Download - PENGUNAAN METODE GEOSTATISTIK
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 1/25
PENGUNAAN METODE GEOSTATISTIK
DALAM PENDIFINISIAN DATA GOLOGI PETROFISIKA
RESERVOIR MINYAK DAN GAS BUMI
USULAN TESIS
OLEH :
ADANG SUHERMAN
22191025
PROGRAM PASCA SERJANA
BIDANG REKAYASA PERTAMBANGAN
INSTITUT TEKNOLOGI BANDUNG
1992
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 2/25
DFATAR ISI
HAL
I.PENDAHULUAN
I.1. LATAR BELAKANGI.1.1. Al!" M#$%&# G#%!$$'!$'(
I.1.2. G#%!$$'!$'( &l) P#"*!'+" D$ G#%l%,'
I.1.-. K#/$/" (" K+($#+'!$'( P#$+%*'!'(
I.2. TUJUAN DAN LINGKUP PENELITIAN
I.2.1. T//" P#"#l'$'"
I.2.2. L'",(/ P#"#l'$'"
II. DASAR TEORI
1. PERUBAH TEREGIONAL
2. STASIONARITAS DAN HIPOTESA INTRINSIK
-. PERHITUNGAN VARIOGRAM
3. SIFAT VARIOGRAM14 P& T'$'( Al
24 P& T'$'( T( H'",,
5. MEMBUAT MODEL TEORITIS
6. TEORI KRIGGING
7. PENURUNAN PERSAMAAN KRIGGING
8. SIFATSIFAT KRIGGING
9. SIMULASI KONDISIONAL
14 P+'"!'
24 P+%!#&/+
III. METODOLOGI
1. SUMBER DATA
2. PEMERAIAN DATA
-. PENYELENGGARAAN GEOSTATISTIK
IV. JADAL PENELITIAN
V. KEPUSTAKAAN
LAMPIRAN
A. KELULUSAN ;PERMEABILITAS4
B. KETERUSAN ;TRANSMISIVITY4
C. KESARANGAN ;POROSITY4
D. HUBUNGAN KESARANGAN DENGAN KELULUSANE. SKEMA :
METODE GEOSTATISTIK DAN INTER STUDI GEOLOGI DALAM
PENDEFINISIAN DATA GEOLOGI.
DIAGRAM ALIR IDEAL TAHAPAN RISET MODELING KOMPUTER
GEOLOGI.
PREDICTION OF FLUID FLOW AND FLUID ENTRAPMENT .
- INTREGRATION OF GEOPHYSICAL, GEOLOGI AND ENGGINERING
DATA FOR RESERVOIR DESKRIPTION.
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 3/25
I. PENDAHULUAN
I.1.LATAR BELAKANG
I.1.1. Alasan Metode Geostatistik
Dl) #)#+'" +/", &' l)< ('$ $'&( )/",('" )#",&("
#",/(/+" &' !#l/+/ +/", $#+!#/$< (" $#$' !#ll/ $#+('$ & =%"$%
#",)$" >", /)l"> !",$ $#+$!. S#l"/$"> "'l' !#l'"
#",)$"< '!"> &'#+('+(" #+&!+(" #",)$" >", &. Dl)
#+('+" $#+!#/$< '! $#+&' (#!l" >", $#+,"$/", & %!'!' &"
&'!$+'/!' $'$'( #",)$".
M#$%&# #)#+'" >", =%=%( /"$/( )#"#+",(" (#&'" &' l)<
>", )#)#+'$/",(" *=$%+ (#!l" $#+!#/$ &' $! &l )#$%&#
,#%!$$'!$'(. M#$%& '"' )#",,/"(" #/ $#++#,'%"l >", &' #+(#"l("
%l# G. M$#+%". P#/ $#++#,'%"l &l >", $#+!#+ &l) +/", >",
)#"/"/(" !/$/ !$+/($/+ $#+!#/$ $/ #/ >", )#)/">' ('$"
!#=+ !!'l< /(" #/ =(.
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 4/25
I.1.2. Geostatistik dalam Pendifinisian Data Geoloi
Dl) !$/&' ,#%l%,'< #",)$" "$+ l'" #+/ *%$% /&+<
!/+?#> ,#%l%,' &" ,#%*'!'(< &$ !/)/+ %+ ;)#l'/$' !#+/( %+< l%, !/)/+<
'"$' %+< &" &$ #",/'" !/)/+4. A"l'! (%)%!'$ $#+& &$
#",)$" $#+!#/$< )#+/(" +%!#! #"&'*'"'!'" &$ ,#%l%,' /"$/( '!
)#"&'!(+'!' ,#%l%,' l%(l $/ +#,'%"l< "$+ l'" !/$/ =#(" &"
reservoir )'">( &" ,! /)'.
