UNI UNIVERS ERSIDAD NA NACIONAL JO JORGE BA BASAD SADRE GR GROHMANN
GEOESTADISTICA
GEOESTADISTICA EXAMEN 1
1. En un proyecto proyecto de exploración exploración,, e !an per"orado per"orado #$% onda&e onda&e dia'antino El onda&e 11%, tiene el i(uiente re(itro de dato. )*O+NDIDA D 't -E Cu T. / 12 16 21 26 34 42 52 58 63 67 76 81 85 92 100
2.1 1.5 0.9 1.5 1.3 1.6 1.4 1.2 0.9 0.8 2.2 1.9 1.3 2.5 1.6
a Ca!"#!a$% &$a'"a$ ( )*+($,$(+a$ (! -a$)&$a/a (,($)/(*+a!. M(!a$ (! -a$)&$a/a (,($)/(*+a! " Ha!!a$ ! &$'" ( ),($)* ,a$ (! 2 5+ ,#*+ (! -a$)&$a/a "a!"#!a$ (! "('")(*+( ( "$$(!a")*.
HUALL:ACHO;UE MAMANI JOSE RAUL
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UNI UNIVERS ERSIDAD NA NACIONAL JO JORGE BA BASAD SADRE GR GROHMANN
GEOESTADISTICA
Solución0 a Calcular, Calcular, (ra2car e interpretar el 3ario(ra'a experi'ental e xperi'ental 1. Ca!"#! ( )+a*")a= S( "a!"#!a ( !a )&#)(*+( /a*($a
*an (o
DISTAN CIA
1<<2 2<<3 3<<4 4<<5 5<<6 6<<7 7<<8 8<<9 9<<10 10<< 11 11<< 12 12<< 13 13<< 14 14<< 15
4 5 5 8 8 10 6 5 4 9 5 4 7 8
La #/a+$)a ( !a )+a*")a (= 88 H++a! H/)* H/a
88 4 46
L )*+($-a! >#( ( a!!a$* a "*+)*#a")* ((* (+a$ (*+$( (! H/)* (! H/a ?(+( a+ ( !a /)+a (! H++a! /a 2 ,a$a )*"!#)$ + ! a+.
2. Ca!"#! ( )*+($-a!= si h =8 entonces
intervalo intervalo menor= h−
h 8 =8 − =4 2 2
HUALL:ACHO;UE MAMANI JOSE RAUL
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UNI UNIVERS ERSIDAD NA NACIONAL JO JORGE BA BASAD SADRE GR GROHMANN
GEOESTADISTICA
Solución0 a Calcular, Calcular, (ra2car e interpretar el 3ario(ra'a experi'ental e xperi'ental 1. Ca!"#! ( )+a*")a= S( "a!"#!a ( !a )&#)(*+( /a*($a
*an (o
DISTAN CIA
1<<2 2<<3 3<<4 4<<5 5<<6 6<<7 7<<8 8<<9 9<<10 10<< 11 11<< 12 12<< 13 13<< 14 14<< 15
4 5 5 8 8 10 6 5 4 9 5 4 7 8
La #/a+$)a ( !a )+a*")a (= 88 H++a! H/)* H/a
88 4 46
L )*+($-a! >#( ( a!!a$* a "*+)*#a")* ((* (+a$ (*+$( (! H/)* (! H/a ?(+( a+ ( !a /)+a (! H++a! /a 2 ,a$a )*"!#)$ + ! a+.
