Ashfall Graduate Class 2009 Lecture #4
50
Ashfall Graduate Class 2009 Lecture #4 Lecture #4 William I Rose William I Rose Michigan Technological Michigan Technological University University Houghton, MI 49931 USA Houghton, MI 49931 USA Size of volcanic Size of volcanic ash ash
description
Size of volcanic ash. William I Rose Michigan Technological University Houghton, MI 49931 USA. Ashfall Graduate Class 2009 Lecture #4. Tephra is classified on the basis of pyroclast size: - PowerPoint PPT Presentation
Transcript of Ashfall Graduate Class 2009 Lecture #4
-
Ashfall Graduate Class 2009Lecture #4William I RoseMichigan Technological UniversityHoughton, MI 49931 USA
Size of volcanic ash
-
Tephra is classified on the basis of pyroclast size:ASH -- Very fine-grained fragments (< 2 mm), generally dominated by broken glass shards, but with variable amounts of broken crystal and lithic (rock) fragments. Courtesy of USGS.LAPILLI -- Pea- to walnut-size pyroclasts (2 to 64 mm). They often look like cinders. In water-rich eruptions, the accretion of wet ash may form rounded spheres known as accretionary lapilli (left). Courtesy of USGS.BLOCKS AND BOMBS -- Fragments >64 mm. Bombs are ejected as incandescent lava fragments which were semi-molten when airborne, thus inheriting streamlined, aerodynamic shapes. Blocks (not shown) are ejected as solid fragments with angular shapes. Courtesy of J.P. Lockwood, USGS.www.geology.sdsu.edu/how_volcanoes_work
-
Like many natural and man made materials, volcanic ash is made up of materials of variable size. Some times a sample of ash has a simple size range that can be described in a straightforward way
But there are some methods that have developed to make it easier to compare samples.
-
phi = - log2 d (mm)Lognormal size distributions are expected and we use a biased system to define themASHLAPILLIBOMBS, BLOCKS
-
NON-GENETIC CLASSIFICATION OF PYROCLASTIC ROCKSAsh tuff - rock dominated by ash; sometimes simply referred to as tuff.
Lapilli tuff - rock dominated by lapilli.
Tuff breccia - rock containing 25% to 75% blocks and/or bombs.
Pyroclastic breccia - rock containing at least 75% blocks and bombs.
Agglomerate - rock containing at least 75% bombs.
Agglutinate - rock composed of fused, largely unrecognizable, basalt spatter fragments.www.geology.sdsu.edu/how_volcanoes_work
-
Pyroclastic fall deposits
Ashfall -- finer than 2 mm
Scoria fall --strombolian/cinder cone
Pumice fall highly vesiculated silicic pyroclasts from plinian eruptions
www.geology.sdsu.edu/how_volcanoes_work
-
d < 1000 m > 0d < 30 m > 5
-
from S. K. Friedlander, Smoke, Dust and Haze 2000
-
Normal ashfall, with dominant coarse modeBecause this fine-grained mode is minor and was grouped in the pan portion of sieved samples, it is underappreciated and is quite common.Rose et al., 2007 BVSieve rangeAshfall sample from Fuego Volcano, Guatemala 14 Oct 1974
Chart31
0
0.0049217489
3.9048497683
20.0284079319
35.8841866102
26.56204202
6.9010236209
0.1859685916
0
0.4403701004
1.336282465
1.0688964843
0.4572814362
0.2630975574
0.3393169565
0.5108232052
0.5228395222
0.4749481514
0.4207238091
0.3195822759
0.2637636681
0.1106740764
0
0
0
0
1
10
100
1000
Particle Diameter (mm)
Particle Diameter (f)
Class Weight (%)
Fu74-49
Information
GRADISTAT
Version 4.0
A Grain Size Distribution and Statistics Package for the Analysis of
Unconsolidated Sediments by Sieving or Laser Granulometer
Surface Processes and Modern Environments Research Group
Department of Geology
Royal Holloway
University of London
Egham
Surrey TW20 0EX
E-mail: [email protected]
Tel/Fax: +44 (0)1784 414168
Instructions on the Use of the GRADISTAT Program
The development of this program was inspired by Dave Thornley and John Jack at the Postgraduate Research Institute for Sedimentology at the University of Reading, UK, and the Department of Geology at Royal Holloway University of London, UK. It is provided in Microsoft Excel format to allow both spreadsheet and graphical output. The program is best suited to analyse data obtained from sieve or laser granulometer analysis. The user is required to input the mass or percentage of sediment retained on sieves spaced at any intervals, or the percentage of sediment detected in each bin of a Laser Granulometer. The following sample statistics are then calculated using the Method of Moments in Microsoft Visual Basic programming language: mean, mode(s), sorting (standard deviation), skewness, kurtosis, D10, D50, D90, D90/D10, D90-D10, D75/D25 and D75-D25. Grain size parameters are calculated arithmetically and geometrically (in microns) and logarithmically (using the phi scale) (Krumbein and Pettijohn, 19381; Table 1). Linear interpolation is also used to calculate statistical parameters by the Folk and Ward (1957)2 graphical method and derive physical descriptions (such as very coarse sand and moderately sorted). The program also provides a physical description of the textural group which the sample belongs to and the sediment name (such as fine gravelly coarse sand) after Folk (1954)3. Also included is a table giving the percentage of grains falling into each size fraction, modified from Udden (1914)4 and Wentworth (1922)5 (see Table 2). In terms of graphical output, the program provides graphs of the grain size distribution and cumulative distribution of the data in both metric and phi units, and displays the sample grain size on triangular diagrams. Samples may be analysed singularly, or up to 250 samples may be analysed together.
The program is ideal for the rapid analysis of sieve data and is freely available from the author at the above address. Please note that the copyright for the program is held by author, and any distribution or use of the program should be acknowledged to him.
S. Blott October 2000
1Krumbein, W.C. and Pettijohn, F.J. (1938) Manual of Sedimentary Petrography. Appleton-Century-Crofts, New York.
2Folk, R.L. and Ward, W.C. (1957) Brazos River bar: a study in the significance of grain size parameters. Journal of Sedimentary Petrology, 27, 3-26.
3Folk, R.L. (1954) The distinction between grain size and mineral composition in sedimentary-rock nomenclature. Journal of Geology, 62, 344-359.
4Udden, J.A. (1914) Mechanical composition of clastic sediments. Bulletin of the Geological Society of America, 25, 655-744.
5Wentworth, C.K. (1922) A scale of grade and class terms for clastic sediments. Journal of Geology, 30, 377-392.
Single Sample Analysis
1. Switch to the "Single Sample Data Input" sheet if it is not already active. Enter the aperture sizes of the sieves or Laser Granulometer bins used in the analysis into the cells in column B. Sizes may be entered either in ascending or descending numerical order. For convenience, you can click on one of the standard sieve or Laser Granulometer size intervals and GRADISTAT will enter the size classes for you. Any non-standard sieve sizes can be used, although some of the statistics may not be calculated if you have not used sieves with at least whole phi intervals. See the section below if the sample contains unanalysed sediment, such as material retained in the pan after sieving. At least one size class larger than the largest particles in the sample should also be entered. A large area to the right of the data columns is provided for the cut and paste of data from other spreadsheets, such as the import of Laser Granulometer data.
2. Enter the weight or percentage of sample beside each size class in column C. When you have finished, make sure there are no data further down the spreadsheet which could cause an error. The program will accept data down to row 230.
3. Enter the sample identity, analyst, date and initial sample weight (optional) at the top of the "Single Sample Data Input" sheet.
4. Click the "Calculate Statistics" button and wait a few moments for the program to finish running. When the dialog box appears, click "OK".
5. The results are summarised on the "Single Sample Statistics" sheet, which includes a distribution histogram of the sample. Select "Print..." from the file menu to print the Summary Statistics page. The data is also shown on triangular diagrams on the "Gravel Sand Mud" and "Sand Silt Clay" sheets. Further cumulative and distribution plots are given on other sheets.