P+%!#! #"&'*'"'!'" &$ ,#%l%,'< )#"=(/ ##+ )#$%& "l'!
#!#+$ l$ "$/ #"== &$">< )#l'/$' '"$#++#!$!' ,#%*'!'(< "l'!
,#%(')'< "l'! )'(+%l#%"< "l'! *'!'( '"$' %+< "l'! l%, !/)/+< &"
"l'! ,#%!$$'!$'(. S#)/ !l'", )#",'!' /"$/( )#"&'!(+'!'(" &$
,#%l%,' >#", )#l'/$' l'$%l%,'< #$+%*'!'(< !'*$ $/" '"&/(< /)/+
l#%$')#+>< /+/$" !$+$',+*' &" !$/(+/$ ,#%l%,'.
I.1.!. Ke"#t#$an akan Ka%akte%isasi Pet%ofisika
P#+"#+'" !'*$ $/" &'#+l/(" &l) #)%&#l" ,#%l%,'< "$+ l'"
/"$/( +"#"#"$/(" (#!+","< )!/(" !/#)%&#l" @!"# s$ri%%i&'( $/
'eo)i$or* /"$/( )#"#"$/(" (#l/l/!" )!/(" !/#)%&#l" l'+"
*l/'& #+)/(".
Dl) !$/&' l'" &" #"=#(" *l/'& #)#+'" !'*$ $/"
&'#+l/(" /"$/( +#!#"$!' &$ reservoir !$$'! &" &$ reservoir &'")'!
&l) $', &')#"'</"$/( )#)",/" )%&#l (/"$'$$'* #%l%' !$$'( &"
)%&#l e&'i&eeri&' &'")'!< '",, &'#+%l# )%&#l ,#%l%,'e&'i&eeri&' .
K%+#l!' )%&#l $#+!#/$ &#"," !$$'!$'( $" +%&/(!'< ('+"> &'&$
)%&#l ,#%l%,' '&+%&'")'( "$+ !$/ reservoir &#"," reservoir l'"">
&l) &l) !$/ &#%!'!$#).Dl) #",#l%l" reservoir !')/l!' l'+" *l/'& )#+/(" =+
>", ##($'* /"$/( #+)l" +'l(/ reservoir . U"$/( !/(!#!"? !')/l!'
$#+!#/$ &'#+l/(" (#$#l'$'" #)#+'" reservoir . P#+"#+'" !/$/ reservoir
)#l'/$' :
. K%"*',/+!' !$+/($/+
. S'*$ $/"
=. S'*$ *l/'&
&. J#"'! #"&%+%", reservoir .
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 5/25
M!l >", /)/) &l) #)#+'" reservoir &l (+($#+'+!'
("*',/+!' !$+/($/+ &" !'*$ $/". S'*$ $/" >", +"#"#"$/(" +'l(/
; %er+or!&"e4 reservoir &l (#!+"," ;%+%!'$!4 &" (#l/l/!"
;#+)#'l'$!4 $/".
I.2.TU&UAN DAN LINGKUP PENELITIAN
I.2.1. T#'#an Penelitian
T//" #"#l'$'" >", &'/!/l(" &' !'"' &l #",,/"" )#$%&
,#%!$$'!$'( &l) #"&#*'"'!'" &$ ,#%l%,' (/!/!"> ,#%l%,' #$+%*'!'(
reservoir )'">( &" ,!< >'$/ (#!+"," &" (#l/l/!" $/". P#"#l'$'"
'"' /, )#+/(" #">#l#!'" $#!'! /"$/( P+%,+) S2 P#+$+""" ITB<
'&", (/!/! #(!l%+!'.
I.2.2. Link#( Penelitian
. O>#( S$/&'.
P#",,/"" &$ l%, !/)/+ /"$/( #"(!'+" (#!+"," &" (#l/l/!"+#!#+?%'+ :
14 P#)('" l%, /"$/( )#"(!'+ "'l' (#!+"," &" (#l/l/!" &l)
!/)/+.
24 P#+('+" (#!+"," &" (#l/l/!" >", $'&( &'(#$/' & l%(!'
$#+$#"$/.
-4 M#",&(" (%+#l!' (#!+"," &" (#l/l/!" !!'l !#=+
(%"$'"/#.
. C+ P#">#l#!'".
U"$/( #">#l#!'" l &' $! &'$#)/ &#"," :
14 M#",,/"(" +%,+) ,#%!$$'!$'( >", !/& &.
24 M#",#)",(" +%,+) ,#%!$$'!$'( /"$/( !')/l!' (%"&'!'%"l<
)#"&' !#/ )%&#l s$)o")!$i".
=. D$.
U"$/( $#!$ &" "l'! )%&#l< &$ &'#+,/"(" &$ &" !#/ !(+'!'
