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bulletTable 1
bulletTable 2

Table 1. Best fit functions of statistical distributions for bubble populations in basalt samples from Colorado Plateau.

Sample Mode 1 Mode 2 Mean
Chi-Square		 Void Fraction, % Method Distribution
Sigma v BND, 109
or
Fraction		 Sigma v BND, 109
or
Fraction		 Observed Calculated
01b - - - 1.022 1.709 0.734 2.405 6.036 5.826 Density Normal
- - - 1.013 1.721 1.000 2.107* - - Exceedance
01t 0.801 1.223 0.292 0.503 3.617 0.154 1.145 13.799 11.583 Density Normal
1.057 0.948 0.738 0.484 3.667 0.262 0.467* - - Exceedance
02b 1.013 1.378 1.866 - - - 3.610 5.913 6.512 Density Normal
1.012 1.369 1.000 - - - 5.147* - - Exceedance
02t 0.464 1.385 1.079 0.255 2.812 0.235 1.731 7.097 24.362 Density Logistic
0.508 1.290 0.830 0.268 2.752 0.170 2.692* - - Exceedance
03b 2.383 0.357 0.512 - - - 1.087 3.799 3.270 Density Weibull
2.451 0.299 1.000 - - - 0.555* - - Exceedance
03t 0.495 0.714 0.793 0.424 4.441 0.029 1.615 29.266 64.845 Density Logistic
04b 1.231 0.595 0.641 0.749 3.576 0.152 0.896 23.813 21.654 Density Normal
04t - - - 1.163 3.950 0.113 0.852 30.224 29.602 Density Weibull
- - - 1.276 3.998 1.000 0.133* - - Exceedance
05b 0.852 0.447 0.403 0.225 3.640 0.091 1.609 9.823 99.980 Density Logistic
05t 0.507 0.262 0.145 0.408 4.480 0.029 0.880 32.209 54.287 Density Logistic
06b 1.284 2.479 0.105 0.436 3.650 0.052 0.862 10.298 22.954 Density Normal
1.326 2.416 0.671 0.454 3.668 0.329 0.071* - - Exceedance
06t 1.237 2.494 0.170 0.412 4.360 0.034 0.611 26.466 30.567 Density Normal
1.447 2.555 0.892 0.364 4.298 0.108 0.186* - - Exceedance
07b 1.105 1.678 0.384 - - - 1.071 4.089 4.590 Density Normal
1.106 1.684 1.000 - - - 0.772* - - Exceedance
07t 0.984 1.811 0.311 0.421 2.793 0.205 0.740 4.304 4.576 Density Normal
1.026 1.743 0.596 0.428 2.782 0.404 0.150* - - Exceedance
08b 0.769 1.034 0.202 - - - 1.142 4.663 99.895 Density Logistic
0.777 1.061 1.000 - - - 0.598* - - Exceedance
08t 0.457 1.369 0.512 0.306 3.997 0.069 1.241 19.754 22.974 Density Logistic
0.484 1.336 0.888 0.280 4.043 0.112 0.515* - - Exceedance
09b - - - 1.802 1.954 0.190 0.943 7.171 5.022 Density Weibull
- - - 1.957 1.776 1.000 0.462* - - Exceedance
09t 0.238 1.246 0.396 0.729 1.573 0.476 1.638 14.196 99.946 Density Logistic
10b 0.995 1.327 0.974 - - - 2.855 3.283 2.853 Density Normal
0.967 1.361 1.000 - - - 3.905* - - Exceedance
10t 0.794 1.166 0.352 0.507 3.901 0.123 1.188 19.903 16.825 Density Normal
0.840 1.090 0.753 0.506 3.904 0.247 0.350* - - Exceedance
11b 0.597 1.102 0.443 0.429 3.563 0.118 1.867 20.157 94.885 Density Logistic
0.702 0.959 0.834 0.437 3.663 0.166 0.858* - - Exceedance
11t 0.535 1.492 2.811 - - - 2.085 16.804 95.440 Density Logistic
0.567 1.394 1.000 - - - 5.442* - - Exceedance
12b 0.406 1.545 2.008 - - - 3.406 3.510 8.527 Density Logistic
0.448 1.422 1.000 - - - 14.781* - - Exceedance
12t 0.387 1.400 2.167 - - - 2.366 5.407 4.419 Density Logistic
