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  • 7/26/2019 KRIGING GEOESTADISTICA

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    GEOESTADITICA

    UNIVERSIDAD PRIVADA DEL NORTE

    FACULTAD DE INGENERIA

    ESCUELA ACADMICO PROFESIONAL DE INGENIERIA GEOLGICA

    CURSO:

    GEOESTADISTICA

    CICLO:

    VI

    TITULO DEL TRABAJO:

    TRABAJO DE INVESTIGACION SOBRE KRIGING, TIPOS, METODOS, MODELOS YAPLICACIONES

    DOCENTE:

    Ing. Vctor Gr!r"o R#$!%&'!t! M'g!r

    INTEGRANTES:

    D!( Cr$!nt% L%')

    Gon(!'% C*+$(, Ro%#n!'"o

    -!!n# -!+n Ern%to

    Mor!'% M!'c! G#%'!

    G!rro O)!r% K!r'!

    Gon(!'% Ac-/! T!t#!n!

    C!0!!rc!, 12 " 0-n#o "' 3145.

    1

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    GEOESTADITICA

    1. RESUMEN

    L! go%t!"%t#c! % -n! r!! " '! %t!"%t#c! !&'#c!"! 6- % %&c#!'#(! n ' !n+'#%#% ) '!o"'!c#7n " '! $!r#!8#'#"!" %&!c#!' n c#nc#!% " '! t#rr!. S- o80to " %t-"#o % '!n+'#%#% ) '! &r"#cc#7n " 9n7no% n %&!c#o )o t#&o, t!'% coo: ') " t!'%,&oro%#"!"%, concntr!c#on% " -n cont!#n!nt, tc. A-n6- ' &r9#0o go; % -%-!'nt!%oc#!"o con go'og!, %#n 8!rgo '! go%t!"%t#c! t#n %-% orgn% n '! #nr!.

    E' %t-"#o " 9n7no% con corr'!c#7n %&!c#!', &or "#o " ?2@ 4>?> ) Kr#g =4>4. E' &r#ro o8%r$7 '! n!t-r!'(! !%#

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    GEOESTADITICA

    OBJETIVOS

    OBJETIVO GENERAL

    Conocr ) %t-"#!r ' M

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    GEOESTADITICA

    EL KRIGEADO

    1. Introd!!"#n

    En t

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    GEOESTADITICA

    E' no8r Kr#g!"o &ro$#n " 'o% tr!8!0o% " D!n#' Kr#g n '!% #n!% " oro %-"!9r#c!n!%

    " R!n", n 'o% !/o% 1. L! tor! 9- 9or!'#(!"! -n! "

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    GEOESTADITICA

    H#g-r! : #%togr!! " 8'o6-% ) " -%tr!%.

    D !c-r"o ! 'o &r%!"o !ntr#ornt, ' Kr#g!"o "9#n ' %t#!"or '#n!':

    zK 4 z x = 4 3 z x= 3 ... Nz x= N

    Con '! con"#c#7n " #n%%g!"! =''!!"! t!8#

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    GEOESTADITICA

    E%t-"#!ro% %to% conc&to% con -n 0&'o: L! 9#g-r! %#g-#nt -%tr! -n 8'o6- 6- "8

    %r %t#!"o ! &!rt#r " -%tr!% S4, S3, . . . , S.

    H#g-r! ?: Tr!n%9rnc#! " #n9'-nc#! ) 9cto " &!nt!''!.

    E' Kr#g!"o ncontr!r+ n %t c!%o, %-&on#n"o #%otro&! %&!c#!':

    # 4 # =# 3, , . . . ,

    L! -%tr! S4% '! " !)or &%o.

    ## 3, # =# ?, , . . . ,

    L!% -%tr!% S3) St#nn !)or &%o 6- '!% -%tr!% S?,S,. . ., S

    ### 51

    S "#c 6- '! -%tr! S*!c &!nt!''! ! '! -%tr! S5.

    #$ ? 5 2

    S "#c 6- *!) -n! tr!n%9rnc#! " #n9'-nc#!@ % "c#r, '! #n9'-nc#! " '! -%tr! S? %

    r&!rt ntr '!% -%tr!% S, S5, S2) S. S &-" !9#r!r 6- ' Kr#g!"o "%!gr-&! '!

    #n9or!c#7n.

    7

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    GEOESTADITICA

    L! nor o !)or #ntn%#"!" " 'o% 9cto% !ntr#or% "&n", $#"ntnt, "'

    $!r#ogr!! =9cto " &t!, %t!, !'c!nc.