S1 #+$)","< >'$/ &l &$ L"," M&/+ U$+< >", &/l/
)#+/(" 'l> (#+' K%&#=% C%. L$&.
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 6/25
II. DA)AR TE*RI
1. PEUBAH TEREGI*NAL
B#"$/( $#+#,'%"l &'#+(#"l(" %# G.M$#+%" /"$/( )#"#+",("
(#&'" >", $#+!#+ &l) +/", $/ ($/ &+' )#"/"/(" !/$/
!$+/($/+ $#+$#"$/. P#/ >", )#"='+'(" (#&'" $#+!#/$ &'!#/$ #/
$#++#,'%"l ;R#.V4. P& (#"$""> #/ &l) )#"#+",(" (#&"
&l) $" &" $)%!*'+ $/ !'(l/! '+< &'(#$/' !#,' #/
$#++#,%"l.
S#=+ )$#)$'! !/$/ R#.V +"#+/(" */",! ;4< &l "'l' &'
!/$/ $'$'( ;&l) 1< 2 $/ - &')#"!4 &+' >", )#+/(" (#&'" >",
&'#l+'.
T#%+' #/ $#+#,'%"l &$ )#l'/$' #/ >", l/! !+"'
(!+ /"$/( )#)"$/ :
14 M#"$/(" &!+ $#%+' /"$/( )#"/"/((" !'*$ !$+/($/+ & (#'&'" l)
&l) #"$/( +"$#)$'(.
24 M#l#",(' l$ +($'! /"$/( +"#)#=(" )!l #"(!'+".
U"$/( )/&"> &l) )#",,/"(" #/ $#+#,'%"l & (#&/
(%"!# &' $! #+"( &" $#%+' (#)/",('"" & */"!' =( ;RF4.
S#/ R#.V >", &'"%$!'(" ;4 &'+$'(" !#,' +#l'!!' */",!' =(
>", &'"%$!'(" !#,' ;4 &#"," )#">/!/" (#)l' /(/) &'!$+'/!'
RF &" &$.
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 7/25
K#!/l'$" $')/l &" (#">$" ">( #/ $#++#,'%"l
;!##+$' #+)/(" l'!" &" (#$#+/!" & !$/ ('*#+4 >", /"'( &"
$'&( )/",('" /"$/( &'!')/l(" &#"," "> !$/ +#l'!!' RF<
!#,')" )#",'$/", #(!#($!'. V"'"!' $/ */",!' &#"!'$!
(#)/",('""< & RV >", &'&!+(" !'l "/)#+'( &#"," #+'$/","
$/",,l. J&' !$$'!$'( RF )#)#+l/(" '%$#! >", =/(/ l/#! /"$/(
!#)/ )!l +($'!.
2. )TA)I*NARITA) DAN HIP*TE)A INTRIN)IK
S/$/ RF &'($(" !$'%"#+ '( #(!#($!' ;4 (%"$" &' !#)+",
$'$'( :
E + ,-/ 0 m-/ m
J/, (%?+'" "$+ &/ $'$'( &" $'&( $#+,"$/", & $#+'!">
&" < $' "> & ?#=$%+ ; 4 :
E + ,-/ m 0 + ,-3/ m 0 K - 3 /
& (#&" $#+$#"$/< ?+'"!' $'&( $#+,"$/", :
E + -,-/ m /2 0 4a% + ,-/ 0 K -5/
P& #"/+/"" #+!)" (+',,'", )#)#+l/(" !$!'%"+'$! $'&(
"> /"$/( ;4 !#"&'+'< $' & (#"'(("">. K'$ "> )#)#+l/("
'%$#! < /"$/( !#)+", ?#($%+ (#"'((" ;4 ;4 &l
#(!#(!$!' "%l &" !#/ ?+'"!' >", $'&( $#+,"$/", & $'$'( . I"'
'! &'$/"/((" !#,' #+(/$
E + ,-6$/ ,-/ 0 5
4a% + ,-6$/ ,-/ 0 2 7 -$/
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 8/25
'%$#! $#+!#/$ &'!#/$ '"$+'"!'( '%$#'!. F/",!' =( >", !#!/' &#","
'%$#! $#+!#/$ &'!#/$ */",!' =( '"$+'"!'( ;IRF4. ;4 &'!#/$ !#)'
?+'%,+).
F/",!' =( '"$+'"!'( ;IRF4 &'&#*'"'!'(" !#,' :
7-$/ 1
2 4a% + ,-6$/ ,-/ 0
$/
7-"/ 1
2 E + -,-6$/ ,-//2 0
>", #++$' 2 ;4 &l +$+$ #+#&" (/&+$ "$+ &/ $'$'(
>", $#+'!.
