The topographic shielding factor is 1 (no effect) as a default. If shielding has been measured, then an ascii text or Excel file can be loaded into the worksheet. To do this, right click on the disk icon below and select "Properties". From here you may specify your file type and path.This file should have two columns of data. Column 1 should contain a list of angular measurements of the horizon; column 2 should contain a list of azimuths associated with each horizon measurement. The program then makes a linear interpolation of the horizon based on these values and calculates a shielding factor. Additional shielding from samples collected on a dipping surface can be included if the strike and dip of the surface has been measured. If you already know your net topographic shielding factor, enter the value in the "define" field.
This is your estimate of the percent change in production rate due to assumed periodic cover. Default is 1 (no effect).
This scheme follows the theoretical equations of Heisinger et al. 2002a, 2002b for production of muons vs depth. The approach of Balco 2008 is adopted to generate production rates via negative muon capture and fast muons at any given depth and altitude. A two-term exponential best fit for fast muons and a three-term exponential best fit for negative muon capture is then determined over the depth range defined below and for the altitude of the sampling location. The displayed depth range is for rock with a conservative high density of 2.7g/cm^3, so in most cases the fitted depth will be deeper than indicated. The graphs below show the quality of each fit to the Heisinger equations over the specified mass-depth. A default depth range is set at 20 m. At a minimum, the depth range over which the muon terms are fit should be equal to the depth of your deepest sample plus the maximum net erosion of the surface.
To treat as constant, enter the same high and low value, and 0 for the error; to treat as stochastic between high and low end members, enter the high and low values, and 0 for the error; to treat as normally distributed about a mean value, enter the mean value in both the high and low fields, and your estimate for the relative error. Since the total muogenic production rate is approximated by five exponential terms, only a normally distributed percent error is currently allowed. The entered value is applied to each muon production term.
The power coefficient of exponentially decreasing inheritance with following: C = Csurf*exp(-(z/Λinh)).
Enter depths to the top of each sample (from shallowest to deepest) in your profile. Separate each value with a space.
Enter thickness values for each sample in your profile. Separate each value with a space. Make sure the order of thicknesses matches those you entered in the "depth of samples" field
Enter concentration values for each sample in your profile. Separate each value with a space. Make sure the order of values matches those you entered in the "depth of samples" field
Enter 1 sigma errors in concentration for each sample in your profile. Separate each value with a space. Make sure the order of values matches those you entered in the "depth of samples" field.
You may load your sample data from a text or Excel file rather than using the manual inputs above. To do this, first select the "file input" option below and then right click on the disk icon and select "Properties". From here you may specify your file type and path. Your data should be formatted as follows. Column order: sample depths, sample thicknesses, sample concentrations, 1σ measurement error. They should be in the same units as described above. The rows should should be ordered by sample depth (from shallowest to deepest).
You may vary bulk density with depth by entering parameters for a step function describing measured or assumed changes in density with depth (e.g., if you measured density to be 2.1 +/- 0.2 g cm-3 between 0-30 cm, 2.3 +/- 0.1 g cm-3 between 30-60 cm, and 2.4 +/- 0.2 g cm-3 at depths greater than 60 cm, then you would enter the numbers 0 30 60--space delimited--in the "depths" field, the numbers 2.1 2.3 2.4 in the "densities" field, and the numbers 0.2 0.1 0.2 in the "density errors" field). You may also treat bulk density as a constant with depth; you can chose either a random or normal distribution for this constant value. As a check, your depth function is displayed in the plots below.
Measured values for densities at different depths; values are normally distributed (do not use for constant density with depth):
In the fields below, enter boundary conditions for the parameters you wish to stochastically simulate. To specify a known value for a parameter, enter the expected value in both the "low" and "high" fields; for this option you will have to enter 1s relative error in the expected value as well. You may constrain the simulation by erosion rate, as well as erosion.
The simulation works by creating profiles from values sampled with the desired distribution from each of the above parameters. The total number of profiles needed to get a grood grasp of your solution space depends on how well you can constrain each of the parameters. Thus, it is more useful to specify a population of profiles that fit within a certain degree of confidence for your data, than to specify a number of total random profiles to create. This simulation will generate a profile, generate a reduced chi-squared value from that profile, and determine if that value is as good or better than the value generated from the data in your profile at the confidence window you specify; it will then continue until (n) profiles pass this chi-squared test. The total number of profiles needed to collect (n) "good" profiles is also displayed (m).
*The simulation will only look for solutions with a lower reduced chi-squared value than that shown above. If your profile data is significantly scattered, then you may not be able to obtain low enough chi-squared values for certain confidence levels. In this case, it will be necessary to run the simulation at a higher cutoff for the chi-squared statistic. Although counter-intuitive, increasing your desired confidence level accomplishes this. This is easier to think of in terms of fitting curves to data points with error bars. A dataset may not allow any theoretical profile to fit the 1s (68% confidence) data error, but allow profiles to fit the larger 2s (95.4% confidence) error. Incidentally, a higher confidence results in a faster simulation as it is easier to find possible solutions within the larger error window.
note: the best way to use this simulator is to start with low (n) values and do quick test simulations to tune the model to your data before running a very long high (n) value simulation. This allows you to do three things: 1) you can check the graphs below to see if the ranges you chose for your simulated parameters agree with the span of possible solutions for that parameter and then increase or decrease those ranges accordingly, 2) you can get an estimate for how long your simulation will take at higher (n) values (simulation time is linear), and 3) in the unfortunate circumstance of highly scattered data, you can run a quick test to see if it is even possible to find solutions better than your chi-squared cutoff (if it takes the program more than minute to find just 1 solution, then it probably will not be very useful for you to continue at that level of confidence). An (n) value of at least 100,000 is recommended for any final estimate of a given parameter.
The range in age, inheritance, and erosion values shown in these plots represent the range over your specified confidence.