    Por 0&'o, %# % t#n -n $!r#ogr!! '#n!' #%7tro&o, =*U* , % t#nn 'o% &%o%

    %#g-#nt% &!r! %t#!r ' 8'o6- B:

    H#g-r! : V!r#ogr!! '#n!' ) &%o% "' Kr#g!"o. S t#nn -%tr!%. S &ro"-c -n

    "%!gr-&!#nto

    $. L%& '!%!"on'& d'( Kr")'%do

    P!r! o8tnr '!% c-!c#on% " Kr#g!"o *!) 6- #n##(!r '! &r%#7n " E3

    Pro 'o% #"8n $r#9#c!r '! con"#c#7n:

    i=1

    N

    i=1

    E'

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    GEOESTADITICA

    M#n##(!r '! 9-nc#7n A 3 )3 %# ) 4. E'

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    GEOESTADITICA

    S "-%tr! 6- !' r!'#(!r N 4 "r#$!c#on% % o8t#n ' %#%t! " c-!c#on% %#g-#nt:

    4=4, 4 3=4, 3 . . . N=4, N X =4VZ$=4, "

    4=3, 4 3=3, 3 . . . N=3, N X =4VZ$=3, "

    4=N, 4 3=N,3 . . . N=N, N X =4VZ$=N, "

    4 3

    . . . N 4

    [- % -n %#%t! '#n!' " N4 c-!c#on% con N4 #nc7gn#t!% =4, 3, . . . , N, X

    S "-%tr! 6- ' %#%t! %#&r t#n %o'-c#7n =% %-&on 6- ' o"'o " =* %

    !-tor#(!"o, %!'$o ' c!%o n ' c-!' #%tn "o% =o +% -%tr!% "#9rnt% con '!% #%!%

    coor"n!"!%: E%t c!%o no "8r! &r%nt!r% n '! &r+ct#c! &ro ! $c% oc-rr, 'o c-!'

    *!c nc%!r#o -n! r$#%#7n &r$#! " '! 8!% " "!to%.

    E'

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    GEOESTADITICA

    E0&'o 4:

    En ' c!%o "' )!c##nto #%7tro&o " '! 9#g-r! 41, %t-"#!"o !ntr#ornt:

    H#g-r!: 5: B'o6- ! r#g!r, n ngro '! ') " '! -%tr!, n !(-' ' nro " '! -%tr!.

    zV 4z=43z=3

    S o8t#n, con '! !)-"! " -n &rogr!! co&-t!c#on!':

    4 1.22

    3 1.3

    QV 1.22 \ 1.3 ?4 5.

    3 E 3.2

    QV 5. \ 3.2 =con >] " con9#!n(!

    E0&'o 3:

    En ' c!%o "' )!c##nto !n#%7tro&o, % t#n ' 8'o6- %#g-#nt:

    11

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    GEOESTADITICA

    H#g-r! 2: En ngro ')% " co8r, n ro0o nro " '! -%tr!.

    zV 4z =x43z =x3 z =x ?z =x?z =x

    A' -%!r -n &rogr!! co&-t!c#on!', % o8t#nn 'o% &on"r!"or% %#g-#nt%:

    4 1.?2

    3 1.31

    1.31

    1.1

    ? 1.1

    3E 1.43

    zV 1.54 zV 1.54\ 1.43

    Vo% 6- ' Kr#g!"o *! con%#"r!"o '! !n#%otro&!, !%#gn!n"o !)or &%o ! 'o% "!to% 3 )

    6- ! ? ) .

    12

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    GEOESTADITICA

    Krigeado Puntual

    En !'g-n!% oc!%#on%, n $( " %t#!r '! ') "#! " -n 8'o6- V, #ntr%! %t#!r '! ') n

    -n &-nto 1=&ro8'! " #ntr&o'!c#7n.

    Corr%&on" !' c!%o &!rt#c-'!r n 6- ' $o'-n V t#n" ! cro. S o8t#n ' %#%t!

    %#g-#nt:

    4=4, 4 3=4, 3 . . . N=4, N X =4,

    1

    4=3, 4 3=3, 3 . . . N=3, N X =3,

    1

    4=N, 4 3=N,3 . . . N=N, N X =N,

    1

    4 3

    Con '! $!r#!n(!:

    N 4

    =i=1

    N

    i(x1 , x0 )+

    13

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    GEOESTADITICA

    H#g-r! : Kr#g!"o "' &-nto 1. S &-" gnr!r -n! gr#''! " $!'or% #ntr&o'!"o% !' *!cr

    $!r#!r 1. E%t! t

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    GEOESTADITICA

    *. Pro+"'d%d'& d'( Kr")'%do

    L!% &ro"!"% +% #&ort!nt% "'

    E%t! &ro"!" r! t#' c-!n"o % r%o'$!n 'o% %#%t!% " Kr#g!"o ! !no

    8. Co&o%#c#7n " Kr#g!"o

    S!n "o% $o'n% "#%0-nto% V4) V3@ %!n (4) (3'o% %t#!"or% " r#g!"o r%&ct#$o%:

    15

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    GEOESTADITICA

    H#g-r! 44. Co&o%#c#7n " Kr#g!"o.