Multiple Sample Analysis
1. Switch to the "Multiple Sample Data Input" sheet. Enter the aperture sizes of the sieves or Laser Granulometer bins used in the analysis into the cells in column B. The aperture sizes must be the same for all the samples. Sizes may be entered either in ascending or descending numerical order. For convenience, you can click on one of the standard sieve or Laser Granulometer size intervals and GRADISTAT will enter the size classes for you. Any non-standard sieve sizes can be used, although some of the statistics may not be calculated if you have not used sieves with at least whole phi intervals. See the section below if samples contain unanalysed sediment, such as material retained in the pan after sieving. At least one size class larger than the largest particles in the sample should also be entered.
2. Enter the weight or percentage of sample in column C onwards. Make sure there are no data further down the spreadsheet which could cause an error. The program will accept data down to row 230.
3. Enter the sample identity, analyst, date and initial sample weight (optional) in the green cells above each sample listing.
4. If you require a Summary Statistics printout for each sample, select a tick in the option box.
5. Click the "Calculate Statistics" button and wait for the program to finish running (this may take several minutes). GRADISTAT will give a warning if it detects a sample whose combined weight is greater than the given sample weight. Click "OK" when prompted on the dialog boxes.
6. The resulting statistics for all samples are summarised on the "Multiple Sample Statistics" sheet. The data for each sample included in the analysis are also shown on triangular diagrams on the "Gravel Sand Mud" and "Sand Silt Clay" sheets. Cumulative and distribution plots will show the results for the last sample in the analysis. If graphical plots for other samples are required, use separate single sample analyses (above).
Unanalysed Sediment
Occasionally, samples may contain sediment in a size fraction of unspecified size, such as material retained in the pan after sieving. Ideally, the whole size range in a sample should be analysed, and this may require further analysis of sediment remaining in the pan after sieving. The larger the quantity of sediment remaining in the pan, the less accurate the calculation of grain size statistics, with statistics calculated by the Method of Moments being most susceptible. Errors in Folk and Ward parameters become significant only when more than 5% of the sample is undetermined. If the sample contains sediment in the pan the user should do one of the following:
1. Enter the weight or percentage of sample in the pan with a class size of zero (or leave the class size blank). GRADISTAT calculates the statistics assuming all sediment in the pan is larger than 10 f (1 mm). The grain size distribution graphs do not however plot the quantity of sediment in the pan.
2. Enter the weight or percentage of sample in the pan with a class size which the user considers to be the lower size limit of sediment in the pan. GRADISTAT calculates the statistics assuming all sediment in the pan is larger than this value and plots this quantity on the grain size distribution graphs.
The above two options are recommended where there is less than 1% of the sample remaining in the pan.
3. Do not enter the quantity of sediment in the pan at all. GRADISTAT calculates the statistics ignoring the sediment in the pan as if it were not present in the sample. This is recommended where there is more than 1% of the sample remaining in the pan.
Samples containing more than 5% of sediment in the pan should ideally be analysed using a different technique, such as sedimentation or laser granulometry. Great care must however be taken when merging data obtained by different methods.
Graph Scales
The size scale used in graphical plots is dependent upon the range of sizes specified on the sample input sheets: the first and last values provide the extreme values on the graphs. While one size class larger than the largest particles in the sample should be entered, other size classes outside the grain size range of the sample have no influence on the statistical calculations. These classes may be deleted to narrow the size scale on graphs. Note that unused size classes within the size range of the sample should also be deleted, otherwise GRADISTAT assumes that zero sample weight was present in those size classes.
Copyright Simon Blott (2000)
Single Sample Data Input
Single Sample Data Input ScreenEnter your data in the columns below, and then click the "Calculate
Statistics" button. See the "Information" sheet for more information.
Sample Identity:Fu74-49
Analyst:AJD
Date:6/23/06Auto. add
Initial Sample Weight:(optional)apertures
at:
Aperture
(microns)
20000
14140
10000.004912
7073.900513
50019.988736
35335.990662000-1.52000
25026.4011151414-11414
1766.9779011000-0.51000
1250.1833227070707
8805000.5500
630.4239943531353
441.3818442501.5250
311.0784191762176
220.4517941252.5125
160.24137788388
110.366281633.563
7.80.5059144444
5.50.526252314.531
3.90.4703822522
2.80.40163165.516
1.950.33309811611
1.380.2627277.86.57.8
0.980.1091365.575.5
0.6903.97.53.9
0.4902.882.8
0.3501.958.51.95
0.2401.3891.38
0.989.50.98
0.69100.69
0.4910.50.49
0.35110.35
CalculateStatistics
Half Phi Intervals
Quarter Phi Intervals
Laser Granulometer
Single Sample Statistics
SAMPLE IDENTITY:Fu74-49ANALYST & DATE:AJD, 6/23/2006
SAMPLE TYPE:Unimodal, Moderately SortedTEXTURAL GROUP:Sand
SEDIMENT NAME:Moderately Sorted Medium Sand
fGRAIN SIZE DISTRIBUTION
MODE 1:426.51.251GRAVEL:0.0%COARSE SAND:23.9%
MODE 2:SAND:93.9%MEDIUM SAND:62.4%
MODE 3:MUD:6.1%FINE SAND:7.2%
207.40.653V FINE SAND:0.5%
388.41.364V COARSE GRAVEL:0.0%V COARSE SILT:2.4%
636.12.270COARSE GRAVEL:0.0%COARSE SILT:0.7%
3.0673.478MEDIUM GRAVEL:0.0%MEDIUM SILT:0.8%
428.71.617FINE GRAVEL:0.0%FINE SILT:1.0%
1.7071.760V FINE GRAVEL:0.0%V FINE SILT:0.7%
205.00.772V COARSE SAND:0.0%CLAY:0.4%
METHOD OF MOMENTSFOLK & WARD METHOD
ArithmeticGeometricLogarithmicGeometricLogarithmicDescription
ff
MEAN :404.0323.81.627385.71.375Medium Sand
175.52.5051.3251.8370.877Moderately Sorted
0.152-3.4143.414-0.2980.298Fine Skewed
3.58616.3616.362.0622.062Very Leptokurtic
Single Sample Statistics
0
0.0049217489
3.9048497683
20.0284079319
35.8841866102
26.56204202
6.9010236209
0.1859685916
0
0.4403701004
1.336282465
1.0688964843
0.4572814362
0.2630975574
0.3393169565
0.5108232052
0.5228395222
0.4749481514
0.4207238091
0.3195822759
0.2637636681
0.1106740764
0
0
0
0
1
10
100
1000
Particle Diameter (mm)
Particle Diameter (f)
Class Weight (%)
Fu74-49
Module1
Multiple Sample Data Input ScreenEnter your data in the columns below, and then click the
"Calculate Statistics" button. Enter Sample Info in the green cells.
