- Accuracy tolerance:
- This controls the relative stepsize in the ODE
integrators. A value of 10-6 gives relative
accuracy to about 6 digits and should be more than
sufficient
- Activity:
- The actual
rate of decay of a radioactive
nuclide. ai=Lambdaici,
where Lambda is the decay constant (in s-1)
and c is the concentration in weight percent.
- Bulk Partition coefficients D:
- the constant of proportionality between the
concentration of a trace element in the solid and in
the liquid in chemical equilibrium (Henry's law).
cs=Dcf. D's less than 1 are
"incompatible" implying the element prefers to be in
the melt, D's > 1 are compatible. The effective
velocity of a trace element in this model depends on
the melt and solid velocities (w,W), the porosity
(Phi) and the partition coefficients approximately as
weff~(w+D'W)/(1+D'), where D'=D/Phi. Thus
when the porosity is small relative to D, the tracer
travels with the solid, when Phi>>D, the tracer
travels in the melt. In this model, the Bulk
D's can be a function of pressure and are included in
the input spreadsheet as columns 4-7
- F (Degree of melting):
- F is the mass fraction of solid converted to melt
and is a function of Pressure, F(P) is also included
in the input spreadsheet as column 2. The melting rate in an
adiabatically melting 1-D column is
rhosW0dF/dz; where
rhos is the solid density, W0 is
the upwelling rate at the base of the column and
dF/dz=dF/dP*dP/dz
- Ingrowth:
- The ratio of the concentration of a radioactive
tracer in the melt to that of a stable element with
the same partition coefficient structure. For a 1-D
column, the concentration of a stable element in the
melt is equal to that for a batch melt of degree of
melting F. An ingrowth value > 1 implies that an
excess of that element has been produced by
radioactive decay of the parent. An ingrowth value
less than 1 implies net decay
- Input Spreadsheet:
- A space or tab separated spreadsheet with 7 columns:
| Pressure P | Degree of melting F | Permeability Factor
kr | Bulk partition coefficients
DU| DTh| DRa |
DPa|. This spreadsheet should only be
numbers, no header. See the sample or make one with the spreadsheet
calculator. User supplied spreadsheets are
included by passing the filename to the web-form.
- Maximum Porosity phi0:
- the maximum porosity
at the top of the column. This is used to calibrate the
melt velocity relative to the solid velocity (i.e. the
permeability) which at the top of the column is approximately
F_max/phi_0
- Permeability exponent n:
- Used to calculate the porosity as a function of
height in the column. This model assumes that the
relative permeability scales as kr
phin where kr is the...
- Permeability factor kr:
- The increase (or decrease in permeability)
relative to the model of Spiegelman and Elliott
(1993). kr is a function of pressure and
is input as column 3 in the input
spreadsheet. The value at the top of the column is
always assumed to be 1. A value of kr=1 everywhere,
returns the standard model, a value of
kr=10 at depth, for example, means
the permeability is 10 times higher there. This is
useful for increasing the permeability in the deep
regions of the melting column, for example where a
hydrous melt might have a significantly lower viscosity.
- Pressure:
- Column 1 in the input spreadsheet. Usually
in kb.
- Pressure Gradient dP/dz:
- Pressure gradient in kilobars/km, used to convert
pressure to depth. Default value is 0.32373 kb/km
corresponding to a solid density of 3300 kg/m3.
- Relative initial activities ai:
- The initial activity of each element in the unmelted solid.
Actually, only the initial activity ratio of daughter/parent pairs,
(e.g. a230Th/a238U) is used in the
models so the absolute value of ai is
unimportant. If all the ai's are the same,
the model is equivalent to that of Spiegelman and
Elliott, (1993) and assumes secular equilibrium. To model something like Uranium
addition by a factor of 2: set aU=2,
aTh=aRa=aPa=1. An
equivalent model though is aU=1,
aTh=aPa=.5, because both Th and
Pa have U as a parent. If the radium activity is
assumed to be in secular equilibrium with Th, then aRa=.5.
- Target Data:
- Values of the 3 activity ratios (230Th/238U),
(226Ra/230Th), and
(231Pa/235U) used to highlight
specific contours in the contour plot models. The
target data can be actual measurements of specific samples or ballpark
estimates of the activity ratios for suites of
samples. The important feature is that all three
activities reflect a single analysis, then the only
valid solutions of these models with respect to the
data are for parameter sets where all three target
values are satisfied simultaneously.
- Target Uncertainties sigma:
- For each value of the Target Data, one can also
specify an uncertainty range sigma, such that the
contours d+sigma and d-sigma will also be plotted.
sigma can represent the actual measurement error on a
specific measurement, or a more general range of
values for an area.
- Upwelling Velocity W0:
- the rate of solid upwelling at the base of the melting column in cm/yr
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