0.414 1.314 1.000 - - - 10.404* - - Exceedance
13b 0.925 1.766 0.542 - - - 1.659 4.650 3.057 Density Normal
0.921 1.78 1.000 - - - 1.240* - - Exceedance
13t 1.300 1.791 0.198 0.482 4.077 0.093 0.799 21.332 24.392 Density Normal
1.300 1.797 0.680 0.475 4.084 0.320 0.094* - - Exceedance
14b - - - 1.048 2.176 0.109 0.742 2.528 3.005 Density Normal
- - - 1.073 2.155 1.000 0.173* - - Exceedance
14t 0.758 1.613 0.271 0.575 3.415 0.232 1.666 14.338 13.368 Density Normal
1.035 1.630 0.666 0.530 3.517 0.334 0.595* - - Exceedance
15b - - - 1.454 1.927 2.055 1.424 18.205 14.444 Density Weibull
- - - 1.434 1.951 1.000 1.277* - - Exceedance
15t 0.670 1.184 0.222 0.866 3.976 0.060 1.326 28.938 29.832 Density Normal
0.916 0.765 0.868 0.801 4.083 0.132 0.741* - - Exceedance
17b - - - 0.663 2.833 2.185 4.375 17.944 17.181 Density Weibull
- - - 0.643 2.834 1.000 5.022* - - Exceedance
17t - - - 1.067 2.738 1.841 3.034 25.642 24.745 Density Weibull
- - - 1.06 2.743 1.000 2.467* - - Exceedance
18b 2.646 0.728 0.508 - - - 1.070 13.260 19.379 Density Weibull
2.624 0.864 1.000 - - - 0.339* - - Exceedance
18t 0.660 1.185 1.388 0.976 3.153 0.114 2.648 23.138 17.698 Density Normal
0.844 0.961 0.972 0.548 3.952 0.028 6.318* - - Exceedance
19b 0.563 1.183 0.569 0.768 3.545 0.058 1.692 9.765 9.210 Density Normal
0.726 0.936 0.944 0.636 3.842 0.056 3.456* - -  
19t 0.587 1.233 0.628 0.847 4.016 0.038 1.521 17.580 21.433 Density Normal
0.657 1.154 0.953 0.667 4.206 0.047 3.073* - - Exceedance
20b 0.612 0.906 0.621 0.924 3.713 0.024 2.042 24.294 11.098 Density Normal
20t 0.860 0.410 2.842 0.780 4.203 0.037 5.194 20.139 23.720 Density Normal
21b 0.813 1.441 0.371 0.613 4.123 0.030 1.461 12.030 10.566 Density Normal
0.904 1.353 0.936 0.516 4.221 0.064 1.874* - - Exceedance
21t 0.386 1.546 1.309 0.322 4.112 0.080 1.731 20.164 27.565 Density Logistic
0.455 1.402 0.963 0.227 4.261 0.037 6.837* - - Exceedance
22b - - - 0.972 2.164 1.504 2.479 21.037 21.692 Density Normal
- - - 1.010 2.126 1.000 1.909* - - Exceedance
22t 1.546 0.657 1.039 0.573 3.686 0.166 1.245 26.204 32.146 Density Normal
23b 0.654 1.395 0.570 0.647 4.390 0.079 1.504 33.830 37.819 Density Normal
0.570 1.438 0.856 0.726 4.233 0.144 1.536* - - Exceedance
23t 0.786 0.973 0.810 0.706 4.161 0.069 1.489 27.005 27.908 Density Normal
1.011 0.568 0.955 0.558 4.349 0.045 3.576* - - Exceedance
24b - - - 2.142 2.398 0.222 1.204 27.852 37.864 Density Weibull
- - - 2.196 2.469 1.000 0.836* - - Exceedance
24t 0.819 1.349 0.379 0.639 4.087 0.071 1.354 19.987 21.182 Density Normal
0.857 1.362 0.852 0.589 4.167 0.148 1.169* - - Exceedance
25b 0.325 1.030 0.414 - - - 1.644 5.111 0.151 Density Logistic
25t 0.451 1.282 1.243 - - - 1.582 20.877 13.446 Density Logistic
0.534 0.935 1.000 - - - 9.242* - - Exceedance
26b 0.886 1.246 2.122 - - - 4.831 3.026 2.989 Density Normal
0.922 1.166 1.000 - - - 12.158* - - Exceedance