    Entonc% ' Kr#g!"o ( " V4V3%:

    z =V1z 1+V2z2

    V1+V2

    E% "c#r -n! &on"r!c#7n &or $o'n% o &or ton'!0%.

    E%t! r'!c#7n no % $+'#"! &!r! '!% $!r#!n(!%: %# % "%! conocr '! $!r#!n(! % nc%!r#o

    r#g!r ' 8'o6- V4V3 o 8#n -t#'#(!r -n! !&ro#!c#7n.

    ?. V'!"nd%d d' E&t",%!"#n.

    H#g-r! 43: Vc#n"!" " %t#!c#7n. P!r! ' Kr#g!"o no #&ort! '! !gr-&!c#7n " "!to% !' '!"o

    #(6-#r"o "' 8'o6- =' Kr#g!"o "%!gr-&! '! #n9or!c#7n. ^C-+' r!"#o to!r_

    16

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    GEOESTADITICA

    En %tr#cto r#gor, ' Kr#g!"o " -n 8'o6- V "8r! r!'#(!r% con%#"r!n"o to"o% 'o% "!to%

    "#%&on#8'% =Kr#g!"o co&'to. S#n 8!rgo, %t! %#t-!c#7n #&'#c! c+'c-'o% -) '!rgo%@ &or

    otr! &!rt, '!% -%tr!% !'0!"!% tn"r!n -n &%o c!%# n-'o. Por %t! r!(7n '! &r+ct#c!

    rco#n"! r%tr#ng#r% ! -n! $c#n"!" " %t#!c#7n 6- &-" %r -n! %9r! o crc-'o, o

    8#n -n '#&%o#" o '#&% =D ) 3D. Coo rcon"!c#7n &r+ct#c!, ' r!"#o " 8%6-"! n

    -n! c#rt! "#rcc#7n no "8 %r #n9r#or !' !'c!nc n %! "#rcc#7n.

    L! &r+ct#c! *! "o%tr!"o 6-, n ' %&!c#o " "o% "#n%#on%, con -n! $c#n"!" 6-

    contng! -n &ro"#o "' or"n " -%tr!%, 'o% r%-'t!"o% %on 8-no%. En ' %&!c#o "

    tr% "#n%#on% '! %#t-!c#7n % +% co&'0! ) "8 %r !n!'#(!"! n c!"! c!%o &!rt#c-'!r.

    H#g-r! 4: En ' %&!c#o D *!) 6- 'g#r 'o% &!r+tro% " 8%6-"! " !nr! " 6- %

    &ro"-(c! #ntr&o'!c#7n ntr 'o% %on"!0%. En %t! #n! % o8%r$! 6- 6-"!r+n 8'o6-%

    0or %t#!"o% 6- otro% ) *!8r+ 6- c!tgor#(!r'o% n "#"o%, #n"#c!"o% #n9r#"o%.

    . E&tr%t')"% d' -&/'d%.

    E%t! %tr!tg#! %t!8'c 'o% &!r+tro% 6- *!) 6- -t#'#(!r &!r! '! 8%6-"! " co&7%#to%

    ! -t#'#(!r n '! %t#!c#7n "' 8'o6-. D&n"#n"o "' %o9t`!r -t#'#(!"o, %to% &!r+tro%

    %on:

    a R!"#o% " 8%6-"! =R, R), R(. En &r#r! !&ro#!c#7n % &-"n -t#'#(!r 'o%

    !'c!nc% "' $!r#ogr!! n '!% "#rcc#on% =, ), (, n -n! $c#n"!" con 9or! "

    '#&%o#".

    17

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    GEOESTADITICA

    H#g-r!4?: E'#&%o#" " 8%6-"!. En !'g-n!% %#t-!c#on% %t '#&%o#" &-" %t!r

    #nc'#n!"o. E' cntro#" % ' cntro " gr!$"!" "' 8'o6-.

    a Mn#o " -%tr!% &!r! r#g!r . S#r$ &!r! contro'!r ' c!%o n 6- %o'o -n!

