A%20GENERALIZED%20KOLMOGOROV-SMIRNOV%20STATISTIC%20FOR%20DETRITAL%20ZIRCON%20ANALYSIS%20OF%20MODERN%20RIVERS

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A GENERALIZED KOLMOGOROV-SMIRNOV STATISTIC FOR
DETRITAL ZIRCON ANALYSIS OF MODERN RIVERS

• Oscar M. Lovera Department of Earth Space
  Sciences, UCLA lovera_at_ucla.edu
• Marty Grove Department of Geological
  Environmental Sciences, Stanford University
• mjgrove_at_stanford.edu
• Sara E. Cina Department of Earth Space
  Sciences
• saracina_at_ucla.edu

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Example of Input Files

• Sample input file
• X0
• Age(Ma) s
• -----------
• 336.8 18.2
• 356.7 16.2
• 415.8 16.9
• 430.8 25.0
• 432.0 24.3
• 446.2 5.6
• 448.4 7.1
• 455.6 7.9
• 466.7 24.2
• 485.8 19.9
• 490.6 13.6
• 514.2 7.0
• 515.4 17.9
• 515.5 17.4
• 515.6 15.5

• Sample data are input as two columns (Age(Ma),
  1s(Ma)) files (see example, no head labels).
  Sample filename length must be at least 2
  character and less than 10. Because output
  filenames are form with the two first characters
  of each catchment sample, it is preferable that
  the catchment names do not agree in the 1st two
  characters of their names.
• To calculate the relative erosion rates matrix, a
  predicted relative catchment contribution vector
  must be input. It is read from a simple three
  column file Predicted.in (see example), with
  the predicted relative catchment contributions
  separate by space or tabs. Be sure that the
  predicted catchment contributions are given from
  left to right in the same order that catchment
  sample filenames were input in the 2nd input
  screen.
• NOTE Selecting option a in the 1st input
  screen calculates all matrices, including
  relative erosion estimates. If an Predicted.in
  input file is not provided, a dummy predicted
  uniform relative contributions (1/3,1/3,1/3)
  would be used and the resulting erosion
  probability matrix will be identical to the
  relative contribution probability matrix.

Predicted.in File X1 X2 X3 0.43 0.37
0.20
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RUNNING THE PROGRAM
SELECT THE ROUTINE(S) YOU WANT TO RUN (a) -
RUN ALL THE ROUTINES AT ONCE (1) - CALCULATE
PDF, CPDF CURVES AND STATISTIC AND CORRELATION
VALUES (2) - CALCULATE D MATRIX FOR TERNARY
PLOTS (3) - CALCULATE THE PROBABILITY MATRIX
(4) - CALCULATE THE EROSION MATRIX (5) -
CALCULATE TERNARY CONTOURS (PROB OR EROSION)
ENTER SELECTION? ( a,1,2,3,4 o 5) a
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2nd input screen if 1st selection is ( a,1 or 2)

• Enter name of Main sample distribution
• X0
• ENTER NAME OF CATCHMENT SAMPLE (STOP to end
  reading)
• X1
• ENTER NAME OF CATCHMENT SAMPLE (STOP to end
  reading)
• X2
• ENTER NAME OF CATCHMENT SAMPLE (STOP to end
  reading)
• X3
• ENTER NAME OF CATCHMENT SAMPLE (STOP to end
  reading)
• stop
• total sigma average 3.535128
• GENKS DONE

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2nd Selection screen if 1st selection is ( 3,4 or
5)
ENTER TYPE OF MODEL YOU WANT TO CALCULATE (1)
- INDEPENDENT (2) - IDENTICAL (3) - BOTH 1
GENKS DONE DMATX DONE .
3rd Selection screen if 1st selection is (5)
(1) - CALCULATE CONTOURS OF PROB MATRIX (2) -
CALCULATE CONTOURS OF EROSION MATRIX (3) -
CALCULATE BOTH CONTOURS (PROB EROSION) 1 GENKS
DONE DMATX DONE PROB_DCRIT_MTX DONE EROSION
DONE
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OUPUT FILES

