metode inversi pada pengolahan mt.docx

7/26/2019 Metode Inversi pada Pengolahan MT.docx

1/16

TASK OF ELECTROMAGNETIC EXPLORATION

Inversion Method on Magnetotelluri !ata Proessing

Arranged "#$

Fuad Aulia Bahri 3713100007

M. Arif Budiman 3713100048

Leturer$

Wien lestari, S.T., M.T.

!e%arte&ent o' Geo%h#sial Engineering

Fault# o' Civil Engineering and Planolog#

Se%uluh No%e&"er Institute o' Te(nologi

)*+,


2/16

Some inversion methods that are used for MT modellin

1. Monte !arlo

This &ethod is one o' inversion tehni-ue that onerned o' e.%eri&ents on rando&

nu&"ers/ Monte Carlo also "e used 'or deter&inisti %ro"le&0 'or e.a&%le evaluating

&ultidi&ensional integrals/ Monte Carlo &eant generating disrete Earth Models in a

uni'or& rando& "et1een u%%er and lo1er "ounds0 1hih 1ere hosen a %riori/ For

eletro&agneti data0 suh as Magnetotelluri0 this &ethod 1e a%%lied to inversion data 'or a

&odelling have to%ogra%h# &odels and to &odelling another/ This diagra& "elo1 e.%lain the

%roess o' Monte Carlo Inversion $

Picture.1. Monte Carlo FlowChart Process


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As 'or the a%%liation o' this &ethod are$

Gra%hi0 es%eiall# 'orray tracing

light trans%ort &odelling in a multi-layered tissues (MCML)

Monte Carlo &ethod on 'inanial setor

si&ulation o' %rotein struture %redition

2sed to &odel the 'lo1 o' arrier trans%ort In the researh o' se&iondutor

e-ui%&ent

Geneti Ma%%ing involving hundreds o' geneti &ar(ers and 3TL anal#sis

". #$$am

A si&%le &odel ontaining the essential %ro%erties o' all %ossi"le &odels 'itting the

'ield data/ A large nu&"er o' geoeletri &odels ould &ath the o"served data0 so&e o'

1hih &a# "e ver# o&%le./ 4hen atte&%ting to ahieve a "etter 'it "et1een s&all %ortions

o' the alulated and o"served urve o' 56780 96780 the o&%le.it# o' the o"tained &odel

inreases and the results are o'ten unrelia"le/ The &odel should "e as o&%le. as the

&ediu&0 "ut not &ore o&%le./ The algorith& de%arts 'ro& a hal's%ae and %rodues a

strati'ied &ediu&/ The resistivities var# until an ade-uate 'it "et1een the 'ield and alulated

urves is ahieved/ Roughness 6or the inverse o' so'tness8 is de'ined in ter&s o' the 'irst and

the seond derivatives o' the eletri resistivit# 1ith res%et to the de%th as

R1= ( dm

dz)2

dz

R2= (d2mdz2)2dz

4here $

& 6:8 ; the resistivit# or log resistivit#

< ; the de%th

R+ and R) ; roughness 'untions

3. Bosti$%
https://id.wikipedia.org/w/index.php?title=Ray_tracing&action=edit&redlink=1https://id.wikipedia.org/w/index.php?title=Ray_tracing&action=edit&redlink=1https://id.wikipedia.org/w/index.php?title=Metode_Monte_Carlo_dalam_bidang_finansial&action=edit&redlink=1https://id.wikipedia.org/w/index.php?title=Metode_Monte_Carlo_dalam_bidang_finansial&action=edit&redlink=1https://id.wikipedia.org/w/index.php?title=Ray_tracing&action=edit&redlink=1


4/16

This Inversion &ethod is the 'astest and easiest 1a# to esti&ate the variation o'

resistivit# against de%th that is diretl# 'ro& urve o' %seudo resistivit# sounding/ This

&ethod are derived 'ro& anal#ti relation o' resistivit#0 're-uen#0 and investigation de%th or

s(in de%th/ =ut0 this &ethod an onl# "e done as &odelling and inter%reting 'or %reli&inar#

identi'iation/

On this least>s-uare inversion &ethod0 %reli&inar# &odel is iterativel# &odi'ied to

o"tain a res%onse &odel that 'its the data/ Their a%%ro.i&ation or lineari:ed non>linear