26t 0.946 1.371 1.418 - - - 1.868 4.194 3.559 Density Normal
1.024 1.204 1.000 - - - 6.025* - - Exceedance
27b 0.882 1.782 1.110 - - - 1.631 7.384 5.147 Density Normal
0.929 1.702 1.000 - - - 3.602* - - Exceedance
27t 1.216 2.572 1.375 - - - 2.143 19.049 19.871 Density Weibull
1.269 2.530 1.000 - - - 3.584* - - Exceedance
28b 0.790 1.546 0.350 0.319 3.526 0.208 0.915 29.658 99.980 Density Logistic
28t 0.772 2.235 0.970 0.776 4.838 0.005 1.960 15.326 20.301 Density Normal
29b 0.963 1.654 1.412 - - - 1.830 7.195 7.099 Density Normal
0.963 1.651 1.000 - - - 1.833* - - Exceedance
29t 0.750 2.170 2.832 - - - 4.127 15.752 16.060 Density Normal
0.760 2.163 1.000 - - - 6.484* - - Exceedance
30b 0.864 0.527 0.579 0.848 2.872 0.055 0.957 2.565 2.909 Density Normal
30t 0.398 0.598 0.186 1.477 1.600 0.114 1.071 4.263 13.112 Density Normal
31b 0.344 1.539 0.436 0.357 3.329 0.245 1.759 19.831 21.114 Density Logistic
0.390 1.504 0.667 0.367 3.353 0.333 1.358* - - Exceedance
31t 0.671 1.815 0.170 0.643 3.902 0.202 0.899 33.773 33.313 Density Normal
0.717 1.819 0.472 0.629 3.926 0.528 0.099* - - Exceedance
32b - - - 0.929 3.016 0.392 1.170 25.243 29.171 Density Normal
- - - 0.926 3.023 1.000 0.463* - - Exceedance
32t - - - 0.891 3.271 0.273 0.957 24.888 30.101 Density Normal
- - - 0.897 3.268 1.000 0.357* - - Exceedance
33b 1.218 2.205 0.282 0.375 3.995 0.044 0.967 15.927 23.209 Density Normal
1.330 2.209 0.894 0.304 3.960 0.106 0.359* - - Exceedance
33t 0.476 1.530 0.624 0.827 3.026 0.558 1.516 25.366 27.450 Density Normal
0.554 1.514 0.588 0.795 3.117 0.412 1.360* - - Exceedance
34b 0.801 2.340 1.433 0.434 3.540 0.213 2.122 22.877 23.235 Density Normal
0.839 2.374 0.904 0.406 3.531 0.096 0.596* - - Exceedance
34t 1.101 2.248 0.408 0.377 4.596 0.046 1.292 29.534 31.523 Density Normal
1.174 2.269 0.920 0.309 4.664 0.080 0.387* - - Exceedance
35b 0.420 1.475 0.023 0.686 3.475 0.266 2.061 21.055 22.126 Density Normal
0.322 1.424 0.063 0.715 3.468 0.937 1.171* - - Exceedance
35t 0.679 1.840 0.242 0.627 3.881 0.183 1.292 29.275 29.235 Density Normal
0.691 1.848 0.576 0.632 3.912 0.424 0.198* - - Exceedance
36b 0.574 1.551 0.188 0.722 3.324 0.323 1.150 20.449 21.949 Density Normal
0.603 1.485 0.359 0.755 3.292 0.641 0.148* - - Exceedance
36t 0.873 2.436 0.477 0.591 3.576 0.352 1.310 30.584 30.844 Density Normal
0.932 2.423 0.561 0.638 3.522 0.439 0.294* - - Exceedance
37b 0.942 2.021 0.805 0.497 3.536 0.467 1.252 29.114 29.054 Density Normal
0.970 2.015 0.642 0.497 3.541 0.358 0.222* - - Exceedance
37t 0.709 1.530 0.397 0.77 3.581 0.270 0.913 28.691 34.088 Density Normal
0.852 1.500 0.661 0.733 3.672 0.339 0.543* - - Exceedance
38b 1.08 2.371 0.309 0.489 3.604 0.055 0.775 41.422 17.153 Density Normal
0.905 2.004 0.599 0.719 3.436 0.401 0.063* - - Exceedance
38t 0.704 1.680 0.913 0.642 3.876 0.212 1.327 32.281 33.563 Density Normal
0.727 1.672 0.822 0.619 3.909 0.178 0.806* - - Exceedance