2. Ca!"#! ( )*+($-a!= si h =8 entonces
intervalo intervalo menor= h−
h 8 =8 − =4 2 2
HUALL:ACHO;UE MAMANI JOSE RAUL
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UNI UNIVERS ERSIDAD NA NACIONAL JO JORGE BA BASAD SADRE GR GROHMANN
intervalo intervalo mayor= h +
GEOESTADISTICA
h 8 =8 + =12 2 2
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4
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UNI UNIVERS ERSIDAD NA NACIONAL JO JORGE BA BASAD SADRE GR GROHMANN
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UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
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0%0 1%4 1%2 0%3 0%0 1%2 1%4 9 4 1 6 4 1 1 4 0%8 0%6 0%0 0%0 0%4 0%6 0%8 0 1 4 9 1 9 4 1 0%0 0%3 0%0 0%0 0 1 6 1 4 1 0 0%2 0%8 0%0 0%0 0 5 1 1 0 1 0%1 0%1 0%2 0%3 0 6 6 5 6 0%6 0%8 0 4 1 1 0%0 0%0 0 1 4 0%0 0 1
@
0
1%
1% 11 1# 1; 1< 1= 1%6 1%2 9 1 1%9 1 6 0%0 5%2 1 9 0%0 4%8 4 4 0%4 2%8 9 9 1%2 1%6 1 9 0%0 4%4 9 1 0%0 4%8 4 4 0%0 5%2 1 9 5%7 0 6
11
0
1# 1;
0%0 0%6 0%1 4 4 6 0%0 0%2 0%4 1 5 9 0%1 2%5 1 6 6 0%8 0%0 2%2 1 9 5 0%1 0%0 6 4 1 0%3 0%3 0 6 6 0%6 0%0 1%9 4 4 6 0%8 0%0 2%2 1 9 5 0%1 2%5 1 6 6 1%2 0%2 2%8 1 5 9 1%6 3%6 0%4 9 1 9 0%3 0%3 0 6 6 1%4 0 4
1< 1=
0
N6! B 66x! 6xF# (57#,$8 ! h 8
Rango 4 12
0%2 5 0%0 4 0%4 9 0%3 6 0%0 1 0%0 9 0%2 5 0%3 6 0%4 9 0%6 4 2%5 6 0%0 9 0%0 9 0%8 1 0
5 2 :a$( 44%33 0%426 52%83
N(h) ∑N(h) h 20 147 7,35
HUALL:ACHO;UE MAMANI JOSE RAUL
∑(Z(x+h)Z(x))² 18,18
γ*(h) 0,4545
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
16 24
8 12
24 36
34 40
524 934
15,41 23,35
41,09 40,79
0,60426 0,50988
32 40
16 20
48 60
51 55
1566 2122
30,71 38,58
42,74 53,81
0,41902 0,48918
48 56
24 28
72 84
58 56
2547 2812
43,91 50,21
56,97 47,72
0,49112 0,42607
64
32
96
52
2752
52,92
44,33
0,42625
:A*IOG*AMA EX)E*IMENTA0.7 0.6 0.5 F?
0.4 0.3 0.2 0.1 0 0
10
20
30
40
50
60
70
-a$)&$a/a /# )$$(&#!a$ ,#(+ >#( * )&#( #* /(!. Modelar el 3ario(ra'a S(&* (! &$a'" ( -a$)&$a/a ( ,#(( a,$(")a$ >#( (! ,#*+ / a!+ ?/((+a ( $(&)+$a (* (! (&#* ,#*+% (a "#a* @16 ?a!"a*"(% !#(& !!(&a a aa$ E*+*"( ( "*"!#(= a = 16
Co=0 C 1= 0.604
D(+($/)*a")* (! /(!=
MODE-O ES+E*ICO0
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
:a$a a=
( ) ( )
3 h γ ( h )=0.604 2 16
1 h − 2 16
3
:a$a @ a= γ ( h )= 0.604
h 8 16
γ*(h) ESER!"# 0,4545 0,415431985 0,60426 0,604264706
24 32
0,50988 0,604264706 0,41902 0,604264706
40 48 56 64
0,48918 0,49112 0,42607 0,42625
HUALL:ACHO;UE MAMANI JOSE RAUL
0,604264706 0,604264706 0,604264706 0,604264706
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
MODE-O EX)ONENCIA-0
[
( ) γ ( h )=0.604 1 −e h 16
h
γ*(h)
"$%&R%'!"#
8 16 24 32
0,4545 0,60426 0,50988 0,41902
0,453198529 0,604264706 0,604264706 0,604264706
40 48 56
0,48918 0,604264706 0,49112 0,604264706 0,42607 0,604264706
64
0,42625 0,604264706
]
MODE-O )OTENCIA-0
∝
γ ( h )=0.604 [ h ]
Donde
∝
HUALL:ACHO;UE MAMANI JOSE RAUL
-a$Ka (( 0 a 2
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN h 8
γ*(h) E#NEN"!% 0,4545 0,237759635
16 24
0,60426 0,50988
0,381968144 0,604264706
32 40
0,41902 0,48918
0,604264706 0,604264706
48 56
0,49112 0,42607
0,604264706 0,604264706
64
0,42625
0,604264706
GEOESTADISTICA
E! /(! >#( / ( a(/(a ( (! "#a$+)" ?(+( a+a !!(&a$ a !a /((+a (! -a$)&$a/a.