    -%tr! c! n '! $c#n"!". S#, &or 0&'o, % &on 3, %o'o % r#g!r+n 'o%

    8'o6-% 6- tng!n "o% o +% "!to% n '! $c#n"!".

    a M+#o r " -%tr!% &!r! r#g!r . S# % &on, &or 0&'o r 3, ntonc% c-!n"o n

    '! $c#n"!" " -n c#rto 8'o6-% #%t!n +% " 3 co&7%#to%, %o'o % -t#'#(!r+n n '!

    %t#!c#7n 'o% 3 co&7%#to% +% crc!no% !' cntro "' 8'o6-. E%t &!r+tro %

    -%! &!r! !)or $'oc#"!" " 'o% c+'c-'o%.

    a M+#o ' " -%tr!% &or oct!nt . S# % &on, &or 0&'o ' 3, n c!"! oct!nt %

    -t#'#(!r+n '!% 3 -%tr!% +% crc!n!% !' cntro "' 8'o6-:

    H#g-r! 4: Oct!nt%. ^[-< &!%! %# #%tn %on"!0% !&ro#!"!nt *or#(ont!'% n

    ' c!%o " '! #(6-#r"!_ A'g-no% &!6-t% co&-t!c#on!'% -t#'#(!n ' *#%9r#o

    %-&r#or #n9r#or c!%o " '! "rc*!.

    18

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    GEOESTADITICA

    E' o80t#$o " %t &!r+tro % "%!gr-&!r =&ro, "!"!% '!% &ro"!"% "'

    Kr#g!"o ^% 0-%t#9#c! %- -%o_

    a M+#o % " co&7%#to% &or %on"!0 . S# % &on, &or 0&'o % 3, n c!"! %on"!0

    % -t#'#(!r+ -n +#o " 3 co&7%#to%, 'o% +% crc!no% !' cntro "' 8'o6-. E'o80t#$o " %t &!r+tro % 9or(!r '! #ntr&o'!c#7n ntr %on"!0%.

    Lo% &!r+tro% ' ) % "8n %r -t#'#(!"o% con &rc!-c#7n. P!r! no #ntro"-c#r !rt9!cto%, %

    rcon"!8' 6- %to% $!'or% %!n !'to%, 'o 6- *!c 6- %- -%o no %! #ntr%!nt =$r

    9#g-r!% 45, 42 ) 4.

    H#g-r! 45: E#%tnc#! " %on"!0 #nc'#n!"o: A' -%!r oct!nt% con ' 4, % -t#'#(!n

    c'-%#$!nt 'o% co&7%#to% 4 ) . L-go, *!) 6- -%!r -n ' !)or.

    19

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    GEOESTADITICA

    H#g-r! 42: A' -%!r -n +#o % 4 " co&7%#to% &or %on"!0, %7'o % -%!n 'o% co&7%#to%

    ) =c!%# ! '! #%! cot! 6- ' 8'o6-, %#n to!r n c-nt! '! $!r#!c#7n n '! $rt#c!'.

    L-go, *!) 6- -%!r -n % !)or.

    L! 9#g-r! 4 #'-%tr! -n &r9#' " -n! #n! %t#!"o con oct!nt% =+#o 3 co&7%#to% ) con

    +#o " co&7%#to% &or %on"!0 =+#o 3 co&7%#to% ) ' #%o &r9#' %t#!"o con -n

    +#o " 3 co&7%#to% n '! $c#n"!" =%#n oct!nt% ) %#n +#o " co&7%#to% &or

    %on"!0

    H#g-r! 4: A '! #(6-#r"! %t#!c#7n con oct!nt% ) +#o &or %on"!0 =% &ro"-c ' 9cto

    &!n6-6-. A '! "rc*!, %#n r%tr#cc#on%. To"o% 'o% %on"!0% =no "#8-0!"o% %on $rt#c!'%.

    Lo% co&7%#to% t#nn -n '!rgo #g-!' ! '! !'t-r! "' 8!nco.

    20

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    GEOESTADITICA

    CONCLUSIONES

    A n-"o % &r%nt!n &roc%o% go9%#co% 6- -%tr!n -n! %tr-ct-r! %&!c#!' ) c-)o%

    &ro"#o% o $!'or% &-nt-!'% % *!n c!'c-'!"o tr!"#c#on!'nt %#n con%#"r!r "#c*!

    %tr-ct-r!. E'

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    GEOESTADITICA

    B"-("o)r%0%.

    M. A'9!ro Intro"-cc#7n !' M-%tro M#nro. In%t#t-to " Ingn#ro% " M#n!% " C*#', 311.

    G. M!t*ron c-r%o " Go%t!"%t#c!. Eco' N!t#on!'% %-&