ApertureClass Weight Retained (g or %) in Different Samples
(microns)
Sample Identity:GU-S-1501-68GU/S AF 13/11/03 - AverageGU/S AF 17/12/03 - AverageGU/S COI 25/11/94 - AverageGU/S COI 1500-68 - AverageGU/S COI 1500-68 b - AverageGU/S 1116 - AverageGU/S AF-2 12/1/75 b - AverageGU/S AF-1 12/1/75 - AverageGU/S 1501-68 - Average
Analyst:AJDAJDAJDAJD
Date:6/23/06
Initial Sample Weight:
20000000000000
14140.0270000000.3713634.1008628.466585
10002.0920000015.97323.41206110.07825818.962329
7077.0770000006.66201813.35308122.900704
5009.0120.0106310.29342500010.809858516.88170310.93576117.07827
3537.5420.7910290.88259400004.4548695.4791947.444127
2505.2851.4166912.2280451.479661.86726104.566467072.669471.9534181.584176
1764.4693.2255464.6657797.8050928.054421.89570903.3043481.9663970.747214
1255.2127.0758898.13105214.17903213.4857826.5834986.2159056025.9127654.006241.947578
886.27411.87773411.68484317.81819415.45369311.93329909.1797626.2639862.879663
636.77815.1739113.8672116.91322214.14384816.18571115.97454395211.4561627.5975243.124598
446.6915.45467313.97268212.96206711.76509516.81684011.6330297.6179482.991211
316.34713.18947912.3070788.7302539.57435114.07358319.5661592829.8244426.6020622.66523
225.9349.9129169.6931075.7961527.55799410.1382707.1669145.1738882.201635
165.4346.8351766.9224454.0798545.5417156.76688413.6893059644.7916983.8247511.689559
114.7624.4680054.5693152.9397223.7273734.44875203.1652232.7589461.249823
7.84.022.829132.8690412.0009042.3685062.9224776.8071389122.1582781.9679790.931764
5.53.3831.816441.8325711.2858811.5421051.93575301.5432711.4270960.726606
3.92.8571.2891311.3145810.88361.1286131.3733273.3107201821.1902051.1116060.601544
2.82.3771.0474521.082260.7239910.9229921.09876500.9942360.9356440.510014
1.951.8170.9161620.9495320.6560640.7816660.959662.2982800140.8638240.8059870.422867
1.381.2820.7793890.8045380.5604580.6317160.82618500.7186110.6517940.323775
0.980.8820.6834950.6999880.4709250.5295350.7332011.6314044220.6065420.5278210.248513
0.690.440.642190.6532140.4202640.4904980.69274500.5514240.4628960.208569
0.490.0060.4582780.4663590.289560.3510670.4971621.0923337080.3920620.3205850.093646
0.3500.1066550.1103390.0051050.0817680.11817700.0957190.0762790
0.240000000000
CalculateStatistics
Half Phi Intervals
Quarter Phi Intervals
Laser Granulometer
Auto. addaperturesat:
Multiple Sample Data Input
SAMPLE STATISTICS
ANALYST AND DATE:
SIEVING ERROR:
SAMPLE TYPE:
TEXTURAL GROUP:
SEDIMENT NAME:
METHOD OFMEAN
MOMENTSSORTING
SKEWNESS
KURTOSIS
METHOD OFMEAN
MOMENTSSORTING
SKEWNESS
KURTOSIS
METHOD OFMEAN
MOMENTSSORTING
SKEWNESS
KURTOSIS
FOLK ANDMEAN
WARD METHODSORTING
SKEWNESS
KURTOSIS
FOLK ANDMEAN
WARD METHODSORTING
SKEWNESS
KURTOSIS
FOLK AND
WARD METHOD
(Description)
% GRAVEL:
% SAND:
% MUD:
% V COARSE GRAVEL:
% COARSE GRAVEL:
% MEDIUM GRAVEL:
% FINE GRAVEL:
% V FINE GRAVEL:
% V COARSE SAND:
% COARSE SAND:
% MEDIUM SAND:
% FINE SAND:
% V FINE SAND:
% V COARSE SILT:
% COARSE SILT:
% MEDIUM SILT:
% FINE SILT:
% V FINE SILT:
% CLAY:
Multiple Sample Statistics
&CTriangular Diagram
Sand
Mud
Gravel
80%
30%
5%
Trace
1:1
1:9
9:1
Sand:Mud Ratio
Gravel %
Gravel
Muddy Gravel
Muddy Sandy Gravel
Gravelly Mud
Gravelly Muddy Sand
Slightly Gravelly Mud
Slightly GravellySandy Mud
Slightly GravellyMuddy Sand
Mud
Sandy Mud
Muddy Sand
Sand
Slightly Gravelly Sand
Gravelly Sand
Sandy Gravel
Fu74-49
TEXTURAL GROUP:
SEDIMENT NAME:
Sand
Moderately Sorted Medium Sand
SAMPLE IDENTITY:
Gravel:
Sand:
Mud:
0.0%
93.9%
6.1%
Coarse Gravel:
Medium Gravel:
Fine Gravel:
Coarse Sand:
Medium Sand:
Fine Sand:
Very Fine Sand:
Very Coarse Silt:
0.0%
0.0%
0.0%
23.9%
7.2%
0.5%
2.4%
62.4%
Very Coarse Gravel:
0.0%
Very Coarse Sand:
Coarse Silt:
Clay:
Fine Silt:
Very Fine Gravel:
0.0%
0.0%
Medium Silt:
Very Fine Silt:
0.4%
0.7%
1.0%
0.8%
0.7%
Gravel Sand Mud Diagram
&CTriangular Diagram
Silt
Clay
Sand
90%
50%
10%
1:2
2:1
Silt:Clay Ratio
Sand %
Sand
Clayey Sand
Muddy Sand
Sandy Clay
Sandy Silt
Sandy Mud
Clay
Mud
Silt
Silty Sand
NOTEGravel is also present inthis sample
Fu74-49
TEXTURAL GROUP:IGNORING GRAVELFRACTION
SAMPLE IDENTITY:
Gravel:
Sand:
Mud:
0.0%
93.9%
6.1%
Coarse Gravel:
Medium Gravel:
Fine Gravel:
Coarse Sand:
Medium Sand:
Fine Sand:
Very Fine Sand:
Very Coarse Silt:
Very Coarse Gravel:
Very Coarse Sand:
Coarse Silt:
Clay:
Fine Silt:
Very Fine Gravel:
Medium Silt:
Very Fine Silt:
0.0%
0.0%
0.0%
23.9%
7.2%
0.5%
2.4%
62.4%
0.0%
0.0%
0.0%
0.4%
0.7%
1.0%
0.8%
0.7%
Sand Silt Clay Diagram
0
0.0049217489
3.9048497683
20.0284079319
35.8841866102
26.56204202
6.9010236209
0.1859685916
0
0.4403701004
1.336282465
1.0688964843
0.4572814362
0.2630975574
0.3393169565
0.5108232052
0.5228395222
0.4749481514
0.4207238091
0.3195822759
0.2637636681
0.1106740764
0
0
0
0
&CFrequency Distribution Histogram
Particle diameter (f)
Class weight (%)
Distribution (phi)
0
0
0.004912
3.9054249609
23.8941607611
59.8848204012
86.2859351371
93.2638360674
93.4471580655
93.4471580655
93.8711520613
95.2529960475
96.3314150367
96.7832090322
97.0245860298
97.3908670261
97.896777021
98.4230290158
98.8934090111
99.295039007
99.6281370037
99.8908640011
100
100
100
100
100
&CCumulative Frequency Curve
Particle diameter (f)
Cumulative mass retained (%)
Cumulative (phi)
0
0.0049217489
3.9048497683
20.0284079319
35.8841866102
26.56204202
6.9010236209
0.1859685916
0
0.4403701004
1.336282465
1.0688964843
0.4572814362
0.2630975574
0.3393169565
0.5108232052
0.5228395222
0.4749481514
0.4207238091
0.3195822759
0.2637636681
0.1106740764
0
0
0
0
&CFrequency Distribution Curve
Particle diameter (mm)
Class weight (%)
Distribution (microns)
0
0
0.004912
3.9054249609
23.8941607611
59.8848204012
86.2859351371
93.2638360674
93.4471580655
93.4471580655
93.8711520613
95.2529960475
96.3314150367
96.7832090322
97.0245860298
97.3908670261
97.896777021
98.4230290158
98.8934090111
99.295039007
99.6281370037
99.8908640011
100
100
100
100
100
&CCumulative Frequency Curve
Particle diameter (mm)
Cumulative mass retained (%)
Cumulative (microns)
Method of Moments - LogarithmicDateModeFirstModeSecondModeThirdModePrint
6/23/200635.884186610235.884186610200100
Mean:1.627
Std. Dev.1.325ClassMode1ClassMode2ClassMode3Classmode4ClassMode5
Skewness3.41435.8841866102
Kurtosis16.364
TexureMaximum Frequency
Sum of Sieve Classes35.8841866102
100.00ShapeLine
0095.356385
Sum of Proportion Classes
199.6908586146
Method of Moments - ArithmeticMethod of Moments - GeometricPlease wait while the
Mean (um)404.031Mean (mm)323.785statistics are calculated
Std. Dev. (um)175.512Std. Dev. (mm)2.505
Skewness (um)0.152Skewness (mm)-3.414
Kurtosis (um)3.586Kurtosis (mm)16.364Samples remaining:1
Kurtosis (um) - 30.586Kurtosis (mm) - 313.364
0%100%
STATISTICS BY METHOD OF MOMENTSSTATISTICS BY METHOD OF MOMENTSSTATISTICS BY METHOD OF MOMENTS
APERTUREMID-POINT (m)APERTUREMID-POINT (m)CUM. MASSCLASSCLASSAPERTURELOGARITHMICMID-POINT (m)NORMALISEDARITHMETICGEOMETIC
(metric)(metric)(PHI Scale)(PHI Scale)RETAINEDWEIGHT (f)WEIGHT(metric)(metric)CLASS WEIGHT
(mm)(mm)(PHI)(PHI)(%)(%)(g)fm(no units)(%)fmlog mf log m
2.00-1.0000.000.000.0020000.000.000000.000000.000000.000.000.000000.000000.0000000.000000.000000.00000
1.411.71-0.500-0.74990.000.000.0014140.000.000000.000000.000001681.70.000.000.000.000000.000000.000003.22600.000000.000000.00000
1.001.2070.000-0.24990.000.000.001000-0.000.01730-0.032470.060941189.10.010.005.933167.056682543048.108492041988617.239483.0750.01510550360.001570.000890.00050
0.710.8540.5000.25013.913.903.907070.987.39357-10.1793514.01478840.87.803.903329.09787990.67192354177323.73083159191702536.466002.92511.40786811890.670000.277680.11509
0.500.6041.0000.750123.8919.9919.9950014.9915.36638-13.4730111.81294594.639.9920.0312063.20795308.89806158639414.4871131643634177.978202.77455.45264509761.392490.367530.09701
0.350.4271.5021.251159.8835.9935.9935345.035.08183-1.909570.71755420.171.6635.8815350.0218169.98497408260.110659173167.627752.62394.41690153310.460510.052090.00589
0.250.3022.0001.751186.2926.4026.4025046.230.407490.050620.00629297.153.0426.567959.94277544.89804-28456975.519062917724164.287152.47365.28619080870.03693-0.001380.00005
0.180.2132.5062.253293.266.986.9817615.722.736941.714101.07351209.813.786.901486.29254643.63090-48644845.417249292676896.285712.32216.20077637530.24802-0.046760.00882
0.130.1513.0002.753293.450.180.181250.500.232550.261910.29499148.30.370.1927.5911783.57208-2987501.64467757424490.211312.1710.39803080140.02107-0.007140.00242
0.090.1073.5063.253293.450.000.00880.000.000000.000000.00000104.90.000.000.000.000000.000000.000002.02100.000000.000000.00000
0.060.0763.9893.747493.870.420.42631.591.906564.042938.5731674.50.880.4432.0145762.80161-15034502.205064939301104.457011.8720.79367928360.17277-0.110290.07040
0.040.0544.5064.247495.251.381.38445.879.4894024.8673065.1656252.62.671.3473.93169789.97768-59516662.6426320862439471.061801.7212.37870155750.85992-0.678360.53513
0.030.0385.0124.759096.331.081.08315.1310.5791833.13481103.7807736.92.131.0740.44144880.22679-53103104.6254019463937787.321701.5671.69032167230.95868-0.903890.85223
0.020.0275.5065.259096.780.450.45222.385.9600621.6473878.6249426.10.910.4611.9764394.06680-24310760.977159178067617.333511.4170.64014338250.54009-0.590520.64565
0.020.0195.9665.736197.020.240.24161.384.0757316.7478768.8199318.80.530.264.5935783.88048-13777905.809155304921823.488601.2730.30733841120.36934-0.456870.56514
0.010.0146.5066.236197.390.370.37112.287.7814535.86607165.3129913.30.680.344.9455863.16926-21816303.296188519944281.472731.1230.41124430860.70515-0.978391.35752
0.010.0097.0026.754397.900.510.517.83.4213.3006868.19843349.683179.31.020.514.7678787.22619-31091887.4159512269824816.051200.9670.4890852721.20530-1.860392.87153
0.010.0077.5067.254398.420.530.535.53.8216.6653893.78336527.759986.51.040.523.5083101.35513-33022905.4642913122677525.725300.8160.42954195321.51020-2.558324.33387
0.000.0058.0027.754398.890.470.473.93.6517.66065108.21451663.077644.60.950.472.2175009.28890-29953539.6358811961379049.242600.6660.31313838271.60039-2.951995.44507
0.000.0038.4808.241399.300.400.402.83.3117.57164116.22655768.773533.30.840.421.3564479.81634-25835841.8404110351932766.905200.5190.2084906771.59233-3.170556.31302
0.000.0029.0028.741399.630.330.331.952.9116.85984119.94831853.365072.30.640.320.7953737.90003-21584153.767008669406387.975120.3690.12277869621.52782-3.272087.00767
0.000.0029.5019.251799.890.260.261.382.4315.27439116.46444888.020271.60.530.260.4442535.09489-17114678.990216886366133.836400.2150.05647496751.38415-3.177047.29226
0.000.0019.9959.7480100.000.110.110.981.067.1978258.45441474.715851.20.220.110.1317711.57049-7135125.134302874392798.787380.0660.00715414640.65226-1.594583.89828
0.000.00110.50110.2480100.000.000.000.690.000.000000.000000.000000.80.000.000.000.000000.000000.00000-0.08500.000000.000000.00000
0.000.00110.99510.7480100.000.000.000.490.000.000000.000000.000000.60.000.000.000.000000.000000.00000-0.23500.000000.000000.00000
0.000.00011.48011.2376100.000.000.000.350.000.000000.000000.000000.40.000.000.000.000000.000000.00000-0.38300.000000.000000.00000
0.000.00012.02511.7525100.000.000.000.240.000.000000.000000.000000.30.000.000.000.000000.000000.00000-0.53800.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
MBD00064BFA.unknown
MBD001D9D0D.unknown
MBD001E7DA0.unknown
MBD0021920A.unknown
MBD0021F45B.unknown
MBD00273258.doc
Table 2. Size scale adopted in the GRADISTAT program, modified from Udden (1914) and Wentworth (1922).
Grain Size
Descriptive term
phi
mm
Very Large
Boulder
-10
1024
Large
-9
512
Medium
-8
256
Small
-7
128
Very small
-6
64
Very coarse
Gravel
-5
32
Coarse
-4
16
Medium
-3
8
Fine
-2
4
Very fine
-1
2
Very coarse
Sand
0
1
microns
Coarse
1
500
Medium
2
250
Fine
3
125
Very fine
4
63
Very coarse
Silt
5
31
Coarse
6
16
Medium
7
8
Fine
8
4
Very fine
9
2
Clay
MBD0021CF8D.unknown
MBD0021E384.unknown
MBD0021A2A4.unknown
MBD0021706D.unknown
MBD00218324.unknown
MBD00204A66.doc
Table 1.Statistical formulae used in the calculation of grain size parameters.
f is the frequency in percent; m is the mid-point of each class interval in metric (mm) or phi (m) units; Px and x are grain diameters, in metric or phi units respectively, at the cumulative percentile value of x.
(a) Arithmetic Method of Moments
Mean
Standard Deviation
Skewness
Kurtosis
(b) Geometric Method of Moments
Mean
Standard Deviation
Skewness
Kurtosis
Sorting ((g)
Skewness (Skg)
Kurtosis (Kg)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 1.27
1.27 1.41
1.41 1.62
1.62 2.00
2.00 4.00
4.00 16.00
> 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
< -1.30
-1.30 -0.43
-0.43 +0.43
+0.43 +1.30
> +1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 2.55
2.55 3.70
3.70 7.40
> 7.40
(c) Logarithmic Method of Moments
Mean
Standard Deviation
Skewness
Kurtosis
Sorting (()
Skewness (Sk)
Kurtosis (K)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 0.50
0.50 0.70
0.70 1.00
1.00 2.00
2.00 4.00
> 4.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
> +1.30
+0.43 +1.30
-0.43 +0.43
-0.43 -1.30
< -1.30
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
< 1.70
1.70 2.55
2.55 3.70
3.70 7.40
> 7.40
PAGE
- 29 -
_1023000209.unknown
_1033329752.unknown
_1033334990.unknown
_1034415844.unknown
_1034415916.unknown
_1034415938.unknown
_1034415822.unknown
_1033330713.unknown
_1033334961.unknown
_1033330699.unknown
_1023000485.unknown
_1033329670.unknown
_1023000299.unknown
_1023000010.unknown
_1023000100.unknown
_1023000148.unknown
_1023000022.unknown
_1023000008.unknown
_1023000009.unknown
_1022999982.unknown
MBD001DD4B9.unknown
MBD001DE997.unknown
MBD001DB8B1.unknown
MBD001D4ABF.unknown
MBD001D7669.unknown
MBD001D8724.unknown
MBD001D6191.unknown
MBD0006827A.unknown
MBD0007398E.unknown
MBD00066B8A.unknown
MBD0000D6CE.unknown
MBD000600AD.unknown
MBD00007611.doc
(d) Logarithmic (Original) Folk and Ward (1957) Graphical Measures
Mean
Standard Deviation
Skewness
Kurtosis
Sorting ((I)
Skewness (SkI)
Kurtosis (KG)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 0.35
0.35 0.50
0.50 0.70
0.70 1.00
1.00 2.00
2.00 4.00
> 4.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
+0.3 to +1.0
+0.1 to +0.3
+0.1 to -0.1
-0.1 to -0.3
-0.3 to -1.0
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
Extremely leptokurtic
< 0.67
0.67 0.90
0.90 1.11
1.11 1.50
1.50 3.00
> 3.00
(e) Geometric Folk and Ward (1957) Graphical Measures
Mean
Standard Deviation
Skewness
Kurtosis
Sorting ((G)
Skewness (SkG)
Kurtosis (KG)
Very well sorted
Well sorted
Moderately well sorted
Moderately sorted
Poorly sorted
Very poorly sorted
Extremely poorly sorted
< 1.27
1.27 1.41
1.41 1.62
1.62 2.00
2.00 4.00
4.00 16.00
> 16.00
Very fine skewed
Fine skewed
Symmetrical
Coarse skewed
Very coarse skewed
-0.3 to -1.0
-0.1 to -0.3
-0.1 to +0.1
+0.1 to +0.3
+0.3 to +1.0
Very platykurtic
Platykurtic
Mesokurtic
Leptokurtic
Very leptokurtic
Extremely leptokurtic
< 0.67
0.67 0.90
0.90 1.11
1.11 1.50
1.50 3.00
> 3.00
PAGE
- 29 -
_1023000209.unknown
_1033334990.unknown
_1034415822.unknown
_1036325908.unknown
_1036326416.unknown
_1036327736.unknown
_1036327793.unknown
_1036325926.unknown
_1034415916.unknown
_1034415938.unknown
_1034415844.unknown
_1033335820.unknown
_1033376995.unknown
_1033335795.unknown
_1033329752.unknown
_1033330713.unknown
_1033334961.unknown
_1033330699.unknown
_1023000485.unknown
_1033329670.unknown
_1023000299.unknown
_1023000010.unknown
_1023000100.unknown
_1023000148.unknown
_1023000022.unknown
_1023000008.unknown
_1023000009.unknown
_1022999982.unknown
-
Forward Fraunhofer Diffraction of laser lightHow to measure the fine ash
-
Particle Size Analysis Malvern Mastersizer 2000; Cambridge UniversityDispersion unit
-
VF 74-103 17 Oct 1974 Fuego.This distal fall has only a very minor coarse mode, with a dominant mode at ~5 .
Sieve rangeLaser diffraction expands the range of precise GSD work to submicron diameters.Rose et al., 2007 BV
Chart1
0
0
0.1364367845
1.0530253109
2.082472825
1.8992295527
0.9060321419
0.0708801829
0.7451341756
2.9148447635
6.0092021823
8.7596194874
9.8463622854
9.7939177877
8.9605117845
8.1054446278
7.2245648744
6.6559384219
6.1432717842
5.4020096238
4.4180248942
3.334101832
2.9051966207
1.9588741005
0.6749039561
0
1
10
100
1000
Particle Diameter (mm)
Particle Diameter (f)
Class Weight (%)
Information
GRADISTAT
Version 4.0
A Grain Size Distribution and Statistics Package for the Analysis of
Unconsolidated Sediments by Sieving or Laser Granulometer
Surface Processes and Modern Environments Research Group
Department of Geology
Royal Holloway
University of London
Egham
Surrey TW20 0EX
E-mail: [email protected]
Tel/Fax: +44 (0)1784 414168
Instructions on the Use of the GRADISTAT Program
The development of this program was inspired by Dave Thornley and John Jack at the Postgraduate Research Institute for Sedimentology at the University of Reading, UK, and the Department of Geology at Royal Holloway University of London, UK. It is provided in Microsoft Excel format to allow both spreadsheet and graphical output. The program is best suited to analyse data obtained from sieve or laser granulometer analysis. The user is required to input the mass or percentage of sediment retained on sieves spaced at any intervals, or the percentage of sediment detected in each bin of a Laser Granulometer. The following sample statistics are then calculated using the Method of Moments in Microsoft Visual Basic programming language: mean, mode(s), sorting (standard deviation), skewness, kurtosis, D10, D50, D90, D90/D10, D90-D10, D75/D25 and D75-D25. Grain size parameters are calculated arithmetically and geometrically (in microns) and logarithmically (using the phi scale) (Krumbein and Pettijohn, 19381; Table 1). Linear interpolation is also used to calculate statistical parameters by the Folk and Ward (1957)2 graphical method and derive physical descriptions (such as very coarse sand and moderately sorted). The program also provides a physical description of the textural group which the sample belongs to and the sediment name (such as fine gravelly coarse sand) after Folk (1954)3. Also included is a table giving the percentage of grains falling into each size fraction, modified from Udden (1914)4 and Wentworth (1922)5 (see Table 2). In terms of graphical output, the program provides graphs of the grain size distribution and cumulative distribution of the data in both metric and phi units, and displays the sample grain size on triangular diagrams. Samples may be analysed singularly, or up to 250 samples may be analysed together.
The program is ideal for the rapid analysis of sieve data and is freely available from the author at the above address. Please note that the copyright for the program is held by author, and any distribution or use of the program should be acknowledged to him.
S. Blott October 2000
1Krumbein, W.C. and Pettijohn, F.J. (1938) Manual of Sedimentary Petrography. Appleton-Century-Crofts, New York.
2Folk, R.L. and Ward, W.C. (1957) Brazos River bar: a study in the significance of grain size parameters. Journal of Sedimentary Petrology, 27, 3-26.
3Folk, R.L. (1954) The distinction between grain size and mineral composition in sedimentary-rock nomenclature. Journal of Geology, 62, 344-359.
4Udden, J.A. (1914) Mechanical composition of clastic sediments. Bulletin of the Geological Society of America, 25, 655-744.
5Wentworth, C.K. (1922) A scale of grade and class terms for clastic sediments. Journal of Geology, 30, 377-392.
Single Sample Analysis
1. Switch to the "Single Sample Data Input" sheet if it is not already active. Enter the aperture sizes of the sieves or Laser Granulometer bins used in the analysis into the cells in column B. Sizes may be entered either in ascending or descending numerical order. For convenience, you can click on one of the standard sieve or Laser Granulometer size intervals and GRADISTAT will enter the size classes for you. Any non-standard sieve sizes can be used, although some of the statistics may not be calculated if you have not used sieves with at least whole phi intervals. See the section below if the sample contains unanalysed sediment, such as material retained in the pan after sieving. At least one size class larger than the largest particles in the sample should also be entered. A large area to the right of the data columns is provided for the cut and paste of data from other spreadsheets, such as the import of Laser Granulometer data.
2. Enter the weight or percentage of sample beside each size class in column C. When you have finished, make sure there are no data further down the spreadsheet which could cause an error. The program will accept data down to row 230.
3. Enter the sample identity, analyst, date and initial sample weight (optional) at the top of the "Single Sample Data Input" sheet.
4. Click the "Calculate Statistics" button and wait a few moments for the program to finish running. When the dialog box appears, click "OK".
5. The results are summarised on the "Single Sample Statistics" sheet, which includes a distribution histogram of the sample. Select "Print..." from the file menu to print the Summary Statistics page. The data is also shown on triangular diagrams on the "Gravel Sand Mud" and "Sand Silt Clay" sheets. Further cumulative and distribution plots are given on other sheets.
Multiple Sample Analysis
1. Switch to the "Multiple Sample Data Input" sheet. Enter the aperture sizes of the sieves or Laser Granulometer bins used in the analysis into the cells in column B. The aperture sizes must be the same for all the samples. Sizes may be entered either in ascending or descending numerical order. For convenience, you can click on one of the standard sieve or Laser Granulometer size intervals and GRADISTAT will enter the size classes for you. Any non-standard sieve sizes can be used, although some of the statistics may not be calculated if you have not used sieves with at least whole phi intervals. See the section below if samples contain unanalysed sediment, such as material retained in the pan after sieving. At least one size class larger than the largest particles in the sample should also be entered.
2. Enter the weight or percentage of sample in column C onwards. Make sure there are no data further down the spreadsheet which could cause an error. The program will accept data down to row 230.
3. Enter the sample identity, analyst, date and initial sample weight (optional) in the green cells above each sample listing.
4. If you require a Summary Statistics printout for each sample, select a tick in the option box.
5. Click the "Calculate Statistics" button and wait for the program to finish running (this may take several minutes). GRADISTAT will give a warning if it detects a sample whose combined weight is greater than the given sample weight. Click "OK" when prompted on the dialog boxes.
6. The resulting statistics for all samples are summarised on the "Multiple Sample Statistics" sheet. The data for each sample included in the analysis are also shown on triangular diagrams on the "Gravel Sand Mud" and "Sand Silt Clay" sheets. Cumulative and distribution plots will show the results for the last sample in the analysis. If graphical plots for other samples are required, use separate single sample analyses (above).
Unanalysed Sediment
Occasionally, samples may contain sediment in a size fraction of unspecified size, such as material retained in the pan after sieving. Ideally, the whole size range in a sample should be analysed, and this may require further analysis of sediment remaining in the pan after sieving. The larger the quantity of sediment remaining in the pan, the less accurate the calculation of grain size statistics, with statistics calculated by the Method of Moments being most susceptible. Errors in Folk and Ward parameters become significant only when more than 5% of the sample is undetermined. If the sample contains sediment in the pan the user should do one of the following:
1. Enter the weight or percentage of sample in the pan with a class size of zero (or leave the class size blank). GRADISTAT calculates the statistics assuming all sediment in the pan is larger than 10 f (1 mm). The grain size distribution graphs do not however plot the quantity of sediment in the pan.
2. Enter the weight or percentage of sample in the pan with a class size which the user considers to be the lower size limit of sediment in the pan. GRADISTAT calculates the statistics assuming all sediment in the pan is larger than this value and plots this quantity on the grain size distribution graphs.
The above two options are recommended where there is less than 1% of the sample remaining in the pan.
3. Do not enter the quantity of sediment in the pan at all. GRADISTAT calculates the statistics ignoring the sediment in the pan as if it were not present in the sample. This is recommended where there is more than 1% of the sample remaining in the pan.
Samples containing more than 5% of sediment in the pan should ideally be analysed using a different technique, such as sedimentation or laser granulometry. Great care must however be taken when merging data obtained by different methods.
Graph Scales
The size scale used in graphical plots is dependent upon the range of sizes specified on the sample input sheets: the first and last values provide the extreme values on the graphs. While one size class larger than the largest particles in the sample should be entered, other size classes outside the grain size range of the sample have no influence on the statistical calculations. These classes may be deleted to narrow the size scale on graphs. Note that unused size classes within the size range of the sample should also be deleted, otherwise GRADISTAT assumes that zero sample weight was present in those size classes.
Copyright Simon Blott (2000)
Single Sample Data Input
Single Sample Data Input ScreenEnter your data in the columns below, and then click the "Calculate
Statistics" button. See the "Information" sheet for more information.
Sample Identity:VF-74-103
Analyst:
Date:Auto. add
Initial Sample Weight:(optional)apertures
at:
ApertureClass Weight
(microns)Retained (g or %)
20000
14000
10000
7100.13464
5001.063936
3552.055048
2501.918908
1800.857588
1250.074471
900.705293
632.99559
446.214972
31.18.757624
229.820956
15.69.701094
119.020275
7.788.088584
5.57.219306
3.896.642093
2.756.1388
1.945.430837
1.384.335836
0.973.386764
0.692.851151
0.491.931925
0.350.654313
0.240
CalculateStatistics
Half Phi Intervals
Quarter Phi Intervals
Laser Granulometer
Single Sample Statistics
SAMPLE IDENTITY:VF-74-103ANALYST & DATE:,
SAMPLE TYPE:Bimodal, Very Poorly SortedTEXTURAL GROUP:Mud
SEDIMENT NAME:Coarse Silt
fGRAIN SIZE DISTRIBUTION
MODE 1:26.555.257GRAVEL:0.0%COARSE SAND:1.2%
MODE 2:427.51.247SAND:9.9%MEDIUM SAND:4.0%
MODE 3:MUD:90.1%FINE SAND:0.9%
1.5144.005V FINE SAND:3.8%
12.516.321V COARSE GRAVEL:0.0%V COARSE SILT:14.7%
62.309.368COARSE GRAVEL:0.0%COARSE SILT:19.6%
41.162.339MEDIUM GRAVEL:0.0%MEDIUM SILT:17.1%
60.785.363FINE GRAVEL:0.0%FINE SILT:13.9%
7.8221.591V FINE GRAVEL:0.0%V FINE SILT:11.5%
26.912.967V COARSE SAND:0.0%CLAY:13.3%
METHOD OF MOMENTSFOLK & WARD METHOD
ArithmeticGeometricLogarithmicGeometricLogarithmicDescription
ff
MEAN :41.4611.716.41610.876.524Medium Silt
98.874.6132.2064.8992.292Very Poorly Sorted
4.3190.211-0.211-0.0350.035Symmetrical
23.202.9632.9631.1231.123Leptokurtic
Single Sample Statistics
0
0
0.1364367845
1.0530253109
2.082472825
1.8992295527
0.9060321419
0.0708801829
0.7451341756
2.9148447635
6.0092021823
8.7596194874
9.8463622854
9.7939177877
8.9605117845
8.1054446278
7.2245648744
6.6559384219
6.1432717842
5.4020096238
4.4180248942
3.334101832
2.9051966207
1.9588741005
0.6749039561
0
1
10
100
1000
Particle Diameter (mm)
Particle Diameter (f)
Class Weight (%)
Module1
Multiple Sample Data Input ScreenEnter your data in the columns below, and then click the
"Calculate Statistics" button. Enter Sample Info in the green cells.
ApertureClass Weight Retained (g or %) in Different Samples
(microns)
Sample Identity:GU/S-COI 12/1/96 - AverageGU/S AF 13/11/03 - AverageGU/S AF 17/12/03 - AverageGU/S COI 25/11/94 - AverageGU/S COI 1500-68 - AverageGU/S COI 1500-68 b - AverageGU/S 1116 - AverageGU/S AF-2 12/1/75 b - AverageGU/S AF-1 12/1/75 - AverageGU/S 1501-68 - AverageGU/S 1501-68 b - AverageGU/S-COI 30/11/98 - Average
Analyst:
Date:
Initial Sample Weight:
2000
1400
100000000000000.1596550
7100000000000.027290.9115980
500000000000.1247622.0924593.6491850
3550.0040144.67568100.16618700003.0628867.0773867.1053250.529458
2500.09823812.9938502.3635640000.0655576.4894839.0121158.5956590.854595
1800.07632917.2739321.205015.0301060001.7677118.0541947.5415727.4119830.455526
1250.43035815.7383084.6398257.0281663.9876153.6045573.1602434.1008127.9314255.2852835.3301710.747293
903.03532511.6682468.1238427.74222511.95398411.49576613.1492026.1720866.7756244.4688724.4194442.632942
636.5657128.66972411.5665257.74054416.97402616.64277324.0712027.4207515.6103075.212015.0142775.928417
4410.0528646.97465614.5299597.76102717.51463917.47798126.9308517.8614675.0609216.2742576.0037239.435427
3112.4893735.33708915.9742087.95340514.46424314.71456418.7363957.9670715.0947336.7777136.49995711.869631
2213.1481053.51825814.8197788.1184910.11683310.4733057.4673658.1311595.4231876.6900726.43745912.536753
15.612.1505512.17572711.212698.0955676.4740936.7484921.273928.4175785.8399056.3469326.12843811.572834
1110.1239451.6385126.7645917.7632824.2206754.3444370.0432118.5653856.1670965.9337745.7425829.647779
7.87.8090711.6022723.3112227.0454253.0695943.0832410.6022598.2593656.2323385.4337185.2638247.543366
5.55.7180631.6049481.536185.9177192.459062.4384320.9216167.3257035.8866764.7624624.619135.736241
3.94.1916941.4661981.0043094.6080862.0358812.0330510.7434726.0129125.2315234.0196863.904464.467094
2.763.3139341.251580.9772633.457221.6910931.7176820.5340334.7650614.5031523.3827273.2885413.7471
1.952.8482771.0353990.9935822.612121.3934711.4358130.5066273.7742623.772322.8569742.7815643.327422
1.382.5151490.8455740.9401872.059311.1472021.189580.550533.0414483.0594012.3773752.3263992.95619
0.982.065980.646930.8182241.6187790.9114180.9467280.5119332.3688332.2840671.8170721.7952262.398056
0.691.5699050.4610320.6850581.2618670.7119950.7408480.4006581.7852941.6030871.2820181.2796351.764383
0.491.1530720.3137390.5614660.9930020.5578770.5813990.2894891.3442741.1280580.8822350.8843981.23028
0.350.6124410.1083440.3307730.5771670.311540.3263330.1069930.7496430.5953430.4396340.4409710.610376
0.240.027600.0053060.0867430.0047610.00501700.1036290.0695110.0063640.0063970.008838
0.17
CalculateStatistics
Half Phi Intervals
Quarter Phi Intervals
Laser Granulometer
Auto. addaperturesat:
Multiple Sample Data Input
SAMPLE STATISTICS
ANALYST AND DATE:
SIEVING ERROR:
SAMPLE TYPE:
TEXTURAL GROUP:
SEDIMENT NAME:
METHOD OFMEAN
MOMENTSSORTING
SKEWNESS
KURTOSIS
METHOD OFMEAN
MOMENTSSORTING
SKEWNESS
KURTOSIS
METHOD OFMEAN
MOMENTSSORTING
SKEWNESS
KURTOSIS
FOLK ANDMEAN
WARD METHODSORTING
SKEWNESS
KURTOSIS
FOLK ANDMEAN
WARD METHODSORTING
SKEWNESS
KURTOSIS
FOLK AND
WARD METHOD
(Description)
% GRAVEL:
% SAND:
% MUD:
% V COARSE GRAVEL:
% COARSE GRAVEL:
% MEDIUM GRAVEL:
% FINE GRAVEL:
% V FINE GRAVEL:
% V COARSE SAND:
% COARSE SAND:
% MEDIUM SAND:
% FINE SAND:
% V FINE SAND:
% V COARSE SILT:
% COARSE SILT:
% MEDIUM SILT:
% FINE SILT:
% V FINE SILT:
% CLAY:
Multiple Sample Statistics
&CTriangular Diagram
Sand
Mud
Gravel
80%
30%
5%
Trace
1:1
1:9
9:1
Sand:Mud Ratio
Gravel %
Gravel
Muddy Gravel
Muddy Sandy Gravel
Gravelly Mud
Gravelly Muddy Sand
Slightly Gravelly Mud
Slightly GravellySandy Mud
Slightly GravellyMuddy Sand
Mud
Sandy Mud
Muddy Sand
Sand
Slightly Gravelly Sand
Gravelly Sand
Sandy Gravel
VF-74-103
TEXTURAL GROUP:
SEDIMENT NAME:
Mud
Coarse Silt
SAMPLE IDENTITY:
Gravel:
Sand:
Mud:
0.0%
9.9%
90.1%
Coarse Gravel:
Medium Gravel:
Fine Gravel:
Coarse Sand:
Medium Sand:
Fine Sand:
Very Fine Sand:
Very Coarse Silt:
0.0%
0.0%
0.0%
1.2%
0.9%
3.8%
14.7%
4.0%
Very Coarse Gravel:
0.0%
Very Coarse Sand:
Coarse Silt:
Clay:
Fine Silt:
Very Fine Gravel:
0.0%
0.0%
Medium Silt:
Very Fine Silt:
13.3%
11.5%
13.9%
17.1%
19.6%
Gravel Sand Mud Diagram
&CTriangular Diagram
Silt
Clay
Sand
90%
50%
10%
1:2
2:1
Silt:Clay Ratio
Sand %
Sand
Clayey Sand
Muddy Sand
Sandy Clay
Sandy Silt
Sandy Mud
Clay
Mud
Silt
Silty Sand
NOTEGravel is also present inthis sample
VF-74-103
TEXTURAL GROUP:IGNORING GRAVELFRACTION
SAMPLE IDENTITY:
Gravel:
Sand:
Mud:
0.0%
9.9%
90.1%
Coarse Gravel:
Medium Gravel:
Fine Gravel:
Coarse Sand:
Medium Sand:
Fine Sand:
Very Fine Sand:
Very Coarse Silt:
Very Coarse Gravel:
Very Coarse Sand:
Coarse Silt:
Clay:
Fine Silt:
Very Fine Gravel:
Medium Silt:
Very Fine Silt:
0.0%
0.0%
0.0%
1.2%
0.9%
3.8%
14.7%
4.0%
0.0%
0.0%
0.0%
13.3%
11.5%
13.9%
17.1%
19.6%
Sand Silt Clay Diagram
0
0
0.1364367845
1.0530253109
2.082472825
1.8992295527
0.9060321419
0.0708801829
0.7451341756
2.9148447635
6.0092021823
8.7596194874
9.8463622854
9.7939177877
8.9605117845
8.1054446278
7.2245648744
6.6559384219
6.1432717842
5.4020096238
4.4180248942
3.334101832
2.9051966207
1.9588741005
0.6749039561
0
&CFrequency Distribution Histogram
Particle diameter (f)
Class weight (%)
Distribution (phi)
0
0
0
0.1346399946
1.1985759521
3.2536238699
5.1725317931
6.0301197588
6.1045907558
6.8098837276
9.8054736078
16.0204453592
24.7780690089
34.599024616
44.300118228
53.3203928672
61.4089765436
68.6282822549
75.2703749892
81.4091747436
86.8400115264
91.175847353
94.5626112175
97.4137621034
99.3456870262
100
100
&CCumulative Frequency Curve
Particle diameter (f)
Cumulative mass retained (%)
Cumulative (phi)
0
0
0.1364367845
1.0530253109
2.082472825
1.8992295527
0.9060321419
0.0708801829
0.7451341756
2.9148447635
6.0092021823
8.7596194874
9.8463622854
9.7939177877
8.9605117845
8.1054446278
7.2245648744
6.6559384219
6.1432717842
5.4020096238
4.4180248942
3.334101832
2.9051966207