c 4allar el (r2co de diperión H!H para el e(undo y uinto punto del 3ario(ra'a y calcular el coe2ciente de correlación. T(*)(* !a +a!a )*)")a! N 1 2 3 4 5 6 7 8 9 10 11
o . /() 12 2,10 16 1,80 21 0,90 26 1,00 34 1,50 42 1,90 52 1,10 58 1,00 63 0,90 67 0,80 76 3,20
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 81 85
1,90 1,30
92 100
2,50 1,60
12 13 14 15
•
GEOESTADISTICA
:#*+ 2 @ 16 La !(( >#( )*+($-)(*(* (* (! )*+($-a! ( )+a*")a
[ 8−24 ]
(+* $/a ,$ (+ ,#*+= Z(x) Z(x+h) 2,1 0,9 2,1 2,1
1 1,5
1,8 1,8 0,9
1 1,5 1,5
0,9 1 1 1,5 1,5 1,5 1,9 1,9 1,9 1,1 1,1 1,1 1 1 1 0,9 0,9
1,9 1,5 1,9 1,9 1,1 1 1,1 1 0,9 0,9 0,8 3,2 0,8 3,2 1,9 3,2 1,9
0,9 0,8 0,8 0,8 3,2
1,3 3,2 1,9 1,3 1,3
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 3,2 3,2
2,5 1,6
1,9 1,9
2,5 1,6
1,3 1,3
2,5 1,6
2,5
1,6
GEOESTADISTICA
&$a'" ( ),($)*
G*A+ICO DE DIS)E*SION
6x!
3.5 3 2.5 2 1.5 1 0.5 0 0
*J %.;?
0.5
1
1.5
2
2.5
3
3.5
6x
•
:a$a (! ,#*+ 5 @ 40 La !(( >#( )*+($-)(*(* (* (! )*+($-a! ( )+a*")a
[ 20−60 ]
(+* $/aa ,$ (+ ,#*+= Z(x) Z(x+h) 2,1 1,5 2,1 1,9 2,1 1,1 2,1 1 2,1 0,9 2,1 0,8 1,8 1,9 1,8 1,1 1,8 1 1,8 0,9
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 1,8 1,8
0,8 3,2
0,9 0,9
1,9 1,1
0,9 0,9
1 0,9
0,9 0,9
0,8 3,2
0,9 1
1,9 1,1
1 1
1 0,9
1 1 1
0,8 3,2 1,9
1 1,5 1,5 1,5 1,5 1,5 1,5 1,5 1,9 1,9 1,9 1,9 1,9 1,9 1,9 1,1 1,1 1,1 1,1 1,1 1 1
1,3 1 0,9 0,8 3,2 1,9 1,3 2,5 0,9 0,8 3,2 1,9 1,3 2,5 1,6 3,2 1,9 1,3 2,5 1,6 1,9 1,3
1 1 0,9 0,9 0,9 0,8
2,5 1,6 1,3 2,5 1,6 2,5
HUALL:ACHO;UE MAMANI JOSE RAUL
GEOESTADISTICA
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 0,8 3,2
1,6 1,6
1,9
1,6
GEOESTADISTICA
&$a'" ( ),($)*
G*A+ICO DE DIS)E*SION 3.5 3 2.5
*J %.;?
2
6x!
1.5 1 0.5 0 0
0.5
1
1.5
2
2.5
3
3.5
6x
:$(&#*+a 2 DATA@ 14
1 2 3 4 5 6 7 8 9 10
D)+a* ")a 10 10 10 10 10 10 10 10 10 10
!( 3 3 4 3 3 2 4 7 8 9
@1 @3 0 @20 0 0 1 1 0 1 4 9 1 1
1 0 1 1 1 25 16 4
0 0 4 1 16 36 25
HUALL:ACHO;UE MAMANI JOSE RAUL
@40
@50
@60
@70
@80
0 1 0 16 25 49
1 1 9 25 36
1 16 16 36
16 25 25
25 36
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 11 12 13 14
10 10 10 10
7 5 3 2
4 4 4 1
N?