39b 0.641 2.089 3.828 0.439 4.019 0.148 3.720 29.638 29.050 Density Normal
0.663 2.097 0.973 0.206 4.089 0.027 1.355* - - Exceedance
39t 0.714 1.590 0.727 0.727 3.967 0.115 1.694 23.884 31.315 Density Normal
0.771 1.560 0.884 0.629 4.074 0.116 0.807* - - Exceedance
40b - - - 0.912 2.327 2.109 5.173 28.848 29.447 Density Normal
- - - 0.929 2.327 1.000 4.883* - - Exceedance
40t 0.815 0.941 0.582 0.839 4.092 0.044 0.828 34.807 26.651 Density Normal
0.982 0.652 0.953 0.672 4.308 0.047 1.212* - - Exceedance
41b 0.726 1.864 0.450 0.712 3.734 0.119 1.292 22.765 21.208 Density Normal
0.725 1.843 0.777 0.726 3.699 0.223 0.623* - - Exceedance
41t 0.569 1.844 0.621 1.043 3.168 0.203 1.592 28.248 35.968 Density Normal
0.619 1.817 0.794 1.000 3.315 0.206 1.069* - - Exceedance
42b - - - 1.048 1.765 2.334 4.202 16.540 20.454 Density Normal
- - - 1.130 1.671 1.000 2.537* - - Exceedance
42t - - - 0.708 2.083 11.500 15.850 35.575 35.065 Density Normal
- - - 0.713 2.080 1.000 9.294* - - Exceedance
44b 0.626 1.717 1.810 0.590 4.047 0.056 2.115 16.675 15.905 Density Normal
0.623 1.709 0.963 0.845 3.891 0.037 2.568* - - Exceedance
44t 0.396 1.692 0.378 0.398 4.019 0.069 0.991 23.326 43.601 Density Logistic
0.431 1.646 0.862 0.364 4.064 0.138 0.886* - - Exceedance
45b 0.616 1.524 0.246 0.774 3.613 0.147 1.214 21.704 23.457 Density Normal
0.711 1.503 0.676 0.717 3.725 0.324 0.428* - - Exceedance
45t 0.669 1.718 0.461 0.854 3.747 0.098 1.290 21.655 28.370 Density Normal
0.684 1.718 0.831 0.849 3.770 0.169 0.613* - - Exceedance
46b 0.767 1.682 0.380 0.648 3.839 0.116 1.171 20.562 20.661 Density Normal
0.760 1.677 0.755 0.671 3.828 0.245 0.344* - - Exceedance
46t 0.707 1.762 0.425 0.793 3.593 0.150 0.682 25.296 24.821 Density Normal
0.752 1.790 0.783 0.702 3.750 0.217 0.503* - - Exceedance
47b 0.612 1.451 0.320 1.059 3.889 0.051 1.240 21.862 44.329 Density Normal
0.687 1.414 0.897 0.810 4.112 0.103 0.929* - - Exceedance
47t 0.790 2.042 0.668 0.475 4.324 0.056 1.812 23.420 20.671 Density Normal
0.785 2.041 0.915 0.544 4.288 0.085 0.425* - - Exceedance
48b - - - 0.713 1.917 3.534 4.794 14.734 10.367 Density Normal
- - - 0.729 1.911 1.000 4.940* - - Exceedance
48t 0.550 1.646 0.352 1.265 2.203 0.140 0.921 29.682 14.070 Density Normal
0.532 1.655 0.640 1.409 1.979 0.360 0.357* - - Exceedance
49b 0.977 2.160 0.176 0.713 3.989 0.063 0.652 23.158 21.716 Density Normal
1.037 2.178 0.760 0.712 4.026 0.240 0.063* - - Exceedance
49t 0.529 1.734 0.105 1.030 2.999 0.222 0.972 22.205 27.580 Density Normal
0.528 1.699 0.305 1.044 2.939 0.695 0.171* - - Exceedance
50b 0.634 1.942 2.423 0.967 2.247 1.491 4.661 24.942 27.915 Density Normal
0.647 2.067 0.603 1.500 1.317 0.397 2.627* - - Exceedance
50t 0.933 2.351 0.613 0.673 4.348 0.026 0.951 28.707 25.476 Density Normal
0.950 2.373 0.971 0.520 4.576 0.029 0.286* - - Exceedance
* Chi-Square is not adjusted for exceedance rescaling, and so not reliable. 100 sample points were used for function fit.


