Welcome to UserCalc version 2.0. A
webbased Uranium series calculator based on the
models of Spiegelman and Elliott, 1993. A full
description of the model and a rationale for this website can be
found in the PDF document here. The remainder of this page will
provide enough background and hints on the use of this website to get
started exploring the wide range of behaviour inherent in this
model. Outline
The ModelThis section describes the different components of the models and this website. You can read the manual or go directly to the models and start hacking around General PropertiesThis model calculates the concentrations and activity ratios for the two parallel Uranium Series decay chains ^{238}U>^{230}Th>^{226}Ra and ^{235}U>^{231}Pa in a one dimensional upwelling and melting column. The principal user inputs into this model are
Melting is assumed to occur by adiabatic decompression
at a melting rate proportional to
W_{0}dF/dz. The porosity throughout the
column is determined by the balance of melting and melt
extraction, which is primarily controlled by the
permeability. The permeability is assumed to scale as
k_{r}(P) Phi^{n} Where. n is
the "permeability exponent" and k_{r}(P) is
a "enhanced permeability
factor" which can be a function of position in the
column. Given the upwelling rate, the maximum porosity at
the top of the column, the degree of melting and the
permeability factors, the porosity is determined
everywhere in the column. Given F(P) and
Phi(P), a useful rule of thumb for the ratio of the
melt velocity relative to the upwelling velocity at any
height is w/W~F(P)/Phi(P). (see Spiegelman, 2000
for more details) In these models, the degree of melting, the partition coefficients and the permeability factor can all be arbitrary functions of pressure. They are input into the models as a tab or space separated spreadsheet supplied by the user. Sample spreadsheets are supplied for all models and a more general 2layer model can be generated using the Spreadsheet Calculator 1D column calculatorThis model calculates the vertical porosity and concentration profiles for a single 1D upwelling column. If requested, this module also produces simple XY graphs and returns output as comma separated spreadsheets, EPS files and/or PDF files. Contour plot calculatorThis is the more interesting model. It runs a series of 1D columns that have the same melting and partition coefficient structure but are calculated over a 2D grid of values of upwelling rate and maximum porosity. (The user chooses the range of velocities and porosities and the number of points in each direction). The activity ratios and concentrations of each nuclide in the melt at the top of each column is gridded and made available in a variety of formats. If requested, contour plots of activity ratios at the top of the column are also made for the three principal parentdaughter pairs. The contour calculator also allows the user to input target values and ranges for measured activity ratios of (^{230}Th/^{238}U), (^{226}Ra/^{230}Th), and (^{231}Pa/^{235}U). These specific contours are superposed on the model plots and on each other. Valid solutions that are consistent with the target data will be regions where all three contours cross. Because of the coupled nature of these different ratios, finding valid regions of parameter space can be quite a challenge suggesting that these sorts of measurements can place strong constraints on mantle processes. The main purpose of this website is to allow any user to easily compare their data to theory and map out the inferences and viability (or not), of this simple model. Hints for Users
Usage Etiquette/Policy
Credits and AcknowledgementsThis site was cobbled together using a vast array of freely available and extremely useful software. Grateful credits go to:
