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Layer (i) Vi (m/s) Hi (m) True RMS Velocity (m/s) Zi (m)1 2000 600 0.6000 0.6000 2000 6002 4000 400 0.2000 0.8000 2646 1000

000 1000 0.666! 1.466! 2812 2000

t0i 0i

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Layer (i) 1 2Vi 2000 4000 000Hi 600 400 1000

0.6000 0.2000 0.666!

0.6000 0.8000 1.466!L"#$R 1 L"#$R 2 L"#$R

% Te % Te % Te0 0.600 0 0.800 0 1.467

21 0.600 4& 0.800 101 1.46742 0.600 &8 0.801 20 1.4686 0.601 14! 0.802 0' 1.47184 0.601 1&! 0.803 40! 1.474

10' 0.602 24! 0.805 '10 1.478126 0.603 2&! 0.808 61' 1.483

14! 0.605 48 0.811 !20 1.48916& 0.606 400 0.814 82! 1.4961&0 0.607 4'4 0.818 & 6 1.504212 0.609 '08 0.823 104! 1.5132 0.611 '64 0.828 1161 1.5232'' 0.613 621 0.833 12!! 1.5352!! 0.616 680 0.840 1 &! 1.5482&& 0.618 !41 0.847 1'20 1.562

22 0.621 806 0.855 1648 1.57844 0.624 8! 0.864 1!81 1.5966! 0.627 &44 0.874 1&20 1.616&0 0.631 101& 0.885 206' 1.638

41 0.635 1100 0.898 221& 1.6624 ! 0.639 118! 0.913 2 82 1.689461 0.643 128 0.929 2''8 1.72048' 0.647 1 &0 0.949 2!48 1.755'0& 0.652 1'11 0.972 2&'8 1.795' 4 0.657 16' 1.001 1& 1.842'60 0.662 182' 1.036 464 1.898

'8' 0.668 2044 1.083 !8& 1.968611 0.673 2 4' 1.151 420' 2.0616 8 0.680 2821 1.261 480' 2.20066' 0.686 8 6 1.504 '&'' 2.4756& 0.693 401& 1.548 61'2 2.523!21 0.700 42 ' 1.600 6 82 2.579!'0 0.708 44& 1.664 66'' 2.645

t0i

0i

0 1000 2000.000

0.'00

1.000

1.'00

2.000

2.'00

.000

.'00

4.000

T ( s )

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!!& 0.715 481 1.742 6&8& 2.72780& 0.724 '222 1.843 !41 2.832840 0.732 '!!4 1.979 !&80 2.9718!2 0.742 6'80 2.178 8801 3.174&04 0.751 !&26 2.512 10162 3.512& 8 0.761 10&' 3.266&!2 0.772

100! 0.783104 0.7951080 0.807111& 0.82011'& 0.8341200 0.849124 0.864

128! 0.8801 0.8971 80 0.91514 0 0.9331482 0.9531' 6 0.9751'&2 0.99716'2 1.0211!14 1.0461!!& 1.073

1848 1.1021&20 1.1321&&! 1.16520!8 1.200216' 1.23822'! 1.2782 '' 1.3222460 1.3692'! 1.42026&' 1.475282! 1.5362&!0 1.602

126 1.6742&! 1.75448' 1.8436& 1.942&2' 2.052

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418' 2.17744!8 2.318481 2.480'1&8 2.667'646 2.88661! 3.1456806 3.455!'!! 3.8358' 8 4.311&!! 4.923

1141! 5.740

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0 000 4000 '000 6000 !000 8000 &000 10000

L"#$R 1L"#$R 2

L"#$R

% (m)

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%0 0.0 1.467 0 2.1511111111

101 0.1 1.467 10254 2.1524075470203 0.1 1.468 41097 2.1563064405

305 0.2 1.471 92771 2.1628367606407 0.2 1.474 165689 2.1720475054510 0.3 1.478 260441 2.1840088120615 0.3 1.483 377810 2.1988135865720 0.4 1.489 518789 2.2165797367827 0.4 1.496 684614 2.2374531269936 0.5 1.504 876788 2.2616114225

1047 0.5 1.513 1097133 2.28926905701161 0.6 1.523 1347844 2.32068364691277 0.6 1.535 1631562 2.35616431071397 0.7 1.548 1951476 2.39608254471520 0.8 1.562 2311445 2.44088659911648 0.8 1.578 2716177 2.49112075211781 0.9 1.596 3171468 2.54745159411920 1.0 1.616 3684528 2.61070460762065 1.0 1.638 4264469 2.68191630242219 1.1 1.662 4922995 2.76241063492382 1.2 1.689 5675482 2.85391478462558 1.3 1.720 6542671 2.95874159042748 1.4 1.755 7553487 3.08009092562958 1.5 1.795 8750015 3.22257709333193 1.6 1.842 10196916 3.39322046503464 1.7 1.898 12001050 3.60349172733789 1.9 1.968 14357718 3.87407614874205 2.1 2.061 17680864 4.24808227164805 2.4 2.200 23086862 4.83907444485955 3.0 2.475 35463157 6.12486391826152 3.1 2.523 37851321 6.3642023068

6382 3.2 2.579 40730115 6.64956906026655 3.3 2.645 44292183 6.99830069096989 3.5 2.727 48851418 7.43829285407413 3.7 2.832 54958993 8.01782519977980 4.0 2.971 63687175 8.82923668308801 4.4 3.174 77459752 10.0769717688