!. PERHITUNGAN 8ARI*GRAM
D+' '%$#! &' $! ;4 &#"," )/& &$ &''$/", &#","
(/&+$ #+#&" >", &''$/", & +#l'!!' $/",,l. J'( (#&'" >",
&')$' &l) !$/ &')#"!'< )( )#"&#($' !(l+. J'( $'$'( #",)$"
$#+l#$( #+$/+" )( ?+'%,+) &$ &''$/", & "'l' &'(l' '/)l
/"'$ l,">.
7-$/ 1
2 N (h) ∑i=1
N (h)
E + -,- x i 6 $/ ,-
xi //2 0
&')" ; x i 4 "'l' #(!#+')#" & $'$'(
xi 9 &$ >", &',/"(" &
x i &" x i &" N;4 /)l !"," $'$'( >", $#+'! !#+( .
Sl !$/ !$/&' >", )" )#+/(" ?#($%+< &l ?+'%,+)
>", )#+/(" */",!' &" &/ (%)"#" $/ &l) (%%+&'"$ %l+< >'$/
!#/ */",!/ &+' )%&/l/! |h| &l '+( "$+ $'$'( &" !/&/$ %l+ .Ɵ
J'( $'$'( #",)$" $'&( #+$/+" &l) '&", &$+ )(
&'(#l%)%((" )#"&' ##+ (#l! &+' +( &" !/&/$ .Ɵ
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 9/25
P#+"&'"," &+' ?+'%,++" &#"," + >", #+#& ("
)#"/"/((" !&iso$ro%i &+' (#&'". Dl) l '!%$+%'(< ;4 ">
)#+/(" */",!' &+'
|h|.
:. )I;AT 8ARI*GRAM
1/ Pada Titik A<al
P& (+',,'",.< !'*$ ?+'%,+) & $'$'( l !",$ #+'$'",
!# )#"='+'(" (#!'")/"," R#.V. E)$ #"$/( (l!'( !#,'
#+'(/$ :
4 B#"$/( P+%l
S'*$ ?+'#l >", !",$ #+$/+" ;&$ &'$/+/"(" &#"," =+
(/&+$ (%"?#+,#"4 !##+$' $'",,' (%l%) '+ ;)e! 4 &
#",)$" !/)/+ &l) !#,' */",!' &" ($/.
4 B#"$/( L'"'#+
S'*$ ?+'#l >", (/+", #+$/+" &'!"&'", 4 ;!'")/", $'
$'&( &$ &'$/+/"(" &#"," =+ (/&+$ (%"?#+,#"4< !##+$'
l"> (#$#l" *%+)!' ,#%l%,'.
=4 K#$'&(!'")/"," ; Dis"o&$i&i$*4
A+$'"> ?+'#l >", !",$ $'&( #+$/+". D/ $'$'( #+#&
!#(l'/" !",$ #+&#($"< (" +"#"/"/((" !#/ ?+'"
#+#& )'"')l !) &#"," &''e$ e++e"$, Co. B#"$/( '"' &
& !$/&' %",( #"&" #+"! >", )" !",$ #+?+'!'
$#+,"$/", $'$'( &' &l) &" &' l/+ %",( #)!. B#"$/( '"'
&'(' /"$/( )#"#+",(" (#$'&(!'")/"," l ?+'%,+)
>", )#">#(" +#,'%"l'!!' )'(+% & !#(l >", / l#'
(#='l &" $'$'( #",)$" &$. R#,'%"l'!!' )'(+% !##+$' )'&')$' & &$ /". N''e$ e++e"$ '/, )#">#("
(#!l" #",/(/+" '( (/+", '"*%+)!'< '"' $'&( +"Ll",('"
/"$/( )#)"&'",(" !')","&$ &#"," #"># >",
!).
&4 V+'%,+) D$+ ; %re &''e$ e++e"$ $/ /)i$e &oise4
A&l l >", !/",,/ =(< ;4 &" ;4 $'&( & (%+#l!'
/"$/( !#$' !#($%+ >", $'&( "%l< !##+$' & l"> $! $%$l
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 10/25
!$+/($/+ 'l", >", &'$#)/(" & #+,"$'" /" $/"" &
!$!'%" $#+$#"$/.
G)+ 1.
4 M%&#l 4 )%&#l !#+'=l
=4 )%&#l #(!%"#!'l &4 )%&#l ,/!!'"
2/ Pada Titik Tak Hina
S#l'" !'*$ & $'$'( l< !'*$ #"$'", & ?+'%,+) &l
+'l(/ & +( >", #!+. S#l) (#"'(" &l) !$!'%"#+<
?+'%,+) &$ "'( $( $#+$!< $' &$ /, !$'l !#('$+ +,
!'ll >", !)' &'"," ?+'" &$ l",". J+( &')" !'ll &'='&'!#/$ &#+ #",+/ ;r!&' 4. D#+ #",+/ )#"/"/(("
l/!"> &+ #",+/ &" $'$'( #",)$"< & +( &' $! &#+
#",+/ (%+#l!'"> &l "%l.