Table 2. Graphs of bubble distributions presented in Table 1.


01b (Normal)
02b (Normal)
03b (Weibull)

04b (Normal)

01t (Normal)
02t (Logistic)

03t (Logistic)
04t (Weibull)

05b (Logistic)

06b (Normal)
07b (Normal)
08b (Logistic)

05t (Logistic)
06t (Normal)
07t (Normal)
08t (Logistic)

09b (Weibull)
10b (Normal)
11b (Logistic)
12b (Logistic)

09t (Logistic)
10t (Normal)
11t (Logistic)
12t (Logistic)

13b (Normal)
14b (Normal)
15b (Weibull)
17b (Weibull)

13t (Normal)
14t (Normal)
15t (Normal)
17t (Weibull)

18b (Weibull)
19b (Normal)

20b (Normal)
21b (Normal)

18t (Normal)
19t (Normal)

20t (Normal)

 21t (Logistic)

22b (Normal)
23b (Normal)
24b (Weibull)

25b (Logistic)

22t (Normal)
23t (Normal)
24t (Normal)
25t (Logistic)

26b (Normal)
27b (Normal)

28b (Logistic)
29b (Normal)

26t (Normal)
27t (Weibull)

28t (Normal)
29t (Normal)

30b (Normal)
31b (Logistic)
32b (Normal)
33b (Normal)

30t (Normal)
31t (Normal)
32t (Normal)
33t (Normal)

34b (Normal)
35b (Normal)
36b (Normal)
37b (Normal)

34t (Normal)
35t (Normal)
36t (Normal)
37t (Normal)

38b (Normal)
39b (Normal)
40b (Normal)
41b (Normal)

38t (Normal)
39t (Normal)
40t (Normal)
41t (Normal)

42b (Normal)
44b (Normal)
45b (Normal)
46b (Normal)

42t (Normal)
44t (Logistic)
45t (Normal)
46t (Normal)

47b (Normal)
48b (Normal)
49b (Normal)
50b (Normal)

47t (Normal)
48t (Normal)
49t (Normal)
50t (Normal)

 

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Last modified: Tuesday May 08, 2007