INFORME TOPOGRAFICO Quebrada Sahuanay, Abancay.docx

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    2014INFORME

    TCNICOLEVANTAMIENTO TOPOGRFICO YGEORREFERENCIACIN DELA QUEBRADA

    SAHUANAY ETAPA N 1 ETAPA N 2.

    Alfonso Daz C.Centro de Estudios y Prevencin de

    Desastres - PREDE

    IPa. 1!"#$%& T'(!)(#

    L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/aSa3a!a4 E+a,a N 51

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

    Pa. 2

    I!"#$%& T'(!)(#L&*a!+a%)&!+# +#,#$-(# /& 0a

    6&$a/aSa3a!a4 E+a,a N 1

    E+a,a N 2.

    E0a#$a/# ,#$7

    I!. A0"#!8# D9a: C. C##$/)!a/#$ /&&8+/)# Ba(3. ;0)# C&8a$ H$+a/# S.

    T'(!)(# T#,

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# +#,#$-(# /& 0a 6&$a/a Sa3a!a4

    E+a,a N 1 E+a,a N 2.

    N#%$& /&0 8#0)()+a!+&

    CENTRO DE ESTUDIOS Y PREVENCION DE DESASTRES ? PREDESCa00& Ma$+9! /& P#$$&8 1@1 Sa! I8)/$#? L)%a &7 3++,7.,$&/&8.#$.,&

    CENTRO DE ESTUDIOS Y PREVENCION DE DESASTRES

    A$6. M8(. ;#8' M. Sa+# OP$&8)/&!+& /&0 C#!( D)$&(+)*# PREDES

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    Q&/a +&$%)!a!+&%&!+& ,$#3))/# 8 )%,$&8)

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    INDICE

    1.MEMORIA DESCRIPTIVA ........................................................................................ @

    1.1 GENERALIDADES................................................................................................. @1.2 UBICACINY DESCRIPCIN DEL REA DE ESTUDIO.................................................... @1. RECOPILACIN DE INFORMACIN............................................................................

    2.GEOREFERENCIACION Y COLOCACION DE PUNTOS DE CONTROL GEODESICOS ...

    2.1 ALCANCES DE LOSTRABA;OS DE GEORREFERENCIACIN............................................. 2.2 OB;ETIVOS DE LA GEORREFERENCIACIN................................................................. 2. ONA DETRABA;OSY DURACIN...........................................................................

    2..1 P!+# Ba8& /&0 IGN .................................................................................. 2.> EQUIPO DE INGENIERJA EMPLEADO..........................................................................

    2.>.1 O,&$a/#$&8 /&0 GPS ................................................................................. K

    2. PROCEDIMIENTOY E;ECUCIN............................................................................... K2..1 P0a!&a%)&!+# ........................................................................................... K2..2 T$aa#8 /& Ca%,# .................................................................................. K2.. P$#(&/)%)&!+# .......................................................................................... K2...1 C#!+$#0 H#$):#!+a0............................................................................... K2...2 C#!+$#0 V&$+)(a0 ............................................................................... 11

    2..> C-0(0#8 /& Ga)!&+& ........................................................................... 122.@ DESCRIPCIN DE LOS DATOSY EL PROCESAMIENTO DE LA DATA OBTENIDA A TRAVS DE

    GPS DIFERENCIAL ........................................................................................ [email protected] R&)8+$#8 /&0 GPS &! Ca%,# ................................................................ 12

    [email protected] Pa$-%&+$#8 ,a$a &0 P#8+ P$#(&8# .......................................................... 12.@. P#8+ P$#(&8# ......................................................................................... 12. RESULTADOS .................................................................................................. 1

    2..1 C##$/&!a/a8 UTM GS?> .................................................................. 12..2 Fa(+#$&8 /& E8(a0a ............................................................................... 1

    .LEVANTAMIENTO TOPOGRAFICO ....................................................................... 1>

    .1 OB;ETIVOY ALCANCES DEL LEVANTAMIENTOTOPOGRFICO ..................................... 1>.2 METODOLOGJA ............................................................................................... 1>. TRABA;OS DE CAMPO ...................................................................................... 1

    ..1 R&(#!#()%)&!+# /&0 $&a /& &8+/)# .................................................... 1