B##+ (#&'" >", $#+l'$ &+' '"$#++#$!' ?+'%,+)<
&l (##+(l" ; %erioi"i$*4< S$+/($/+ #+!+", ;#+l'!" ?+'"
& !(l #+#&4< @)o0e e++e"$( ;$')/l"> (%+#l!' "#,$'* (+#"
&"> %" (> &'!#('$+ %"# )'!('"4. K#">(" *l/($/!' ,+*'(
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 11/25
)'+ )#+/(" *l/($/!' !)l'",. N'l' !/$/ #(!#+')#"$l
?+'%,+) $#+(&", &'#+('+(" &+' !#&'('$ !"," &$.
K+#""> #+('+" $ !##l/)"> &'#+l/(" /"$/( )#)/$
#(!#+')#"$l ?+'%,+) )#"&' )%&#l $#%+'$'! !#&#+". I"' l"
!$/!$/"> /"$/( )#")'" (%"!'!$#"!' )$#)$'( /"$/( #+'$/","
(+',,'",.
=. MEMBAUT M*DEL TE*RITI)
V+'" &" (%"'"!' l'"'#+ ;4 (" &'#+,/"(" (#)/&'" &
#"/+/"" #+!)" ("',,'",. M%&#l $#%+'$'! /"$/( ;4 )#">$("
!#$' !"," ".
T#l 1M%&#l V+'%,+)
T'# R/)/! S0o%e
l
R!&'
eSi00
N''e$
E++e"$ ;4 C ; 1 δ 4 ∞ ∅ C
M%"%)'l ;4 |h|
{
∅< λ<1 λ=1
1< λ<2
∞ ∞ ∞
S#+'=l ;4 {w[ 32 |h|α −
1
2 (|h|α )
3
]w h ≤ a
h ≤ a-2
E%"#"$'l ;4
(−¿|h|/a)1−exp¿
¿ -
G/!!'"
;4
(−¿|h|2/a2)1−exp¿
¿
∅ V-
$'$'( x i &" " (%#*'!'#" !#)+",
λi &')" ∑ λ i ∅ ;/"$/(
)#)/$ (%)'"!' (#"'(" >", l'"'#+< >", )" "> #!+" &l)
+'"" '%$#! '"$+'"!'(4< #+'$/"," & :
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 12/25
4a% ∑i=1
N
λ i z ( xi )=−∑i=1
N
∑i=1
N
λi λ j γ - xi
x j /
!#ll/ )#",!'l(" +, %!'$'
K#">(" >", &',/"(" &l) )%&#l ?+'%,+) &l $#+l'$
& $#l 1 &" ,+*'( >", $#+l'$ & ,)+ 1.
T')/l"> &''e$ e++e"$ C !'l #")" (%"!$"$ C $#+& )%&#l 7*9
(#=/l' & $'$'( l :
7-$/ >-1?/ 6 7* -$/
&')" δ &$ &'&#*'"'!'(" !#,' @/(/+" D'+= & $'$'( l.
?. TE*RI KRIGGING
K'$ ",, #(!#($!' &" R.F. ;4 ;#/ >", &'#l+'4
&l */",!' ) ;4 E ;4 >", #+?+'!' +#l$'* !#&'('$ $#+& !(l
(#+. F/",!' '"' &'!#/$ ri+$ ;M$#+%"4< >", =/(/ #+$/+" /"$/(
&'">$(" &#"," :
m -/ ∑i=1
N
al
f
l
-/
&')" * l &l */",!' &!+ >", &'$#"$/(" &"al &l (%#*'!'#"
>", $'&( &'(#$/'. S/#+(+' & * l )#">$(" $'",($ (# 1. Dl)
+($#( /)/))> */",!' $#+!#/$ !#ll/ )%"%)'l. J'( &" &lƹ ƞ
(%%+&'"$ $'$'( < ('$ &$ )#">$(" :
m - 9 / aƹ ƞ 1 6 a2 6 aƹ !ƞ
$/
m - 9 / aƹ ƞ 1 6 a2 6 aƹ ! 6 aƞ :ƹ2 6 a= 6 aƞ ?ƹƞ
2
>", #+$) &l l'"'#+ &+'*$ &" (#&/ &l (/&+$'( &+'*$. M%&#l
$#+$#"$/ & >", $" &+'*$ &')" */",!' &!+"> !) &#"," !$/.