'untion "et1een data and &odel %ara&eters lead =osti( inversion &ethod to "e ver#

sensitive to the seletion o' the initial &odel/ There'ore0 the initial &odel is usuall#

deter&ined 'ro& the results o' the indiret &odeling or inversion results =osti(/ =iosti(

Inversion$

4here0

: ; s(in de%th

5a ; a%%arent resistivit#

7 ; 're-uen#

1 & MT 'ro$essin &ata (sin For)ad Modellin *Matla+

The sri%t 1ere ta(en 'ro& htt%$??111/digitalearthla"/o&?tutorial?tutorial>+d>&t>

'or1ard?that is 1ritten "# Andre1 Petti(0 )*+@/ This sri%t e.%lain a"out ho1 to %roessing

&agnetotelluri data/ =ut0 this sri%t is not using inverse &odelling %roess0 "ut using

'or1ard &odelling/ This sri%t also o"tain onstantl# out%ut "eause it doesnt have iteration/

Main S$ri-t
http://www.digitalearthlab.com/tutorial/tutorial-1d-mt-forward/http://www.digitalearthlab.com/tutorial/tutorial-1d-mt-forward/http://www.digitalearthlab.com/tutorial/tutorial-1d-mt-forward/http://www.digitalearthlab.com/tutorial/tutorial-1d-mt-forward/


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clear all;

clc;

figure(1);

close(1);

disp('====================================' );

disp('1D MAGNETOTELLUR! MODELLNG "ROGRAM');

disp('====================================' );

disp(' LA#T U"DATED $%T& DE!EMER $1 ');

disp(' DE*ELO"ED + ANDRE, "ET&!- ');

disp(' ,,,.DGTALEART&LA.!OM ');

disp('====================================' );

disp('');

disp(' lice/sed u/der ,T0"L')

disp('');

daa = load('daa.2');

daa0re3ue/cies = daa(451);

daaAppare/Resisi6iies = daa(45$);

daaError = daa(45);

7daa a8e/ fro9 elford

resisi6iies = : $ .< $;

>ic8/esses = :$ ? ? ;

daaModelledAppare/Resisi6iies =

@eros(le/g>(daaAppare/Resisi6iies)51);

fori = 1 4 le/g>(daa0re3ue/cies)

fre3ue/c = daa0re3ue/cies(i);

:appare/Resisi6i = 9odelMT(resisi6iies5 >ic8/esses5

fre3ue/c);

daaModelledAppare/Resisi6iies(i) = appare/Resisi6i;

e/d

7!alculae Misfi

9isfi = @eros(le/g>(daaAppare/Resisi6iies)51);

fori = 1 4 le/g>(daa0re3ue/cies)

d = daaAppare/Resisi6iies(i);

9 = daaModelledAppare/Resisi6iies(i);

e = daaError(i);

9isfi(i) = ((9 B e)C$)((de1))C$;

e/d

7!reae arra of fre3ue/cies fro9 1CB? o 1C?&@

7i.e. fre3ue/cies = 1C/5 F>ere / = B?5B.%5B.(fre3ue/cies)51);

fori = 1 4 le/g>(fre3ue/cies)

fre3ue/c = fre3ue/cies(i); :appare/Resisi6i = 9odelMT(resisi6iies5 >ic8/esses5

Input therequired MT Data

Syntax is for

calculating the


6/16

fre3ue/c);

appare/Resisi6iies(i) = appare/Resisi6i;

e/d

ear>ModelTe2 = rep9a(cellsr('')5 le/g>(resisi6iies $)51);

ear>ModelTe2H1I = :'Misfi = ' /u9$sr(su9(9isfi)) '7';

ear>ModelTe2H$I = :'Laer '' Resisi6i '' T>ic8/ess';

fori = 1 4 le/g>(resisi6iies)

resisi6i = resisi6iies(i);

9ai/Te2 = :'Laer '/u9$sr(i) ' ' /u9$sr(resisi6i) ' O>9 9

';

ear>ModelTe2Hi $I = 9ai/Te2;

if(i == le/g>(resisi6iies))

ear>ModelTe2Hi$I = :ear>ModelTe2Hi$I '&alfspace';

else

ear>ModelTe2Hi$I = :ear>ModelTe2Hi$I /u9$sr(>ic8/esses(i))