    ..2 E6),# 4 P&$8#!a0 /& I!&!)&$9a &%,0&a/# .......................................... 1.. E!0a(& (#! &0 S)8+&%a /& C#!+$#0 H#$):#!+a0 /&0 IGN ........................... 1@..> M&/)().1 C-0(0# /&0 A!0# H#$):#!+a0 ......................................................... 1..>.2 C-0(0# /&0 A!0# V&$+)(a0 ............................................................. 1

    ..>. M&/)().> C#$$&(()

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    ..>. C#$$&(()

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    INFORME TCNICOLEVANTAMIENTO TOPOGRFICO DE LA QUEBRADA

    SAHUANAY ETAPA N 1 ETAPA N 2.

    1. MEMORIA DESCRIPTIVA

    1.1 G&!&$a0)/a/&8

    Pa$a 0#8 S&$*)()#8 /& T#,#$a"9a ? $$&"&$&!()a()

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    C##$/&!a/a8 UTMPUNTO NORTE ESTE ALTITUD

    1 >KK51 2>2 >522 >KK 2K51 5K >K111 2K 2

    F&!+&7 Ma,a a8& /& 0a (&!(a Sa3a!a4

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    F)$a 517 Ma,a /& 0a :#!a /& 0&*a!+a%)&!+# +#,#$a(#

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    1. R&(#,)0a()

    I!8+)++# G$-(# Na()#!a0 IGN= P&$+&!&()&!+& a Aa!(a4 E8(a0a17155555.

    P0a!#8 &! "#$%a+# D))+a0 /& 0a ()/a/ /& Ha$)= "a()0)+a/#8 ,#$ 0aM!)(),a0)/a/ /& /)(3a C)/a/.

    F)(3a8 /&0 P!+# G/'8)(#8 /& #$/&! A %#!%&!+a/# ,#$ &0I!8+)++# G$-(# Na()#!a0 IGN= (#! 0a /&8($),()

    V)8+a8 a'$&a8 a(+a0&8 /&0 (&!+$# ,#0a/# /& 0a (&!(a /& Sa3a!a4

    2. GEOREFERENCIACION Y COLOCACION DE PUNTOS DE CONTROLGEODESICOS

    2.1 A0(a!(&8 /& 0#8 T$aa#8 /&G$$&"&$&!()a()

    E0 +$aa# (#!8)8+)< &! 0a /&+&$%)!a()

    4 (2.2 O&+)*#8 /& 0aG$$&"&$&!()a()

    D&+&$%)!a()

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    GPS 51 GPS DIFERENCIAL=

    o Ma$(a7 T$)%0& Na*)a+)#!.o M#/&0#7 >55 8&$)&8o F$&(&!()a7 L1L2

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    51 GPS DIFERENCIAL

    o Ma$(a7 T$)%0& Na*)a+)#!.o M#/&0#7 R@ S&$)&8.o F$&(&!()a7 L102

    2.>.1 O,&$a/#$&8 /&0 GPS

    Ca/$# N 5 P&$8#!a0 /& (a%,#

    PERSONAL CARGO

    Ba(3. ;0)# C&8a$ H$+a/# O,&$a/#$ /& GPS 4T&(. Ma$(# A$#8+&) O,&$a/#$ /& GPS

    2. P$#(&/)%)&!+# 4 E&(()

    2..1 P0a!&a%)&!+#

    E! &8+a &+a,a 8& 3a $&(#,)0a/# )!"#$%a()

    Pa$a &"&(+a$ &0 ,#8)()#!a%)&!+# /& 0#8 ,!+#8 /& (#!+$#0= 8& %)/& /&8/& 0a&8+a().

    2.. P$#(&/)%)&!+#

    2...1 C#!+$#0H#$):#!+a0

    Pa$a &0 (#!+$#0 H#$):#!+a0= 8& +)0):< &0 %'+#/# D)"&$&!()a0 # E8+-+)(#= &0 (a0(#!8)8+& &! (#0#(a$ ! &6),# GPS Ma8+&$ BASE= &! &0 P!+# G/'8)(# (#!

