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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.
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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 $'oc#"!" " 'o% c+'c-'o%.
a M+#o ' " -%tr!% &or oct!nt . S# % &on, &or 0&'o ' 3, n c!"! oct!nt %
-t#'#(!r+n '!% 3 -%tr!% +% crc!n!% !' cntro "' 8'o6-:
H#g-r! 4: Oct!nt%. ^[-< &!%! %# #%tn %on"!0% !&ro#!"!nt *or#(ont!'% n
' c!%o " '! #(6-#r"!_ A'g-no% &!6-t% co&-t!c#on!'% -t#'#(!n ' *#%9r#o
%-&r#or #n9r#or c!%o " '! "rc*!.
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GEOESTADITICA
E' o80t#$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.
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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.
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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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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!'% %-&