'9';

e/d

e/d

7"lo for eac> resisi6i

scrs@ = ge(5'#cree/#i@e');

figure(1)

se(15'"osiio/'5: % ?);

= spli/e(daa0re3ue/cies5daaAppare/Resisi6iies5daa0re3ue/cies);

suJplo(15 ?5 :15)

loglog(fre3ue/cies5appare/Resisi6iies5 'Br'5'Li/e,id>'5$);

>old o/

loglog(daa0re3ue/cies5daaAppare/Resisi6iies5 'B

Js'5'Li/e,id>'515'Mar8er#i@e'55'Mar8er0ace!olor'5'J');

loglog(daa0re3ue/cies5daaModelledAppare/Resisi6iies5 'rs'5'Li/e,id>'

515'Mar8er#i@e'55'Mar8er0ace!olor'5'r');

7se(ge(AK($)5'+laJel')5'#ri/g'5'Error (7)');

lege/d('0ield Daa'5'Modelled Daa');

>old off

ile(H:'Appare/ Resisi6i (O>9 9) 6s 0re3ue/c(&@)'I);

2laJel('0re3ue/c (&@)');

laJel('Appare/ Resisi6i (O>9 9)');

suJplo(15?5?);

e2(5.5ear>ModelTe2);

a2is off

2laJel('0re3ue/c (&@)');

laJel('B0ield (T)');


7/16

Fro& that sri%t0 Authors 1ill need 'untion 6'.8 to in%ut MT e-uation/ This sri%t

"elo1 is ontents 'ro& &odel MT/M

Script Model MT.M7 Digial Ear> LaJ

7 FFF.DigialEar>LaJ.co9

7 ,rie/ J A/dreF "e>ic8 $1

7 Las Updaed OcoJer $%> $1

7 Lice/sed u/der ,T0"L

fu/cio/:appare/Resisi6i5 p>ase = 9odelMT(resisi6iies5

>ic8/esses5fre3ue/c)

9u = ?pi1EB; 7Mag/eic "er9eaJili (&9)

F = $ pi fre3ue/c; 7A/gular 0re3ue/c (Radia/s);

/=le/g>(resisi6iies); 7Nu9Jer of Laers

i9peda/ces = @eros(/51);

7Laeri/g i/ >is for9a

7 Laer

7 Laer 1 1

7 Laer $ $

7 Laer

7 Laer ? ?

7 ase9e/

7

7 #eps for 9odelli/g (for eac> geoelecric 9odel a/d fre3ue/c)

7 1. !o9pue Jase9e/ i9peda/ce / usi/g s3r((F 9u resisi6i))

7 $. erae fro9 Joo9 laer o op(/o >e Jase9e/)

7 $.1. !alculae i/ducio/ para9eers

7 $.$. !alculae E2po/e/ial facor fro9 i/ri/sic i9peda/ce

7 $. !alculae reflecio/ coeficie/ usi/g curre/ laer

7 i/ri/sic i9peda/ce a/d >e JeloF laer i9peda/ce

7 . !o9pue appare/ resisi6i fro9 op laer i9peda/ce

7 appare/ resisi6i = (/C$)(9u F)

7#9Jols

7 / B ase9e/ 9peda/ce

7 i B Laer 9peda/ce

7 Fi B /ri/sic 9peda/ce

7 di B /ducio/ para9eer

7 ei B E2po/e/ial 0acor

7 ri B Reflecio/ coeficie/

7 re B Ear> R.!.

7#ep 1 4 !alculae Jase9e/ i9peda/ce

/ = s3r(s3r(B1)F9uresisi6iies(/));

i9peda/ces(/) = /;


8/16

7erae >roug> laers sari/g fro9 laer =/B1 (i.e. >e laer aJo6e

>e Jase9e/)

for = /B14B141

resisi6i = resisi6iies();

>ic8/ess = >ic8/esses();

7 . !o9pue appare/ resisi6i fro9 op laer i9peda/ce

7#ep $. erae fro9 Joo9 laer o op(/o >e Jase9e/)

7 #ep $.1 !alculae >e i/ri/sic i9peda/ce of curre/ laer

d = s3r(s3r(B1) (F 9u (1resisi6i)));

F = d resisi6i;