1.9588741005
0.6749039561
0
&CFrequency Distribution Curve
Particle diameter (mm)
Class weight (%)
Distribution (microns)
0
0
0
0.1346399946
1.1985759521
3.2536238699
5.1725317931
6.0301197588
6.1045907558
6.8098837276
9.8054736078
16.0204453592
24.7780690089
34.599024616
44.300118228
53.3203928672
61.4089765436
68.6282822549
75.2703749892
81.4091747436
86.8400115264
91.175847353
94.5626112175
97.4137621034
99.3456870262
100
100
&CCumulative Frequency Curve
Particle diameter (mm)
Cumulative mass retained (%)
Cumulative (microns)
Method of Moments - LogarithmicDateModeFirstModeSecondModeThirdModePrint
9.84636228549.84636228542.0824728250100
Mean:6.416
Std. Dev.2.206ClassMode1ClassMode2ClassMode3Classmode4ClassMode5
Skewness-0.2119.84636228542.082472825
Kurtosis2.963
TexureMaximum Frequency
Sum of Sieve Classes9.8463622854
100.00ShapeLine
0095.356385
Sum of Proportion Classes
199.7191843621
Method of Moments - ArithmeticMethod of Moments - GeometricPlease wait while the
Mean (um)41.461Mean (mm)11.714statistics are calculated
Std. Dev. (um)98.871Std. Dev. (mm)4.613
Skewness (um)4.319Skewness (mm)0.211
Kurtosis (um)23.204Kurtosis (mm)2.963Samples remaining:1
Kurtosis (um) - 320.204Kurtosis (mm) - 3-0.037
0%100%
STATISTICS BY METHOD OF MOMENTSSTATISTICS BY METHOD OF MOMENTSSTATISTICS BY METHOD OF MOMENTS
APERTUREMID-POINT (m)APERTUREMID-POINT (m)CUM. MASSCLASSCLASSAPERTURELOGARITHMICMID-POINT (m)NORMALISEDARITHMETICGEOMETIC
(metric)(metric)(PHI Scale)(PHI Scale)RETAINEDWEIGHT (f)WEIGHT(metric)(metric)CLASS WEIGHT
(mm)(mm)(PHI)(PHI)(%)(%)(g)fm(no units)(%)fmlog mf log m
2.00-1.0000.000.000.0020000.000.000000.000000.000000.000.000.000000.000000.0000000.000000.000000.00000
1.401.70-0.485-0.74270.000.000.0014000.000.000000.000000.000001673.30.000.000.000.000000.000000.000003.22400.000000.000000.00000
1.001.2000.000-0.24270.000.000.0010000.000.000000.000000.000001183.20.000.000.000.000000.000000.000003.07300.000000.000000.00000
0.710.8550.4940.24710.130.130.137100.035.12330-31.60371194.95128842.60.270.14115.1289110.8712872495156.5826458977626996.194302.9260.39390669630.464270.862121.60090
0.500.6051.0000.74711.201.061.065000.7934.18772-193.797181098.56254595.82.101.05643.68337880.57458190408833.60534107302776904.199002.7752.95254375843.098065.286609.02119
0.360.4281.4941.24713.252.062.063552.5654.89984-283.756421466.62904421.34.162.08878.53306255.57294118226552.0536845640043302.219402.6255.39367707724.974977.7406112.04368
0.250.3032.0001.74715.171.921.922503.3541.82454-195.26286911.60803297.93.791.90580.47130756.8538034132619.971228909940184.646742.4744.74753973743.790105.326597.48596
0.180.2152.4742.23706.030.860.861801.9214.97486-62.57559261.48517212.11.810.91184.3825826.892524481969.46984777795869.533332.3271.99526952681.357011.707002.14727
0.130.1533.0002.73706.100.070.071250.201.00781-3.7074313.63857150.00.140.0711.36918.19971101955.8486611321061.141652.1760.16205568570.091330.101140.11200
0.090.1083.4743.23706.810.710.71902.287.12641-22.6527972.00663106.11.490.7575.823075.87501203127.2769713414293.678132.0261.42862470090.645790.617950.59131
0.060.0773.9893.73129.813.003.006311.1821.58714-57.94974155.5635575.35.822.91229.163677.75060128864.186024515254.092111.8775.62209771281.956211.580811.27746
0.040.0544.5064.247416.026.216.214426.4029.21838-63.35263137.3640852.612.006.01332.50900.7615510844.14168130551.096731.72110.69843132262.647741.728201.12801
0.030.0385.0074.756624.788.768.7631.141.6624.10423-39.9895766.3437837.017.498.76328.85133.96555-523.958122049.273881.56813.73288685652.184301.090880.54480
0.020.0275.5065.256634.609.829.822251.6313.19292-15.2909517.7226326.219.679.85260.752183.61204-32560.14620485508.918861.41813.92210353361.195530.417120.14553
0.020.0196.0025.754344.309.709.7015.655.824.24301-2.806081.8557818.519.569.79182.384981.77636-112892.734612558278.134891.26812.29879075640.384500.076550.01524
0.010.0136.5066.254353.329.029.021156.420.23481-0.037890.0061113.117.908.96119.977153.52737-201451.490345673103.749261.11710.07797979160.021280.001030.00005
0.010.0097.0066.756261.418.098.097.7854.650.937840.319340.108749.316.198.1175.958319.57794-266818.354228557168.960470.9667.81507744910.08499-0.008710.00089
0.010.0077.5067.256268.637.227.225.552.385.100124.286703.603016.514.437.2247.948753.49361-304806.6320910613714.600490.8165.88857934290.46217-0.116940.02959
0.000.0058.0067.756275.276.646.643.8951.5211.9356115.9997921.447864.613.296.6631.188978.44285-330102.6925912136602.017740.6654.41802880061.08159-0.436460.17613
0.000.0038.5068.256281.416.146.142.7550.6820.7950238.2734370.442603.312.276.1420.388930.39812-340615.5706712991466.381110.5153.15927895041.88443-1.044060.57846
0.000.0029.0108.758086.845.435.431.9447.5629.7972569.79607163.487932.310.795.4012.748309.57378-325038.4566812714249.981020.3641.97447418732.70020-1.903971.34253
0.000.0029.5019.255491.184.344.341.3840.1334.9649099.29149281.962771.68.824.427.206868.53106-273375.3704910880651.565110.2140.92717690293.16849-2.708582.31543
0.000.00110.0109.755494.563.393.390.9733.0437.77567126.16121421.346591.26.663.333.985496.62674-221437.877788920877.484740.0630.21446821143.42320-3.441563.46002
0.000.00110.50110.255497.412.852.850.6929.2442.03640161.40918619.770490.85.802.912.374706.93531-191248.150667770630.50436-0.087-0.24859066963.80930-4.403095.08944
0.000.00110.99510.748099.351.931.930.4920.7636.26078157.09435680.587560.63.911.961.143227.18425-131898.701335390850.37095-0.235-0.4549246863.28592-4.285395.58886
0.000.00011.48011.2376100.000.650.650.357.3515.2136973.35994353.739430.41.350.670.271102.10856-45231.792481856364.35595-0.383-0.2505154591.37865-2.001192.90484
0.000.00012.02511.7525100.000.000.000.240.000.000000.000000.000000.30.000.000.000.000000.000000.00000-0.53800.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.000.000.000.000000.000000.000000.00000.000000.000000.00000
0.000.0000.0000.0000100.000.0000.000.000000.000000.000000.00.00
