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Layer (i) Vi (m/s) Hi (m) Dt0i T0i True RMS Velocity (m/s) Zi (m)1 2000 600 0.6000 0.6000 2000 600
2 4000 400 0.2000 0.8000 2646 1000
3 3000 1000 0.6667 1.4667 2812 2000
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Layer (i) 1 2 3
Vi 2000 4000 3000
Hi 600 400 1000
Dt0i 0.6000 0.2000 0.6667T
0i0.6000 0.8000 1.4667
LAYER 1 LAYER 2 LAYER 3
X Te X Te X Te
0 0.600 0 0.800 0 1.467
21 0.600 49 0.800 101 1.467
42 0.600 98 0.801 203 1.468
63 0.601 147 0.802 305 1.471
84 0.601 197 0.803 407 1.474
105 0.602 247 0.805 510 1.478
126 0.603 297 0.808 615 1.483
147 0.605 348 0.811 720 1.489169 0.606 400 0.814 827 1.496
190 0.607 454 0.818 936 1.504
212 0.609 508 0.823 1047 1.513
233 0.611 564 0.828 1161 1.523
255 0.613 621 0.833 1277 1.535
277 0.616 680 0.840 1397 1.548
299 0.618 741 0.847 1520 1.562
322 0.621 806 0.855 1648 1.578
344 0.624 873 0.864 1781 1.596
367 0.627 944 0.874 1920 1.616390 0.631 1019 0.885 2065 1.638
413 0.635 1100 0.898 2219 1.662
437 0.639 1187 0.913 2382 1.689
461 0.643 1283 0.929 2558 1.720
485 0.647 1390 0.949 2748 1.755
509 0.652 1511 0.972 2958 1.795
534 0.657 1653 1.001 3193 1.842
560 0.662 1825 1.036 3464 1.898
585 0.668 2044 1.083 3789 1.968
611 0.673 2345 1.151 4205 2.061638 0.680 2821 1.261 4805 2.200
665 0.686 3836 1.504 5955 2.475
693 0.693 4019 1.548 6152 2.523
721 0.700 4235 1.600 6382 2.579
750 0.708 4493 1.664 6655 2.645
779 0.715 4813 1.742 6989 2.727
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 2000
T
(s)
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809 0.724 5222 1.843 7413 2.832
840 0.732 5774 1.979 7980 2.971
872 0.742 6580 2.178 8801 3.174
904 0.751 7926 2.512 10162 3.512
938 0.761 10953 3.266
972 0.772
1007 0.783
1043 0.795
1080 0.807
1119 0.820
1159 0.834
1200 0.849
1243 0.864
1287 0.880
1333 0.897
1380 0.915
1430 0.933
1482 0.953
1536 0.975
1592 0.997
1652 1.021
1714 1.046
1779 1.073
1848 1.102
1920 1.132
1997 1.165
2078 1.200
2165 1.238
2257 1.278
2355 1.322
2460 1.369
2573 1.420
2695 1.475
2827 1.536
2970 1.602
3126 1.674
3297 1.754
3485 1.843
3693 1.942
3925 2.052
4185 2.177
4478 2.318
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4813 2.480
5198 2.667
5646 2.886
6173 3.145
6806 3.455
7577 3.835
8538 4.311
9773 4.923
11417 5.740
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4000 6000 8000 10000
X (m)
LAYER 1
LAYER 2
LAYER 3
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X /Z T3(X) X T32
0 0.0 1.467 0 2.1511111111
101 0.1 1.467 10254 2.1524075470
203 0.1 1.468 41097 2.1563064405
305 0.2 1.471 92771 2.1628367606407 0.2 1.474 165689 2.1720475054
510 0.3 1.478 260441 2.1840088120
615 0.3 1.483 377810 2.1988135865
720 0.4 1.489 518789 2.2165797367
827 0.4 1.496 684614 2.2374531269
936 0.5 1.504 876788 2.2616114225
1047 0.5 1.513 1097133 2.2892690570
1161 0.6 1.523 1347844 2.3206836469
1277 0.6 1.535 1631562 2.3561643107
1397 0.7 1.548 1951476 2.39608254471520 0.8 1.562 2311445 2.4408865991
1648 0.8 1.578 2716177 2.4911207521
1781 0.9 1.596 3171468 2.5474515941
1920 1.0 1.616 3684528 2.6107046076
2065 1.0 1.638 4264469 2.6819163024
2219 1.1 1.662 4922995 2.7624106349
2382 1.2 1.689 5675482 2.8539147846
2558 1.3 1.720 6542671 2.9587415904
2748 1.4 1.755 7553487 3.0800909256
2958 1.5 1.795 8750015 3.2225770933
3193 1.6 1.842 10196916 3.3932204650
3464 1.7 1.898 12001050 3.6034917273
3789 1.9 1.968 14357718 3.8740761487
4205 2.1 2.061 17680864 4.2480822716
4805 2.4 2.200 23086862 4.8390744448
5955 3.0 2.475 35463157 6.1248639182
6152 3.1 2.523 37851321 6.3642023068
6382 3.2 2.579 40730115 6.6495690602
6655 3.3 2.645 44292183 6.99830069096989 3.5 2.727 48851418 7.4382928540
7413 3.7 2.832 54958993 8.0178251997
7980 4.0 2.971 63687175 8.8292366830
8801 4.4 3.174 77459752 10.0769717688
10162 5.1 3.512 103275478 12.3357843635
y = 2.4894071810E-48x6 - 7.0064843333E-40x5 +
25x3 - 4.6490373668E-16x2 + 1.2646238
R = 9.999999979
0
2
4
6
8
10
12
14
0.0E+00 2.0E+07 4.0E+07 6.