0 9 36 25
9 4 25 49
31 91 152 178 13 12 11 10 1.19 6.90 2 3.792 9 8.900
*(2
)*+($-a! a$(a ( )*#(*")a /)* /a
1 16 16 9
GEOESTADISTICA
25 1 16 36
16 9 1 25
150 9 8.333
120 8
16 4 1 4
91 7
7.500 6.500
9 4 0 0
74 6 6.167
10 / 5 / 10 72.5 N ,a$( 13 12 11 10 9 8 7 6
10 20 30 40 50 60 70 80
?P< ?Q2 31 91 152 178 150 120 91 74
*(2 1.192 3.792 6.909 8.900 8.333 7.500 6.500 6.167
@10
NK pare 6x 1 2 3 4 5 6 7 8
76x! 6x8F#
6x!
3 3 4 3 3 2 4 7
HUALL:ACHO;UE MAMANI JOSE RAUL
3 4 3 3 2 4 7 8
0 1 1 0 1 4 9 1
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 9 10 11 12 13
8 9 7 5 3 #/a+$)a
GEOESTADISTICA
9 7 5 3 2
1 4 4 4 1 31
10 9 8 7 6 5 4 3 2 1 0 1
2
3
4
5
NK par 6x e 1 2 3 4 5 6 7 8 9 10 11 12
6
7
HUALL:ACHO;UE MAMANI JOSE RAUL
9
10
76x! 6x8F#
6x!
3 3 4 3 3 2 4 7 8 9 7 5
8
4 3 3 2 4 7 8 9 7 5 3 2
1 0 1 1 1 25 16 4 1 16 16 9 91
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
10 8 6 4 2 0 1
2
3
4
5
NK par 6x e 1 2 3 4 5 6 7 8 9 10 11
6
7
9
10
76x! 6x8F#
6x!
3 3 4 3 3 2 4 7 8 9 7
8
3 3 2 4 7 8 9 7 5 3 2
0 0 4 1 16 36 25 0 9 36 25 152
10 9 8 7 6 5 4 3 2 1 0 1
2
3
4
5
HUALL:ACHO;UE MAMANI JOSE RAUL
6
7
8
9
10
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
@40
NK pare 6 x 1 2 3 4 5 6 7 8 9 10
76x! 6x8F#
6x!
3 3 4 3 3 2 4 7 8 9
3 2 4 7 8 9 7 5 3 2
0 1 0 16 25 49 9 4 25 49 178
10 8 6 4 2 0 1
2
3
4
5
6
7
8
9
10
@50
NK pare 6x 1 2 3 4 5 6 7 8
76x! 6x8F#
6x!
3 3 4 3 3 2 4 7
HUALL:ACHO;UE MAMANI JOSE RAUL
2 4 7 8 9 7 5 3
1 1 9 25 36 25 1 16
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN 9
8
2
GEOESTADISTICA 36 150
10 8 6 4 2 0 1
2
3
4
5
6
7
8
9
@60
NK pare 6 x 1 2 3 4 5 6 7 8
76x! 6x8F#
6x!
3 3 4 3 3 2 4 7
4 7 8 9 7 5 3 2
1 16 16 36 16 9 1 25 120
10 8 6 4 2 0 1
2
3
4
5
6
7
8
@70 HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
NK pare 6 x 1 2 3 4 5 6 7
76x! 6x8F#
6x!
3 3 4 3 3 2 4
GEOESTADISTICA
7 8 9 7 5 3 2
16 25 25 16 4 1 4 91
10 8 6 4 2 0 1.5
2
2.5
3
3.5
4
4.5
@80
NK pare 6 x 1 2 3 4 5 6
76x! 6x8F#
6x!