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    (##$/&!a/a8 (#!#()/a8= ,a$a &8+& ,$#4&(+# 8& +)0):< &0 ,!+# /& 0a E8+a()

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

    Pa.

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    Ca/$# N 5> C##$/&!a/a G&!&$a/aCOORDENADAS UTM 7 ONA 1 S#+3

    N$# N#%$& N#$+& E8+& A0+$a G)/a0

    1 ABANCAY >KK.55 2K51.55 5K.55

    E! &8+& ,$#4&(+#= 8& 8< 51$&(&,+#$ D)"&$&!()a0 GPS L1L2= ,a$a +&!&$ 0&(+$a88)%0+a!&a8 4 #,+)%):a$ 0a %&+$9a /& 0a $&/ /'8)(a.

    L#8 $&(&,+#$&8 GPS /)"&$&!()a0&8 R#*&$= $&())&$#! 0a8 #!/a8 /& $a/)#&%)+)/a8 ,#$ 0#8 8a+'0)+&8 8)%0+-!&a%&!+&.

    L#8 ,a$-%&+$#8 /& %&/)()

    La )!"#$%a()

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    +)0):a/a8 4# $&(3a:a/a8. V&$)(a$ 0a )!"#$%a()

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    S)8+&%a E8+-+)(# D)"&$&!()a0 GPSE6),#8F$&(&!()a8 T)&%,#

    N$#Sa+'0)+&8

    I!+&$*a0# /&

    52 GPS R#*&$L1= L2575 3$8. C#!+)!a8= /& +#%a /& )!"#$%a() 8a+'0)+&8 (#%# %9!)%#. ,a$a 0a ,#8)()

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

    Pa.

    C#%,$#a$ 0#8 /)#8 $&8)/a0&8 /& (a/a 8a+'0)+&. E8+#8%&8+$a! &0 RMS /& (a/a 8a+'0)+&= +)0):a/# ,a$a /&+&$%)!a$ 0a8#0()

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

    Pa. 11

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    !a $&/ &87

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

    Pa. 12

    2 U! 0#6& /)a#!a0 8#0()

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    A(+a0%&!+& &8 &0 %#/&0# +)0):a/# ,#$ &0 I!8+)++# G$-(# Na()#!a0 /&!&8+$# ,a98.

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    La )!"#$%a()

    [email protected] R&)8+$#8 /&0 GPS &!Ca%,#

    L#8 /a+#8 +#%a/#8 &! (a%,# ,#$ &0 GPS= 00a%a/#8 EPOCAS= 8#! $&)8+$a/#8&! )!+&$*a0#8 /& 15 8&!/#8. L /& 0a8 8&8)#!&8 /& +#%a /& /a+#8='8+#8 8#! /&8(a$a/#8 /&0 $&(&,+#$= 6& &8 ! ,&6 #$/&!a/#$= &! &0

    http://es.wikipedia.org/wiki/Geodesiahttp://es.wikipedia.org/wiki/Geodesia
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    (a0 3a 8)/# $aa/a 0a )!"#$%a()

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    [email protected] Pa$-%&+$#8 ,a$a &0 P#8+P$#(&8#

    La /a+a GPS= &8 )%,#$+a/a ,#$ &0 S#"+a$& T$)%0& G%a+)(8 O(&= &0 (a0&!+)&!/& 0a )!"#$%a()

    3a00a/a8. E!+$& '8+#8 ,a$-%&+$#8 +&!&%#8 0#8 %-8 )%,#$+a!+&87

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    L#8 %#/&0#8 T$#,#8"'$)(#8 4 I#!#8"'$)(a87 0#8 (a0&8 /&!&! 0#8 %#/&0#8 a 8&$+)0):a/#8 &! &0 (-0(0#= /&)/# a 6& 0a +$#,

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    . LEVANTAMIENTOTOPOGRAFICO

    .1 O&+)*# 4 A0(a!(&8 /&0 L&*a!+a%)&!+#T#,#$-(#

    E0 #&+)*# /&0 E8+/)# T#,#$-(# &8 ,$#,#$()#!a$ )!"#$%a()

    E0 #&+)*# /& ! 0&*a!+a%)&!+# +#,#$-(# &8 0a /&+&$%)!a()

    R&a0):a$ &0 0&*a!+a%)&!+# +#,#$-(#= (#$$&8,#!/)&!+& a0 8)+)# /&)!+&$'8 /#!/& 8& (#!8+$)$-! 0a8 #$a8 ,$#,)a8 /& &8+& ,$#4&(+#.