@. PENURUNAN PER)AMAAN KRIGGING
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 13/25
N'l' #/ ;4 >", &'#l+' &l & $'$'( #",)$" 1< 2<
QQ < " &" )!l >", (" &'#+('+(" &l % >", )#+/("
*/",!' l'"'#+ &" #/< )#"/+/$ #"$/( !#,' #+'(/$ :
4 Nl' & $'$'( %
,o , -o/
4 N'l' +$+$ ;4 & l/", !% &" +# ! $#+/!$ & %
,o 1
s ∫so
z ( x ) dx
=4 N'l' +$+$ ;4 & &#+ ;&%)'"4 S
,o 1
s ∫s
z ( x ) ds
U"$/( #">#&#+""< #+'$/"," &'$/+/"(" &l) #"$/( (#$',. B#"$/(
#+$) &l l (#$', &')" &#+"> &'#+(#='l )#"&' !#/ $'$'(
!#&",(" #"$/( (#&/ &l '&#"$'( &#"," #"$/( (#$',.
U"$/( )#)#+('+(" %< &'(#"l +$+$ %%$ &+' " &$ :
,o ∑i=1
N
λ i , -i/
M!l"> &l )#"=+' !#')/"" %%$ λi >", '! )#)#+'("
#+('+" $#+'(
K#)l' & '"$#++#$!' (#)/",('"" R#.V ;4. B % &$
&'(#"l !#,' +#l'!' !#/ R.V.
,o ∑i=1
N
λ i , -i/
&" %$ λi )#!$' !#' l$ #+('+" ,o >", :
14 U"'! ;$'&( +"#)#+'(" &' $! $/ &' #+('+" !'!$')$'4.
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 14/25
24 O$')l ;&#"," (#!l" +$+$ (/&+$ $#+(#='l4. S#=+ )$#)$'(
&'">$(" :
E +,o , 0 5
4a% + ,o ,o0 minimal
(%"&'!' /"'! )#)/$> &+'*$ )#"&' :
∑i=1
k
∑i=1
n
λ i¿ al f s
l / ∑
i=1
k
al f sl 5
&')" :
f il
f l
- x i / dan f s
l
1
s ∫s
f l
-/ d
"'l' l >", $'&( &'(#$/' &$ &'!'l(" &#"," :
∑
n
λ i f il
f sl
5 l 19 k
&#"," )#",)'l f l=1, &'&$ $! #+$) :
∑i=1
n
λ i 1 5
&+' #+!)" &' $!< (#!l" ;% %4 &$ &'$/l'! !#,'
(%)'"!' l'"'#+ &" (#"'((" R.F. :
Co Co ∑i=1
n
λ i C-i/ Co ∑i=1
n
λ i -C-i/ Co/
J&' ?+'" (#!l"< &$ &'">$(" !#$#l !#&'('$ #+'$/","< &l)
#"$/( ?+'%,+) :
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 15/25
V+ Co Co ∑i=1
n
∑i=1
n
λi λ j γ ij 6 2 ∑
i=1
n
λ i γ is
γ ss
D')" :
γ ij γ - x i
x j /
&l "'l' ?+'%,+) "$+ &/ $'$'( #",)$" x i &"
x j .
γ is 1
s ∫s
γ - x i / d
&l "'l' +$+$ ?+'%,+) "$+ $'$'( xi &" !#/ $'$'( >",
)#"#+",(" &%)'" S.
γ ss 1
s ∫s
∫s
γ -3/ d d3
&l "'l' +$+$ ?+'%,+) "$+ &/ $'$'( $'&( #+('$" &l)
&%)'" S.
K#)/&'" )#)'"')l(" #"$/( (/&+$ λi & $! (< )#",'(/$'
!'!$#) l'"'#+ >", &'!#/$ !'!$#) (+',,'", >", &'&$ :
∑ j=1
n
λ i γ ij 6 ∑ μl f il
i 19.. n
∑ j=1
n
λ f il
f sl
i 19.. k
U"$/( )#"&$(" &%)'" >", &'(#='l(" )#"&' $'$'(< ('$ ">
)#",,"$' :
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 16/25
f sl
&#"," f cl
f l
-o/
f is
&#","
γ io
7 -i o/
γ s s &#","γ oo -o o/ 5
S%l/!' !'!$#) '"' " ( #+!)" &" " ( >", $'&( &'(#$/'<
)#",!'l(" " %%$ λi &" ( #",l' L,+",#
μl . B%%$ λi
&'#+,/"(" /"$/( #+('+" (+',,'",. H!'l l'" &" #+('+" &l
?+'" ;?+'" (+',,'",4 >", &'&$ &#"," )#",,"$' :
"
(
.