3 3 4 3 3 2 #/a+$)a
8 9 7 5 3 2
25 36 9 4 0 0 74
10 8 6 4 2 0 1.5
2
2.5
HUALL:ACHO;UE MAMANI JOSE RAUL
3
3.5
4
4.5
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
G*+ICO DE :A*IOG*AMA 10.000 8.000 GRICO DE VARIOGRAMA
6.000 4.000 2.000 0.000 0
10 20 30 40 50 60 70 80 90
#. Calcular el 3ario(ra'a experi'ental, en la direccione Norte L Sur y Ete L Oete, para la "or'ación de 'uetreo dada en la i(uiente tala. Modelar el 3ario(ra'a en a'o cao. COO*DENADAS N E 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
80 80 80 80 80 80 80 80 80 80 80 80 80 80 80
-E / 1 1 2 2 3 5 4 6 7 8 7 9 9 11 10
HUALL:ACHO;UE MAMANI JOSE RAUL
CO*DENADAS N E 100 100 100 100 100 100 100 100 100 100 100 100 100 100
10 20 30 40 50 60 70 90 100 110 120 130 140 150
-E / 3 3 4 3 3 2 4 7 8 9 7 5 3 2
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
160 140 120 100 80 60 40 20 0 20
40
60
80
100
120
140
160
180
SO-CION0 :A*IOG*AMA Norte Sur 1 2 2 2 ( ( 1−10 ) + ( 9−11 ) + … + ( 1−1 ) ) F?10@ 2 ( 14 )
F?10@0%82 1 2 2 2 ( ( 9− 10 ) + ( 9−11 ) + … + ( 1−2 ) ) F?20@ 2 ( 13)
F?20@1%42 1 2 2 2 ( 9−10 ) + ( 7 −11) + … + (1 −2 ) ) ( F?30@ 2 ( 12)
F?30@2%72 1 2 2 2 ( 7 −10 ) + ( 8−11 ) + … + ( 1−3 ) ) ( F?40@ 2 ( 11)
F?40@4%77 1 2 2 2 ( 8−10 ) + (7 −11 ) + … + ( 1−5 ) ) ( F?50@ 2 ( 10)
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
F?50@1%42 1 ( ( 7 −10 )2+ ( 6−11 )2+ …+( 1− 4 )2 ) F?60@ 2 ( 9 )
F?60@10%33 1
F?70@
( )
2 8
( ( 6 −10 ) + ( 9−11 ) + …+ ( 1−6 ) ) 2
2
2
F?70@14%94
:A*IOG*AMA Oete Ete 1 2 2 2 2 2 ( ( 3 −10 ) + ( 4 −3 ) + ( 3 −4 ) + … + ( 3−5 ) + (2 −3 ) ) F?10@ 2 ( 14 )
F?10@0%96 1 ( ( 4 −3 )2 +( 3 −3 )2 + …+ ( 3 −7 )2 + ( 2−5 )2 ) F?20@ 2 ( 13)
F?20@3%04 1
F?30@
( )
2 12
( ( 3−3 ) +( 3 −3 ) + ( 2− 4 ) +… +( 3 −9 ) +( 2− 7 ) ) 2
2
2
2
2
F?30@5%58 1
F?40@
( )
2 11
( ( 3− 3 ) + ( 2−3 ) +( 4 − 4 ) +… + ( 3−8 ) +( 2 −9 ) ) 2
2
2
2
2
F?40@7%55 1 ( ( 2−3 )2 +( 4 −3 )2+ ( 6− 4 )2 +… + ( 3−7 )2+( 2 −8 )2 ) F?50@ 2 ( 10)
F?50@7%9 1 2 2 2 2 2 ( 4 −3 ) + (6 −3 ) + ( 7 −4 ) + … + ( 3 −6 ) + ( 2−7 ) ) ( F?60@ 2 ( 9 )
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
F?60@7%78 1 ( ( 6 −3 )2 +( 7−3 )2+ ( 8− 4 )2 + …+ (3 −4 )2 +( 2−6 )2) F?70@ 2 ( 8 )
F?70@7%44
G*A+ICOS0 NO*TE L S* 16 14 12 10 8 6 4 2 0 0
10
20
30
40
50
60
70
80
:ARAMETROS ASUMIDOS C@0 C1@7%5
a@50/
OESTE L ESTE
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
9 8 7 6 5 4 3 2 1 0 0
10
20
30
40
50
60
70
80
:ARAMETROS ASUMIDOS C@ 0
C1@7%3
a@40/
MODELAMIENTOS DEL :RIMER VARIOGRAMA :a$a/(+$= C@0 C1@7%5
S@CPC1@7%5
a@50/
Modela'iento e"rico P6!