• GenKS.DAT KS Statistic and Correlation
  calculations between the Main Trunk sample and
  the catchment samples (PROB values are not
  corrected by shifting due to incorporation of
  experimental error). Note More than three
  catchments can be input to calculate KS statistic
  and Correlation values, but ternary matrices will
  only be calculated from the first three input
  catchments.
• Name.txt Age vs. PDF and CPDF values. Column 1
  Age(Ma), Column 2 PDF and Column 3 CPDF.
  Plot them using any X-Y Graph application.
• Matrixname_param.dat Information of the sample
  and screen input values. Other calculated values
  like Max. D and Prob., avg. sigma, etc., are also
  output here.
• Matrixname_opt_dist.dat Age vs. PDF and CPDF
  values for the optimum Mixture (Max.
  Probability). (Matrixname first 2 characters
  of catchment sample names i.e. X1_X2_X3).
• Matrixname_matx.dat Matrix of the Max. D
  values computed between the Mixture and the Main
  Trunk CPDFs curves. Catchment contributions fi
  are varying from 0 to 1 at 0.001 intervals
  (Grid1000x1000).
• Matrixname_prob??.dat Matrices of the
  Probability values (ididentical, inindependent
  populations)
• Matrixname_er??.dat Matrices of the Erosion
  contributions (id or in)
• Matrixname_??_cont.dat ternary contours
  calculated from the PROB or erosion matrices.
  Contours are calculated between 0.05 and the max.
  probability value of the matrix at 0.05
  intervals, plus the contours at the 0.01, 0.001
  and 0.0001 values.

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GenKS.dat File
Name.txt File
Matrixname_opt_dist.txt File
Three column file (X,Y1,Y2) without head labels.
Ages between 0 and 4.Ga at 2-12Ga intervals. Avg.
sigma uncertainty quote at the bottom.
Optimum Mixture with Max. Prob. Two column file
(X,Y1,Y2) without head labels. Ages same as
Name.txt.
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Example of Matrixname_param.dat
Total Average sigma 3.535128 D-MATRIX
SUBROUTINE X N 201
(Main Trunk Sample) X1 N 89 X2
N 98 X3 N 178
D S1 S2 S3 0.0364
33.7000 35.3000 31.0000 CONTOUR
SUBROUTINE Pmax contr 33.70000 35.30000
31.00000 Plow 5.0000001E-02
Pmax 0.4421005 N 8
5.0000001E-02 0.1000000 0.1500000
0.2000000 0.2500000 0.3000000
0.3500000 0.4000000 .
average sigma for all the sample data
(X,X1,X2,X3) Size of sample distributions (S1,S2
,S3) relative contributions of the mixture with
the least max. different (D). Relative
contributions of the Mixture with the max. PROB
(Pmax). PROB values of the Contours calculated
between 0.05 and Pmax.
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Example of Matrix File
Note These are triangular matrices. Bottom right
triangle values are set to -1. We use them only
to calculate ternary contours, but they can be
use to plot contours on any 2D graph application.
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Example of Contour Files
Note Output file is taylor to plot ternary
contour using the Origin Graph application.
First to columns (f1,f2) are label as X,Y.
Columns from 3rd and up (f3) must be designed as
Z.
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Files used X0.txt, X1.txt, X2.txt, X3.txt and
X1_X2_X3_opt_dist.dat
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RELATIVE CATCHMENT CONTRIBUTIONS PROBABILITY
CONTOURS
Files used X1_X2_X3_pmatxin.dat and
X1_X2_X3_pmatxid.dat. Note that not all
calculated contours were plot.
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RELATIVE EROSION RATE CONTOURS
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Glossary
Dcrit Critical D value (i.e. P(Dcrit)0.05) PDF
Probability Density Function (Gaussian Kernel
Probability). CPDF Cumulative Probability
Density Function (Integral of the Gaussian
Kernel Probability). CDF Cumulative
Distribution Function CC Cross-correlation
values between two Probability Density Functions
(PDF)