13
@3
I
" (
2 I.
$$
8. SIFATSIFAT KRIGGING
S'E$#) (+',,'", (#">$""> +"#)#+'$/",("
14 J+( "$+ $'$'( #+('+" ;$/ &%)'"4 $#+&
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 17/25
$'$'( &$ &#"" #"$/( ' ;$/ 'S4.
24 J+( +$+ $'$'( &$"> !#"&'+' (#& #"$/( ''.
-4 S$+/($/+ #/ "#ll/ ?+'%+) .
B%%$ (+',,'", &'#!/'(" &#",+' ?+''l'$
(#&'". P& #/ #+$/+" (+','", +"#",!'l("
%%$ l#' $'",,' (#& &$ $#+&#($ $#$"> #l)
'"+"/",< &/ $'$'( >", #+&#($" +"#)/">' "'l' >"
!).
(#$'( $#+'#$( & $'$'( &$ )( !%l/!'
0
(+ )#=#+(" . 1 &" @.. W /"$/( ' )(
&'&$ ;.4 &" W. K#!/l'$" $#+&' 'l &
@"/,#$ #**#=$ K%)%"#" !#)#+/$ & (#&'" >"
&')%&#l(" '= @"/,,#$ #**#=$. $'&( '! &'+)l("
!##+$' $'&( &"> (%+#l!' !!'l. P& $'$'(
#",'"$".< (+',,'", )",#)l'(" "'l' #",/(/+"
!#='' '"$#+%l$%+ !$'.< $' &' l/+ $'$'( $#+!#/$.
&" & +'& $#+$#"$/ !'!$#) (+','" +"#)#+(" &')"
(%)%"#" !#+"#+/$ >", $( '! &'++"l(" $#+!+'",.
S'!$#+" (+',,'", &" ?+'" (+',,'+*, . "> #+)'"
& !$+/($/+ &" (%"*',/+!' ,#%'"#$+' &" $'$'( &$
&" $'$'( ;$/ &%)'"4 >", &'+''(". )' !'*$ >",
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 18/25
#+l/ &'#+$'(" &l) %$')'!!' +'"" #"/(/+".
9. SIMULASI KONDISIONAL
14 P"'"!'
T//" !'+"/l!' (%"&'!'%"l &l /"$/(
)#",!'l(" "#l'!!' >" )/",('" &" R.F >",
15
I
+".. D#"," )#)#"$/( +#l'!!' l'" (" &'&$
?+''l'$! !!'l !##+$' (#&'+' >,
!#!/",,/"> ;)#)/">' ?+'%,+) &" =%?+'" /)/)
>", !)4.. S')/l!' 'L', (" )#)#+$"(" "'l
#"=/(/+" & $'$'( #")$". /"$/( )#")"
#l#$(" >", '( &#"," >", &'(#$/' &l)
(#&'"..
J=l !')/J!' (%"&'!'%"l &$ &'&#*'"'!'("
!#,' !#/ #+)/(" >",
14 M#)L$">' ?+''l'$! >", !) &#","
?+''l'$! (#&'".
24 M#l#$' $'$'( #")$"
S')/l!' )' $'&( +#l'$! $' "> !$/ ?#+!' &"
(#&'" '$/. B#+,' !')/l!' (%"&'!'%"l
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 19/25
)#",,$"!+(" ?"'!' >", )/",('" &" #$ >",
!#!/"%/">. R$+$ &" ?+'!' $#+!#/$ ("
)#"/"/(" "'l' >", &'#+('+(" %l# ("''+',. &"
?"'""> !#!/' &#"," ?+'" #!$')!'.
24 P+%!#&/+
P+%!#&/+ !'+"/l!' (%"&'!'%"l &'+"/l' &"
&#(%)%!'!' $+'?'l !#,' #"'(/$
N'l' !##"+"> #+('+" ("','", (#!l" ("',,'",
;4 C4 ;;4 ;44
S>","> &' l/+ $'$'( #")$" "'l' !##"+">
;4 $'&( &',/"(" &" (#!l" (+',,'", +"!'
OILI) &'(#$/'.. D#"+< &#=/'('+X ('$ +"#"!')/l!'("
(#!l" $#+!#/$ &#"" +"#'"'l'"> &" +#l'!!'
!;4 >", l'" &" R.F. 5;4 >", +"#+"/">' ?"',+)
>", !=" ;$/ =%?"'" /<"/+" >", !)4 !#,' ;4
M#$%& $/+"'", +& &',/"(" L'"$L'( )#"&$("
+#l '!!' $#+!#/$.
