UserCalc Definitions

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
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
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.
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