( ( ) ( ) )
@0%296
( ( )−( ) )
@0%568
7,5 10 10 ?10@ 2 3 50 − 50
7,5 20 3 ?20@ 2 50
20 50
{
( ( )−( ) )
S h 3 a 2
h a
3
∀ h
S ∀h≥a
3
3
?30@0%792
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
16 14 12 10 8 6 4 2 0 0
10
20
30
40
50
60
70
80
?40@0%944 ?50@S@7%5 ?60@ 7%5 ?70@ 7%5
! 10 20 30 40 50 60 70
6! Q6 ! 0.8 2 1.4 2 2.7 2 4.7 7 7.4 5 10. 33 14. 94
0.2 96 0.5 68 0.7 92 0.9 44 7.5 7.5 7.5
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
({ ( ) ( ) )
GEOESTADISTICA
2 ❑
Modela'iento cuadratico P6!
h h s 2 − 2 a a
∀ h< a
S ∀ h≥ a
?10@2%7 ?20@4%8 ?30@6%3 ?40@7%2 ?50@S@7%5 ?60@ 7%5 ?70@ 7%5 −h
Modelo Eponencial PPP6!61 e
a
?10@1%36 ?20@2%47 ?30@3%38 ?40@4%13 ?50@4%74 ?60@ 5%24 ?70@ 5%65
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
;. -o i(uiente dato en / correponden a un 'uetro e"ectuado en un yaci'iento de alitre, cuya 'alla e'pleada "ue de = x = 'etro. Da+ 22 28 21 <1 20 18 20 <1
22 25 18 <1 15 16 <1 <1
19 <1 <1 16 15 14 19 <1
<1 <1 24 20 19 13 16 <1
<1 18 21 21 15 14 1 <1
16 18 20 23 19 <1 10 <1
17 13 13 <1 17 13 1 11
<1 <1 <1 12 12 10 <1 <1
<1 11 <1 11 <1 10 13 18
<1 9 14 17 16 18 19 22
a Ca!"#!a$ (! -a$)&$a/a (,($)/(*+a! (,($)/(*+a! (* !a )$("")* N
1. Ca!"#! ( ( 90.
F?% "* #*a )$("")* ( *$+( a #$ % (a "* #* a*&#!
Da+= H@ 5
22
22
19
<1
<1
16
17
<1
<1
<1
28
25
<1
<1
18
18
13
<1
11
9
21
18
<1
24
21
20
13
<1
<1
14
<1
<1
16
20
21
23
<1
12
11
17
20
15
15
19
15
19
17
12
<1
16
18
16
14
13
14
<1
13
10
10
18
20
<1
19
16
1
10
1
<1
13
19
<1
<1
<1
<1
<1
<1
11
<1
18
22
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
D)$("")* = *$+( #$ ?90 γ ( h) =
Np ( h )
1 2 Np(h)
∑ [ Z ( xi ) − Z ( xi + h)]
2
i =1
H@5
N (h)=numero de pares = 72
γ
F?@Va!$ (,($)/(*+a! :a$a @5= γ ∗( 5 ) =
1
[ ( 22 −28 ) +( 28−21 ) +( 21−−1 ) +(−1−20 ) +( 20− 18 ) + (18−20) + ( 20−−1 0 −a h=1 loeodel 2 ( 70 ) 2
2
2
2
2
2
γ ∗( 5 ) =¿ 50.81
:a$a @10= γ ∗( 10 ) =
1 (22 −21 )2+ ( 28−−1 )2 … … . … . ( 18−22 )2 2 ( 60 )
[
]
γ ∗( 10 ) =¿ 72.61
:a$a @15= γ ∗( 15 ) =
1
[ ( 22 −−1 ) +( 28 −20 ) … … . … . ( 16− 22 ) ] 2 ( 50 ) 2
2
HUALL:ACHO;UE MAMANI JOSE RAUL
2
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
γ ∗( 15 ) =¿ 89.56
:a$a @20= γ ∗( 20 )=
1 ( 22−20 )2+( 28 −18 )2 … … . … . ( 17 −22 )2 2 ( 40 )
[
]
γ ∗( 20 )=¿ 83.9
:a$a @25= γ ∗( 25 )=
1
[ (22 −18 ) + ( 28−20 ) … … . … . (14 −22 ) ] 2 ( 30 ) 2
2
2
γ ∗( 25 )=¿ 95.1
:a$a @30= γ ∗( 30 )=
1 (22 −20 )2 +( 28−1 )2 … … . … . ( 9−22 )2 2 ( 20 )
[
]
γ ∗( 30 )=¿ 78.38
:a$a @35 γ ∗( 35 )=
1
[ ( 22 −−1 ) +( 22−−1 ) 2 ( 10 ) 2
2
… … . … . (−1−22 )
2
]
γ ∗( 35 )=¿ 107.2
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
C#a$ $(#/(* ,a$a NORTE
N? 5 70 1 0 60 1 5 50 2 0 40 2 5 30 3 0 20 3 5 10
γ ?