7 #ep $.$ !alculae E2po/e/ial facor fro9 i/ri/sic i9peda/ce

e = e2p(B$>ic8/essd);

7 #ep $. !alculae reflecio/ coeficie/ usi/g curre/ laer

7 i/ri/sic i9peda/ce a/d >e JeloF laer i9peda/ce

JeloF9peda/ce = i9peda/ces( 1);

r = (F B JeloF9peda/ce)(F JeloF9peda/ce);

re = re;

= F ((1 B re)(1 re));

i9peda/ces() = ;

e/d

7 #ep . !o9pue appare/ resisi6i fro9 op laer i9peda/ce

= i9peda/ces(1);

aJs = aJs();

appare/Resisi6i = (aJs aJs)(9u F);

p>ase = aa/$(i9ag()5real());

A'ter that0 Authors 1ere doing running on Matla" so this 1indo1 1ill %o% out li(e

%iture "elo1/ Inside the 1indo1 thereBs a line 1ith red olour 1hih is a alulation data

su%%osed to "e/ Then0 thereBs a line 1ith "lue olour 1hih is the real data/ The 'arther the

distane "et1een the "lue line and the red line0 the greater the error 6&is'it8/


9/16

Picture.1. !utput fro" MT Data Processing ia "atla#

The data 'ro& Matla" ould "e &odi'ied 'reel# as Authors 1ish/ Other than that0

Author also ould in%ut resistivit# and thi(ness data li(e %itures "elo1$

Picture.$. Input data for 1D MT forward "odelling ia we


10/16

Picture.%. !utput data for 1D MT forward "odelling ia we#

MT 'ro$essin &ata (sin nverse Modellin

Authors didnBt get the sri%t 'or inverse &odelling0 "ut Authors get a so't1are 'or MT

%roessing "ased 'ro& inverse &odelling 'ro& 6I&a& =/ Raharo0 !e%t/ o' Geolog# and

Geo%h#sis0 The 2niversit# o' 2tah0 Salt La(e Cit#0 2T/0 2/S/A/0 )**D8/ These %itures

"elo1 sho1 ala&eda so't1are that is used on inverse modellin 1&/MT.


11/16

Picture.%. Display of app resistiity s period

Firstl# Start?Restart Inver0 one ste% ? invert 'ive ste%s

ere are the result 'ro& ste% "# ste% inversion

ere are the result a'ter &an# iteration

1 $

% &


12/16

Picture.%. Display of plot resistiity s depth

$'

1(

%$

1


13/16

The 'ollo1ing %itures are the dis%la# 'ro& )! MT Modelling so't1are to %roessed

"& MT &ata.

In%ut the data li( alulate

Picture.%. Data and calculation of apparent resistiity

Cli( gra%h to sho1 the geo&etr#

Picture.%. )cquisitions of MT *eo"etry

Cli( urves TE to o"tain the urve


14/16

Picture.%. )cquisitions of MT *eo"etry

Also0 thereBs so't1are o' geother&al %roet tool/ This so't1are an not "e used on

MT alulation0 "ut this so't1are are su%%osed to alulate the %ro"a"ilit# 'ro& e.isting data

1ith Monte Carlo Inversion %rini%le/

Pictu

re.%. Inersion of Monte Carlo


15/16

Picture.%. Inersion of Monte Carlo

Picture.%. Inersion of Monte Carlo


16/16

eferen$es

=aso(ur A T +H !e'initions o' a%%arent resistivit# 'or the %resentation o'

&agnetotelluri sounding data Geo%h#sial Pros%eting H) +H+J+H/

Cagniard L +@ =asi theor# o' &agnetotelluri &ethod o' geo%h#sial %ros%eting

Geo%h#sis +D ,*J,@/

Ni1as S0 Gu%ta P K and Gaur K )** Nor&ali:ed i&%edane 'untion and the

straight'or1ard inversion she&e 'or &agnetotelluri data / Earth S#st/ Si/ ++H )@>@+/

Pederesen F and er&ane +D, Least>s-uare inversion o' one>di&ensional

&agnetotelluri data$ An assess&ent o' %roedures e&%lo#ed "# =ro1n 2niversit# Surv/

Geo%h#s/

D +DJ)@+/

4eidelt P +) The inverse %ro"le& o' geo&agneti indution

metode inversi pada pengolahan mt.docx

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