 26.0 | 0.15 | 1000.0 |
To ensure smooth behaviour, the effective \(Q_S\), \(Q_K\) and \(\alpha\) are given by the linear proportion-weighted sum of the \(Q_S\), \(Q_K\) and \(\alpha\) for each material at every \(P\)-\(T\) point.
| Connolly, 2009 | Connolly J.A., 2009. The geodynamic equation of state: What and how. Geochemistry, Geophysics, Geosystems. 10. 10.1029/2009GC002540 |
| Goes et al., 2004 | Goes S., Cammarano F. and Hansen U., 2004. Synthetic seismic signature of thermal mantle plumes. Earth and Planetary Science Letters. 218, pp.403-419. 10.1016/S0012-821X(03)00680-0 |
| Maguire et al., 2016 | Maguire R., Ritsema J., van Keken P.E., Fichtner A. and Goes S., 2016. P- and S-wave delays caused by thermal plumes. Geophysical Journal International. 206, pp.1169-1178. 10.1093/gji/ggw187 |
| Hirschmann, 2000 | Hirschmann M.M., 2000. Mantle solidus: Experimental constraints and the effects of peridotite composition. Geochemistry, Geophysics, Geosystems. 1, pp.1042-26. 10.1029/2000GC000070 |
| Herzberg et al., 2000 | Herzberg C., Raterron P. and Zhang J., 2000. New experimental observations on the anhydrous solidus for peridotite KLB-1. Geochemistry, Geophysics, Geosystems. 1, pp.1051-14. 10.1029/2000GC000089 |
| Fiquet et al., 2010 | Fiquet G., Auzende A.L., Siebert J., Corgne A., Bureau H., Ozawa H. and Garbarino G., 2010. Melting of Peridotite to 140 Gigapascals. Science. 329, pp.1516. 10.1126/science.1192448 |
| Matas and Bukowinski, 2007 | Matas J. and Bukowinski M.S., 2007. On the anelastic contribution to the temperature dependence of lower mantle seismic velocities. Earth and Planetary Science Letters. 259, pp.51-65. 10.1016/j.epsl.2007.04.028 |