50.81 72.61 89.56 83.9 95.1 78.38 107.2
VARIOGRAMA
:A*IOG*AMA 120 100 80
VARIOGRAMA
60 40 20 0 0
5
10
15
20
25
HUALL:ACHO;UE MAMANI JOSE RAUL
30
35
40
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
HUALL:ACHO;UE MAMANI JOSE RAUL
GEOESTADISTICA
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
γ
1. Ca!"#! ( F?% "* #*a )$("")* ( (+( a (+( % (a "* #* a*&#! ( 0. Da+= H@ 5
22
22
19
<1
<1
16
17
<1
<1
<1
28
25
<1
<1
18
18
13
<1
11
9
21
18
<1
24
21
20
13
<1
<1
14
<1
<1
16
20
21
23
<1
12
11
17
20
15
15
19
15
19
17
12
<1
16
18
16
14
13
14
<1
13
10
10
18
20
<1
19
16
1
10
1
<1
13
19
<1
<1
<1
<1
<1
<1
11
<1
18
22
D)$("")* = *$+( #$ ?90 γ ( h) =
1 2 Np(h)
Np ( h )
∑ [ Z ( xi ) − Z ( xi + h)]
2
i =1
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
D)$("")* = *$+( #$ ?90 γ ( h) =
Np ( h )
1 2 Np(h)
∑ [ Z ( xi ) − Z ( xi + h)]
2
i =1
H@5
N (h)=numero de pares = 72
γ
F?@Va!$ (,($)/(*+a! :a$a @5= γ ∗( 5 ) =
1
[ ( 22− 22 ) +( 22 −19 ) + ( 19−1 ) + (−1 −−1 ) + (−1−16 ) + ( 16 −17 ) + ( 17 −−1 0 −a h =1 lo eo delv 2 ( 72 ) 2
2
2
2
2
2
γ ∗( 5 ) =¿ 50.81
:a$a @10= γ ∗( 10 ) =
1 ( 22−19 )2 +( 22−−1 )2 … … . … . (−1−22 )2 2 ( 64 )
[
]
γ ∗( 10 ) =¿ 88.7969
:a$a @15= γ ∗( 15 ) =
1
[ ( 22−−1 ) +( 22−−1 ) … … . … . ( 11−22) ] 2 ( 56 ) 2
2
HUALL:ACHO;UE MAMANI JOSE RAUL
2
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
γ ∗( 15 ) =¿ 80.2768
:a$a @20= γ ∗( 20 )=
1 ( 22−−1 )2 +( 22−16 )2 … … . … . (−1−22 )2 2 ( 48 )
[
]
γ ∗( 20 )=¿ 78.0104
:a$a @25= γ ∗( 25 )=
1 ( 22−16 )2+( 22 −17 )2 … … . … . (−1−22 )2 2 ( 40 )
[
]
γ ∗( 25 )=¿ 65.7125
:a$a @30= γ ∗( 30 )=
1
[ ( 22− 17 ) + ( 22−−1 ) … … . … . (−1 −22) ] 2 ( 32 ) γ ∗( 30 )=¿
2
2
2
68.0469
:a$a @35 γ ∗( 35 )=
1
[ ( 22−−1 ) + ( 22−−1 ) … … . … . (−1− 22 ) ] 2 ( 24 ) 2
2
HUALL:ACHO;UE MAMANI JOSE RAUL
2
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
γ ∗( 35 )=¿ 123.813
:a$a @40=
γ ∗( 40 )=
1
[ ( 22−−1 ) + ( 22−−1 ) … … . … . (−1 −22 ) ] 2 (16 ) 2
2
2
γ ∗( 40 )=¿ 138.125
:a$a @ 45= γ ∗( 45 )=
1
[ ( 22−−1 ) +( 28− 9 ) … ….… . (−1 −22 ) ] 2 ( 8) 2
2
2
γ ∗( 45 )=¿ 113.063
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
C#a$ $(#/(* ,a$a ESTE WOESTE ?0 = α @0º
N? 5 72 1 0 64 1 5 56 2 0 48 2 5 40 3 0 32 3 5 24 4 0 16 4 5 8
γ ?
