A comment on missing data
The Perple_X thermodynamic data file format is described in detail in the program documentation (vdoc.ps), for present purposes it is only necessary to know that the file consists of a header section followed by entries for the thermodynamic entities (e.g., fluid and mineral species) described by the data base (Figure 1).
1. An abridged example of a Perple_X
thermodynamic data file (hp98ver.dat).
The header section contains various data (the first 13 lines here), which may
be followed by comments that describe the data base and its entries, the header
section is terminated by a left justified line beginning with the word
“end” (marked here in red). The header section is followed by
entries (shown in blue) that define the thermodynamic properties of the mineral
and fluid species included in the data base. The first line of each entry is
formatted and begins with the name of the species (usually abbreviated). The
remaining numeric data is unformatted. Comments may be placed between entries,
as between the entry for fo (forsterite) and fa (fayalite).
To create a thermodynamic data base for seismic velocity calculations it is necessary to modify the entries for all entities of interest to include the parameters necessary to compute the shear modulus as a function of pressure (p) and temperature (T) (the units of pressure and temperature are defined by the data base header section, typically these are bars and Kelvin). Optionally, the user may also provide parameters for the adiabatic bulk modulus (Ks) and density (r). Currently Perple_X expects the following functional forms
where pr and Tr are the reference pressure and temperature for the data base as defined in the header (typically 1 bar, 298.15 K); r0, m0 and K0 are the density, shear modulus and bulk modulus at the reference conditions and the pressure and temperature derivatives are constants. If the user provides empirical data for Ks and r0 then Perple_X computes seismic velocities using phase compositions, and proportions determined by free energy minimization in combination with the shear modulii and density computed from equations 1 and 2. However, if data is not provided for either or both Ks and r, then the requisite parameters are computed by differentiation of the free energy function as
where G is the molar free energy and N is the molar formula weight.
The first line of each modified entry must be altered to indicate the nature of the modifications. This line is formatted, such that the first 8 characters are reserved for the entry name (left justified), the name is followed by four integer numbers, each of which occupies two columns, and the remaining part of the line may be used to for comments, e.g., for forsterite the first line reads
fo 1 0 0 0 H= -2171830.
If the entry is to be modified to include only parameters for the shear modulus, the second integer (JEMOD) after the name must be changed to 1, i.e.
fo 1 1 0 0 H= -2171830.
Alternatively, if the entry is to include parameters for both shear and bulk modulus the JEMOD must be changed to 2, and if the entry is to include parameters for the computation of density JEMOD must be 3. The parameters are then appended to the end of the entry in the order
the last 4-9 values are only read if JEMOD > 1, there are no formatting constraints for this data. Note that the amount of numeric data following the initial line may vary depending on the other integers specified on the first line (for a complete discussion of these parameters refer to the program documentation).
WARNING 1: If JEMOD = 0 for a mineral or fluid species Perple_X will not compute seismic velocities for any phase or phase assemblage involving the species.
WARNING 2: be careful to modify the entries consistently, Perple_X expects JEMOD*3 additional parameters at the end of each entry. Any inconsistency will cause the programs to crash with a data file format error.
Thermodynamic data file entries modified from Figure 1
to permit seismic velocity calculations (modifications in red; the header
section is not modified). A more complete version of this data base (seismo.dat)
is described elsewhere (Connolly &
Kerrick, 2002). Here JEMOD has been set to 1 for all phases except
“q” and “ftat”, for which it is zero. JEMOD = 1
instructs Perple_X to read only the
parameters for the shear modulus (Eq 1) and to compute the density and bulk
modulus from the thermodynamic data used for phase equilibria calculations.
Because JEMOD = 0 for “q” (quartz) and “ftat” (a talc
endmember species), with this file Perple_X
would not compute seismic velocities for any assemblage involving quartz or
talc (if the talc contains ftat species).
As customary in seismic velocity computations, in Perple_X it is assumed that all phases are elastically isotropic. Currently no corrections for anelastic behavior are made, though such corrections could be implemented by modification of WERAMI. Compressional- and shear-wave velocities (vp and vs) through an elastically isotropic fluid or homogeneous single crystal are given by
As a consequence of the pseudocompound approximation employed in pre-07 versions of Perple_X a homogeneous solution phase may be represented by more than one pseudocompound. When this is the case the parameters used in equations 6 & 7 are computed as
where is the value of the property in the phase of interest, is the molar proportion of the ith pseudocompound representing the phase, and is the value of property in that pseudocompound. Once the seismic velocities in each phase of an assemblage have been computed from equations 6 & 7, the elastic moduli of the aggregate are computed as
where is the moduli of interest, xj is the volume fraction of the jth phase, is the corresponding modulus, and is a weighting factor taken to be 0.5 for the Voigt-Reuss-Hill averaging scheme.