    G&!&$a$ +#/a 0a )!"#$%a()

    A,0)(a$ (#!#()%)&!+#8 -8)(#8 /& +#,#$a"9a ,a$a 0a &!&$a()

    +a0&8 (#%# Ca$+a8 !a()#!a0&8= F)(3a8 /&0 IGN /& ,!+#8 /'8)(#8 /&,$)%&$ #$/&!= ,0a!#8 +#,#$-(#8 $&a0):a/#8 &! &0 -$&a /& &8+/)#= &+(.

    D&8,0a:a%)&!+# /& !a $)a/a /& +#,#$a"9a a 0a :#!a &! &8+/)# L /& 0a &!+$&a /&0 +&$$&!#= 8& ,$#(&/)< (#! &0 $&(#!#()%)&!+# /& 0a

    :#!a &! (a%,#= *&$)(a!/# &0 -$&a /& +$aa# a89 (#%# 0a8 :#!a8a0&/aa8 ,a$a 8 /&0)%)+a()

    Pa$a ,#/&$ &!0a:a$ &0 -$&a /& &8+/)# /&0 P$#4&(+# a 0a R&/ G/'8)(aNa()#!a0 Sa+&0)+a0 8& &%,0&< 0a8 (##$/&!a/a8 /'8)(a8 /& /#8 52

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    ,!+#8 /& (#!+$#0 /& #$/&! C= #+&!)/# (#! 0#8 +$aa#8 /&G$&"&$&!()a()#!.

    Pa$a &0 0&*a!+a%)&!+# +#,#$-(# /&0 -$&a /& &8+/)# 8& &8+a0&()< 0a,#0)#!a0 -8)(a7 6& 8)$*)< /& a,#4# ,a$a &0 0&*a!+a%)&!+# /& 0#8/&+a00&8 ,$#,)#8 /&0 ,$&8&!+& &8+/)#.

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    Pa$a &0 0&*a!+a%)&!+# +#,#$-(# 8& &%,0&< 51 E8+a()

    La a+#%a+):a()

    D$a!+& 4 !a *&: +&$%)!a/# &0 +$aa# &! (a%,# /& +#,#$a"9a 8&,$#(&/)< a0 ,$#(&8a%)&!+# &! a)!&+& /& 0a )!"#$%a()

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    &!0a:a$ 0a P#0)#!a0 B-8)(a 6& 8& &8+a0&()&$#! ,a$a &0 L&*a!+a%)&!+#T#,#$-(# (#! 0a R&/ G/'8)(a H#$):#!+a0 Na()#!a0.

    Pa$a 0a #!a /& &8+/)# 8& &8+a0&()< 0a P#0)#!a0 B-8)(a= (#! !a 09!&a a8& /&)!)()# BM? 51 BM?52

    ..2E6),# 4 P&$8#!a0 /& I!&!)&$9a&%,0&a/#

    E0 (#!+$#0 +#,#$-(# "& 00&*a/# a (a# &! "#$%a /)a$)a /&8/& &0 1 /&Ma$:# a0 2 /& Ma$:# /& 2512= %&/)a!+& &0 8# /&7

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    P&$8#!a0E%,0&a/#7

    51 I!&!)&$# G&

    COORDENADAS TOTALES

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    REFERENCIA BM?52 >KKK. [email protected] 21K.52

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    &0)%)!a 0#8 &$$#$&8 /&0 (-0(0# /& -!0#8 3#$):#!+a0&8 4 *&$+)(a0&8 6& 8&,$#/(&! !#$%a0%&!+& &! 0#8 +/#0)+#8 (#!*&!()#!a0&8. E0 ,$)!(),)# /&0&(+$a &8+- a8a/# &! 0a 0&(+$a /& !a 8&a0 )!+&$a/a 8#$& 0a 8,&$()&(#%,0&+a /&0 /)8,#8)+)*# &0&(+$