16
S
K+','", &$ &l(/(" & !;4 &#"," )#)(
&$ l%(!' !#"+">.< S#,')" ?+'%,+)"> S)<
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 20/25
)( #+('+" (+',,'", !;4 & $'$'( ("
&''$/", &#"," %%$ (+','", >", ) !##+$' /"$/(
;4. P& ($/ '$/ &#(%+"%!'!' !#)/ >",
&'(#$/':
!;4 ! ;4 ;!;4 ;44
!#&", &'(#$/'
;4 ;4 ;L4 ! ;44
S
)' (" )#l#",(' ;4 &l !#/ !')/l!
(%"&'!'%"l >", #+!'*$ !##+$' &'&#*'"'!'(" &'
$!.
Al!" #",,/"" $#("'( ')/l!' (%"&'!'%"l
;$/ &'!#/$ '/, )%&#l !$%=!$'= &l
I"*%+)!' $'&( l#",(
D'$+'/!' !!'l (%)'#(
V+''l'$! !'*$ $/" >", !#++!'$*
K#=#$" &" (#">)""
Y", &'=+' &l) )%&#l !$%=!$'=
P#",+',(/$" &l) )#&' #+%+'
Al'+" *l/'& &" )#("'!) $/"
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 21/25
P#)+%!#!" ,)+ &" #",'"&#+" '/
(+($#+<! +#!#+?%+
III. METODOLOGI
1.. SUMBER DATA
S/)#+ &$ /"$/( #)#+'" +#!#+?%'+ &l:
S##l/) +%&/(!'
G#%l%,'
17
S#'!)'(
l%, !/)/+
A"l'! !#+/( %+ %, l/)/+
DST
I"$' $/"
. S#$#l ++%&/(!' >'$/ /' %+%&/!'
2. PEMERIAN DATA
P#)#+'" &$ +/! )#">Z''(" &$# #%1%,' &"
!'*$ $/" +#!#+?%'+. D$ #%l%,' &'#+1/(" /"$/(
)#"&$(" %"*'/+!' !$+/($/+. M#$%& #%!$$'!$'(
$'&( &'"/+(" /"$/( (#&" #%l%,' >", [/)'$ l%(
$" >", !#)'$< +#!#+?%'+ &#"," "> $"
A=/" &''+. #**"#+'" !'*$ $/" +#!#+?%'+ !#'
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 22/25
#+'(Ll$
. P+)#$#+
P+)#$#+ >", (" &'%l &l 0 &" K. K+#" K
)#+/(" +)#$#+ &'")'! )( ( &'$#"$/("
P. <
&#"," =+ $'&( l",!/", >'$/ &" l%$ K ?! 0
>", '!"> l/+/!
. S(l #)#+'"
Dl) #+"#+'" +#!#+?%'+ &'#&(+X #$#+%,#+X'$!
&#"" #+,' $'",($ !(l >'$/
!(l "
!(l '"$' $/"
!(l l%, !/)/+
!($ +#!#+?%'+
=. U"'$ #)#"'" +#!#+?%'+ $#+' )#"&'
/"'$ l'++X /$)
!#('$+ !/+"/+
("&'!' $!
-. PENVELENGGARAAN GEOSTATISTIK
. M#",&*+" "l'! !$$'!$'( #+)/l"
M#)#+'(! !$!%"+$,
18
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 23/25
I
A"l'! S$$'!$'( Al
S$!'%"+' $!
D$ %/l!'
P#)#+!'" &$
A"l'! (#!'")/","
?+'%,+)
M#)/$ M%&#l
L
K+',,'",
S')/l!' K%"&'!'%"l
G)+ 2
S(#) P#">#l#!'" M!l
19
N
D$
G#Gl'
S#'!)'=
D$ R#!#+?%'+
L% !/)/+
S#+/( +
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 24/25
I"$' $/"
K%"*',/+!' S$+/($/+
R#!#+?%'+
S'*$ *'!'( R#!#+?%'+
0 &" K
!(l &" /"'$
!#!/'
S
M#",'&#"$'*'(!' &$ %/l!'
M#l(/(" #)#+!'" &$
. M#",&(" "l'! (#!'")/"," +( ?+'%+)
S'*$ & $'$'( l
S'*$ & $'$'( $( '"=$
S'*$ "'!%$+%' "'!$+%' ,#%)#$+'.<
"'!%$+%' %"l $/ !$+/($/+ #+!+"
=. M#)/$ )%&#l
M%&#l P%#+
M%&#l S#+'=l
M%&#l E(!%"#+'$'l
M%&#l G/!!'"
&. M#",'$/", #+('+" "'l' & (#!l" l%(l
7/18/2019 PENGUNAAN METODE GEOSTATISTIK
http://slidepdf.com/reader/full/pengunaan-metode-geostatistik 25/25
&#"," =+ (+',,'"
0. M#",&(" !'+"/l!' (='"&'!'%"' ;/"$/(
)#"&$(+' "#+('+" !!'l >"= (%"$'">/4.
20
L \\\\\\\\\
I