58.3264 88.7969 80.2768 78.0104 65.7125 68.0469 123.813 138.125 113.063
VARIOGRAMA
:A*IOG*AMA 160 140 120 100
VARIOGRAMA
80 60 40 20 0 0
5
10 15 20 25 30 35 40 45 50
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
4. el anlii 3ario(ra2co para un yaci'iento no da el i(uiente
reultado →
δ ( h )=0.15 + 0.7 [ 1 −exp
NS →
δ ( h )=0.1 + 0.9 [ 1− exp
E
( )] −h 30
( )] −h 90
[ ( )]
N
→ δ ( h )= 0.2+ 0.7 1−exp
NE
→ δ ( h )= 0.25+ 0.8 [ 1−exp
−h 60
( )] −h 65
DATOS0 X
-E
80 50 50
40 70 40
10&X+ 5&X+ YBZ
a Ca!"#!a$ !a -a$)a*a ( (+)/a")* ,a$a (! !>#( ( 1010 /+% "# "(*+$ ( &$a-(a (+a (* (! ,#*+ ?50%40
DESA**O--O0
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
SE2 @ 2 [
?V%B
GEOESTADISTICA
W [BB < [VV
V @ 1 B@B
DISC*ETIACION DE- 9-ORE 9 6U @
MAT*I DE DISTANCIAS 6)O* )ITAGO*AS
V1
1
#
;
<
HUALL:ACHO;UE MAMANI JOSE RAUL
=
$
>
?
@ 05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
GEOESTADISTICA
9 V1
25%49 51
29%15 48
35%35 53
15%81 14
21%21 32
29%15 48
7%071 07
15%81 14
25%49 51
MAT*I DE :A*IOG*AMA REEM:LAANDO DISTANCIA ? DE ACUERDO AL MODELO=
NE
V1 9 V1
→ δ ( h )= 0.25+ 0.8 [ 1−exp
1
#
;
( ) −h 65
]
<
=
$
>
?
@
6V1,9
0%509 0%539 0%585 0%422 0%472 0%539 0%332 0%422 0%509 0%481 56 15 63 74 76 15 46 74 56 53
MAT*I DE DISTANCIAS DE- 9-ORE 6
HUALL:ACHO;UE MAMANI JOSE RAUL
69,9
05<27308
UNIVERSIDAD NACIONAL JORGE BASADRE GROHMANN
9 1 # ;
1 %
#
;
10
20
%
10
%
<
< 10 14%1 42 22%3 61
%
= $ > ? @
=
$
14%1 42
22%3 61 14%1 42
10 14%1 42
10
10
20
%
10
%
> 20 22%3 61 28%2 84 10 14%1 42 22%3 61
%
GEOESTADISTICA
?
@
22%3 61
28%2 84 22%3 61
20 22%3 61 14%1 42 10 14%1 42
20 22%3 61 14%1 42 10
10
20
%
10
%
MAT*I DE :A*IOG*AMA DE ACUERDO A LOS MODELOS=
HUALL:ACHO;UE MAMANI JOSE RAUL
05<27308