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    ..>.1 C-0(0# /&0 A!0# H#$):#!+a0

    La "AH =AHS

    + EH

    1

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    V

    + YH

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    tanV

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    ..>. M&/)()

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    A (#!+)!a()

    DH = DG senZ DG

    2 sen 2Z K 1

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    2

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    2 RT

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    ( )

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    &!0a:a$ &8+a a0+$a (#! +#/#8 0#8 *'$+)(&8 /& 0a P#0)#!a0 -8)(a= %&/)a!+&!)*&0a()

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    La 0&(+$a 31 *)8+a a+$-8 8& &"&(+a 8#$& 0a %)$a (#0#(a/a &! &0 ,!+# BME8+a %)$a 8& +$a!8,#$+a &!8&)/a a0 ,!+# 1 /#!/& a 8 *&: 8& 3a(& 0a0&(+$a 32 *)8+a a/&0a!+& 4 a89 8(&8)*a%&!+& (#! &0 $&8+# /& 0#8 ,!+#8.

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    NIVELACIN APRO\IMADA TERCER ORDEN S& +)0):a ,a$a

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    ERROR TOLERABLE= 0.15 DISTANCIAENkm

    NIVELACIN ORDINARIA S& +)0):a ,a$a +$a:#8 /& $+a8 &!(a%)!#= *)8a0&8 /& 3a8+a 15 %= 0&(+$a &! 0a %)$a (#!a,$#)%a()

    ERROR TOLERABLE= 0.04 DISTANCIAENkm

    NIVELACIN PRECISA SEGUNDO ORDEN S& +)0):a ,a$a (#0#(a$BM. &! #$a8 /& )!&!)&$9a= *)8a0&8 /& 3a8+a 155 %= 0&(+$a8 &!0a %)$a (#! a,$#)%a()

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    0&(+$a8 &%,0&a!/# ,a$a 0#8 ,!+#8 /& (a%)# &8+a(a8 (#!(0a*#8 # &8(#)&!/# #&+#8 )&! #8.

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

    Pa.

    ERROR TOLERABLE= 0.02DISTANCIAENkm

    NIVELACIN DE PRECISIN PRIMER ORDEN S& +)0):a ,a$a&8+a0&(&$ BM. (#! $a! ,$&()8)

    %%= 0&4&!/# (#! 0#8 3)0#8 &8+a/)%'+$)(#8 ,a$a ,$#%&/)a$ 4(#$$##$a$ 0a 0&(+$a /&0 3)0# %&/)#. E0 !)*&0 /&& &8+a$ ,$#+&)/#/&0 8#0 ,a$a 6& 0a $a /& !)*&0 !# 8& /&8"a8&. La /)8+a!()a/& *)8+a a+$-8 4 *)8+a a/&0a!+& /&&! 8&$ )a0&8 4 %&/)/#8 (#!0#8 3)0#8 &8+a/)%'+$)(#8.

    ERROR

    TOLERABLE= 0.01DISTANCIAENkm

    Pa$a &0 ,$&8&!+& ,$#4&(+# 8& &%,0&< 0a !)*&0a()

    U!a *&: %a+&$)a0):a/#8 0#8 *'$+)(&8 /& 0a ,#0)#!a0 &! &0 +&$$&!# 8& ,$#(&/).1 E6),#&%,0&a/#

    L#8 /a+#8 (#$$&8,#!/)&!+&8 a0 0&*a!+a%)&!+# +#,#$-(# 3a! 8)/# ,$#(&8a/#8&! 8)8+&%a8 (#%,+a$):a/#8= +)0):a!/# 0#8 8))&!+&8 &6),#8 4 3&$$a%)&!+a87

    51 PC I!+&0 R TM ) CPU 2.K GH: /& >.5 GB /& RAM. S#"+a$& G/)%&+&$ S#"+a$& T##08 2.5= ,a$a +$a!8%)+)$ +#/a 0a

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    S& (#%,&!8a! 0#8 -!0#8 3#$):#!+a0&8 #8&$*a/#8 &! (a%,# ,a$a 6&(%,0a! 0a (#!/)()

    La /)"&$&!()a &!+$& 0a8 (##$/&!a/a8 (a0(0a/a8 4 0a8 (##$/&!a/a8 /&0,!+# /& )!)()# 8& /&& $&,a$+)$ ,$#,#$()#!a0%&!+& &! +#/a 0a,#0)#!a0= #+&!)&!/# (##$/&!a/a8 +#,#$-(a8.