10162 5.1 3.512 103275478 12.3357843635

/Z T (%) %2 T2

0 20000000 40000000 60000000 80000000 10.0000000000

2.0000000000

4.0000000000

6.0000000000

8.0000000000

10.0000000000

12.0000000000

14.0000000000

( ) * 2.48&40!1! &$+48 ,6 + !.006484 22!$+40 ,' - 6.18 &6 &' 4R * &.&&&&&&&86!$+01

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0000000 120000000

'188!1!'8$+2' , + 4.64&0 ! '16$+16 ,2 - 1.26462 8 01$+0! - 2.1'11111111$-00

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Terms loy omial e3ree ( ) True RMS Velocity (m/s)2 2 2812 1.0462E-07

4 2812 1.1887E-074 6 2812 1.2539E-07

' 8 2812 1.2685E-076 10 2812 1.2676E-07! 12 2812 1.2646E-07

5 1

otes(1) We find C1 by fitting a polyno ial of deg!ee " and #opying t$e #oeffi#ient(2) Cal#'lated * +elo#ity,1 (C1) (1 2).(3) E,/ !'e * - Cal#'lated */ !'e * 100.(4) "ote t$e de#!ea&e in E a& " in#!ea&e&. $i& indi#ate& t$at a& e '&e o!e te

* +elo#ity f!o C1 be#o e& bette!.(5) e!e e a!e '&ing all off&et&. $e!efo!e yo' &ee t$at e get !elati+ely $ig$off&et a&&' ption. o! e a ple #o pa!e t$e 2-te! e!!o! it$ t$at in &$o!t off

0 2 4 6 8 10 12 140.007

2.007

4.007

6.007

8.007

10.007

12.007

oly omial e3ree ( )

$ r r o r

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5alculate RMS Velocity (m/s) $3092 9.942900 3.132824 0.42

2808 0.162809 0.132812 0.01

of % and pa&ting it into t$e C1 #ol' n.

! & of t$e e pan&ion t$e e&ti ation of t$e

e!!o!& be#a'&e e a!e +iolating t$e &$o!t-et&.

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%0 0.0 1.467 0 2.1511111111

101 0.1 1.467 10254 2.1524075470203 0.1 1.468 41097 2.1563064405

305 0.2 1.471 92771 2.1628367606407 0.2 1.474 165689 2.1720475054510 0.3 1.478 260441 2.1840088120615 0.3 1.483 377810 2.1988135865720 0.4 1.489 518789 2.2165797367827 0.4 1.496 684614 2.2374531269936 0.5 1.504 876788 2.2616114225

1047 0.5 1.513 1097133 2.28926905701161 0.6 1.523 1347844 2.32068364691277 0.6 1.535 1631562 2.35616431071397 0.7 1.548 1951476 2.39608254471520 0.8 1.562 2311445 2.44088659911648 0.8 1.578 2716177 2.49112075211781 0.9 1.596 3171468 2.54745159411920 1.0 1.616 3684528 2.61070460762065 1.0 1.638 4264469 2.6819163024

%/Z T (%) %2 T2

0 '00000 1000000 1'00000 2000000 2'00000 0000000.0000000000

0.'000000000

1.0000000000

1.'000000000

2.0000000000

2.'000000000

.0000000000

( ) * 4. '644!!&!2$+4! ,6 - 8.'&020 18&8$+40 ,' + .! 2282!126$+ 2

R * 1.0000000000$-00

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'00000 4000000 4'00000

1.''68&&104 $+24 , + 4.668!0416'&$+16 ,2 - 1.264 6!81! $+0! - 2.1'11111111$-00

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Terms loy omial e3ree ( ) True RMS Velocity (m/s)2 2 2812 1.2497E-07

4 2812 1.2643E-074 6 2812 1.2644E-07

' 8 2812 1.2644E-076 10 2812 1.2644E-07! 12 2812 1.2644E-07

5 1

otes(1) We find C1 by fitting a ployno ial of deg!ee " and #opying t$e #oeffi#ient(2) Cal#'lated * +elo#ity,1 (C1) (1 2).(3) E,/ !'e * - Cal#'lated */ !'e * 100.(4) "ote t$e de#!ea&e in E a& " in#!ea&e&. $i& indi#ate& t$at a& e '&e o!e te

* +elo#ity f!o C1 be#o e& bette!.(5) e!e e a!e '&ing short off&et& only ( a % ,:1.0). $e!efo!e yo' &ee t$a!e ;eeping t$e &$o!t-off&et a&&' ption. o! e a ple #o pa!e t$e 2-te! e!!o!

0 2 4 6 8 10 12 140.007

0.207

0.407

0.607

0.807

oly omial e3ree ( )

$ r r o r

59esseus

ase

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5alculate RMS Velocity (m/s) $2829 0.582812 0.002812 0.00

2812 0.002812 0.002812 0.00

of % and pa&ting it into t$e C1 #ol' n.

! & of t$e e pan&ion t$e e&ti ation of t$e

at e get !elati+ely lo e!!o!& be#a'&e eit$ t$at in all off&et&.

clusioe ca ac:ie;e t:e same accuracy iimati 3 t:e true T+% cur;e t:rou3: aies e