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.1839640395E-32x4 + 2.3518865606E-
19E-07x + 2.1511111111E+00
7E-01
.0E+07 8.0E+07 1.0E+08 1.2E+08
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# Terms Ploynomial Degree (N) True RMS Velocity (m/s) C1
2 2 2812 1.0462E-07
3 4 2812 1.1887E-07
4 6 2812 1.2539E-07
5 8 2812 1.2685E-07
6 10 2812 1.2676E-077 12 2812 1.2646E-07
Notes:
We find C1 by fitting a polynomial of degree N and copying the coefficient of.
(2)Calculated RMS velocity=1/(C1)^(1/2.)(3)E=|True_RMS - Calculated_RMS|/True_RMS * 100.
Note the decrease in E as N increases. This indicates that as we use more terms
RMS velocity from C1 becomes better.Here we are using al l offsets. Therefore, you see that we get relatively high err
offset assumption. For example, compare the 2-term error with that in short of.
0%
2%
4%
6%
8%
10%12%
0 2 4 6 8 10 12 14
Error
Polynomial Degree (N)
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Calculated RMS Velocity (m/s) E
3092 9.94%
2900 3.13%
2824 0.42%
2808 0.16%
2809 0.13%2812 0.01%
(1)X and pasting it into the C1 column
(4)of the expansion, the estimation of the
(5)ors because we are violating the short-
fsets
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X X/Z3 T3(X) X T32
0 0.0 1.467 0 2.1511111111
101 0.1 1.467 10254 2.1524075470
203 0.1 1.468 41097 2.1563064405
305 0.2 1.471 92771 2.1628367606407 0.2 1.474 165689 2.1720475054
510 0.3 1.478 260441 2.1840088120
615 0.3 1.483 377810 2.1988135865
720 0.4 1.489 518789 2.2165797367
827 0.4 1.496 684614 2.2374531269
936 0.5 1.504 876788 2.2616114225
1047 0.5 1.513 1097133 2.2892690570
1161 0.6 1.523 1347844 2.3206836469
1277 0.6 1.535 1631562 2.3561643107
1397 0.7 1.548 1951476 2.39608254471520 0.8 1.562 2311445 2.4408865991
1648 0.8 1.578 2716177 2.4911207521
1781 0.9 1.596 3171468 2.5474515941
1920 1.0 1.616 3684528 2.6107046076
2065 1.0 1.638 4264469 2.6819163024
y = 4.3544682657E-47x6 + 8.5970221306E-40x5 -
24x3 - 4.6687049018E-16x2 + 1.26436781
R = 1.000000000
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.0E+00 1.0E+06 2.0E+06
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.7325425102E-32x4 + 1.5569100820E-
82E-07x + 2.1511111111E+00
0E+00
3.0E+06 4.0E+06 5.0E+06
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# Terms Ploynomial Degree (N) True RMS Velocity (m/s) C1
2 2 2812 1.2497E-07
3 4 2812 1.2643E-07
4 6 2812 1.2644E-07
5 8 2812 1.2644E-07
6 10 2812 1.2644E-077 12 2812 1.2644E-07
Notes:
We find C1 by fitting a ploynomial of degree N and copying the coefficient of.
(2)Calculated RMS velocity=1/(C1)^(1/2.)(3)E=|True_RMS - Calculated_RMS|/True_RMS * 100.
Note the decrease in E as N increases. This indicates that as we use more terms
RMS velocity from C1 becomes better.Here we are using shortoffsets only (maxX/Z=
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Calculated RMS Velocity (m/s) E
2829 0.58%
2812 0.00%
2812 0.00%
2812 0.00%
2812 0.00%2812 0.00%
(1)X and pasting it into the C1 column
(4)of the expansion, the estimation of the
(5)e get relatively low errors because we
r with that in all offsets
onclusione can achieve the same accuracy in
imating the true T-X curve through a
ies expansion by limiting the maximum
ed offset to less than the reflector depth
ter than including more terms in the
ries