    D&)/# a0 E$$#$ /& C)&$$& L)!&a0= 0a8 (##$/&!a/a8 (a0(0a/a8 /&&! (#$$&)$8&%&/)a!+& !a (#%,&!8a()

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0aQ&$a/a

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    >. P0a!# T#,#$-(# /& 0a :#!a ($)+)(a.

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    :#!a8 ($9+)(a 4 &0 -$&a8 /&0 +$aa# 6& (#!8)/&$# &0 ,$#4&(+#.

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    !a"#$% N& 02 Le'antam#ent% T%(%)!a"#$%

    CENTRO DE EST*DIOS Y

    +REVENCION DE DESASTRES+LANO DE +LANTA + , 01

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    !a"#$% N& 0- +e!"#. t!ans'e!sa/es

    CENTRO DE EST*DIOS Y ST , 01

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    4$&$&8

    !a"#$% N& 04 +e!"#/ L%n)#td#na

    CENTRO DE EST*DIOS Y+REVENCION DE DESASTRES

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    . CONCLUSIONES

    A(+a0%&!+& &! 0a :#!a /&0 ,$#4&(+# ,$&8&!+a $a!/& *a$)a()#!&8+#,#$-(a8= -$&a8 (#%,0&a8 &! $&0a()

    E0 +$aa# /'8)(# &8+- $&"&$)/# a0 Ma$(# /& R&"&$&!()a T&$$&8+$&I!+&$!a()#!a0 1KK> ITRFK> /&0 8&$*)()# I!+&$!a()#!a0 /& R#+a()

    T)&$$a IERS (#! /a+#8 /& 0a ',#(a 1KK.>= 6& &8 &0 S)8+&%a G/'8)(# /&R&"&$&!()a O()a0 ,a$a &0 P&$.

    E0 DATUM # %#/&0# &8 &0 &0),8#)/& GS>. E0 %#/&0# )/a0 &8 &0 EGMK@ G0#a0 S& 3a +)0):a/# &0 &0),8#)/& #$0/ G/&+)( S48+&%8 1K> GS?> La :#!a 0&*a!+a/a 8& &!(&!+$a &!+&$a%&!+& &! 0a #!a 1L. Pa$a &0 (#!+$#0 H#$):#!+a0= 8& +)0):< &0 %'+#/# D)"&$&!()a0 # E8+-+)(#= &0 (a0

    (#!8)8+& &! (#0#(a$ ! &6),# GPS Ma8+&$ BASE= &! &0 P!+# G/'8)(# (#!(##$/&!a/a8 (#!#()/a8= ,a$a &8+& ,$#4&(+# 8& +)0):< &0 ,!+# /& 0a

    E8+a()

    S& 3a $&a0):a/# &0 &!0a(& a 0a E8+a()

    a$a!+):a 0a (#!a)0)/a/ /& 0#8 ,!+#8= ,a$a &0 /&8a$$#00# /& ,$#4&(+#8 /&)!&!)&$9a.

    E0 (#!+$#0 +#,#$-(# /& (a%,# "& 00&*a/# a (a# &! "#$%a /)a$)a+)0):a!/#7 U!a E8+a() &6),# /& $a/)# (#%!)(a()= ,a$a &0 ,$#(&8a%)&!+# /& 0#8 /a+#8 +#%a/#8 &! (a%,#= &0 S#"+a$&A+#CAD= ,a$a 0a ,$&8&!+a()

    L#8 +$aa#8 $&"&$&!+&8 a0 0&*a!+a%)&!+# +#,#$-(# &8+-! $&"&$)/#8 a(##$/&!a/a8 /& ,$#4&(().

    La (#%,&!8a()@=555= 0a (#%,&!8a()

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    I!"#$%& T'(!)(#L&*a!+a%)&!+# T#,#$-(# /& 0a Q&$a/a

    Sa3a!a4 E+a,a N 51 E+a,a N 52 Pa. 2