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11--D D MagnetotelluricMagnetotelluric (MT)(MT)ModellingModelling

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ApparentApparent resistivityresistivity and phase sounding curves and phase sounding curves

??

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data processing data processing

field datafield data

measurementmeasurement

observed parameters observed parameters (Earth(Earth’’s response / signals)s response / signals)

Geophysics framework (1)Geophysics framework (1)

interpretationinterpretation

Data presentation Data presentation

PseudoPseudo--section section

→→ 22--D plot of apparent D plot of apparent resistivityresistivity and phase data from and phase data from MT soundingsMT soundings on a profile on a profile

→→ horizontal axis is distance or station position horizontal axis is distance or station position

→→ vertical axis is frequency or period (increasing vertical axis is frequency or period (increasing periods downward ~ increasing depth)periods downward ~ increasing depth)

→→ Color contoured: Color contoured: low low resistivityresistivity (or high impedance phase) ~ red(or high impedance phase) ~ redhigh high resistivityresistivity (or low impedance phase) ~ blue(or low impedance phase) ~ blue

→→ Qualitative 2Qualitative 2--D D resistivityresistivity distribution for preliminary distribution for preliminary interpretationinterpretation

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Data presentation Data presentation

Apparent Apparent resistivityresistivity and phase maps and phase maps

→→ Plot of data from MT soundingsPlot of data from MT soundings on a map (on a map (for a for a certain frequency or period)certain frequency or period)

→→ Qualitative lateral parameter variation at a certain Qualitative lateral parameter variation at a certain depth (equivalent with frequency or period) depth (equivalent with frequency or period)

Maps of other parameters Maps of other parameters

PseudoPseudo--sectionsection

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Apparent Apparent resistivityresistivitymapmap

ρρaaTETE TT == 1 sec.1 sec.

Apparent Apparent resistivityresistivitymapmap

ρρaaTETE TT == 10 sec.10 sec.

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data processing data processing

field datafield data

measurementmeasurement

observed parameters observed parameters (Earth(Earth’’s response / signals)s response / signals)

Geophysics framework (2)Geophysics framework (2)

modellingmodelling + interpretation+ interpretation

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ApparentApparent resistivityresistivity and phase sounding curves and phase sounding curves

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Geophysical Modeling

MaxwellMaxwell’’s equations (with constitutive equations)s equations (with constitutive equations)

EM wave (diffusion) equation EM wave (diffusion) equation

solution to diffusion equation solution to diffusion equation boundary conditions boundary conditions

EM fields in the medium (MT response) EM fields in the medium (MT response)

Concept of MT forward Concept of MT forward modellingmodelling

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Elementary solution to MaxwellElementary solution to Maxwell’’s equations in 1s equations in 1--DD

Impedance in 1Impedance in 1--DD

→→ A and and B are constants to be determined from are constants to be determined from boundary conditions boundary conditions

EExx = = A A exp (exp (–– kk zz)) ++ B B exp (exp (++ kk zz))

HHyy == ((A A exp (exp (–– kk zz)) –– B B exp (exp (++ kk zz))))kk________________

ii ωωµµ00

EExx__________

HHyyZZxyxy = == =

A A exp (exp (–– kk zz)) ++ B B exp (exp (++ kk zz))______________________________________________________________

A A exp (exp (–– kk zz)) –– B B exp (exp (++ kk zz))ii ωωµµ00______________

kk

Consider Consider NN––layer medium with layer layer medium with layer resistivityresistivity ρρjj and and layer thickness layer thickness hhjj ; ; jj = = 1,1, 2, 3, 2, 3, …… NN

Impedance at each layer is defined at the top of the layer Impedance at each layer is defined at the top of the layer then impedance at the surface is then impedance at the surface is ZZ11

surface

ρ 1 h 1

z 1= 0

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.

z 2

z 3

z N-1

z N

ρ 2 h 2

ρ N -1 h N-1

ρ N

jj––thth layerlayer

ZZjj

ZZ11

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Applying boundary conditions for 1Applying boundary conditions for 1--D or layered medium D or layered medium results in a recursive formula relating impedance of two results in a recursive formula relating impedance of two consecutive layersconsecutive layers

→→ Z00jj == ((iiωωµµ00ρρjj))1/21/2 = intrinsicintrinsic impedanceimpedance

kjj == ((iiωωµµ00/ρρjj))1/21/2 = = Z00jj /ρρjj

→→ impedance at impedance at jj––thth layer as function of the layerlayer as function of the layer’’s s parameters (parameters (ρρjj ,, hhjj ) and impedance at the ) and impedance at the subsequent subsequent layerlayer Zj+j+11

ZZjj = = ZZ00jj1 1 –– RRjj exp (exp (–– 22 kkjj hhjj))________________________________________________

11 ++ RRjj exp (exp (–– 22 kkjj hhjj))RRjj = =

ZZ00jj –– ZZjj+1+1________________________

ZZ00jj ++ ZZjj+1+1

Algorithm for MT 1Algorithm for MT 1--D forward D forward modellingmodelling

→→ calculate calculate impedance at impedance at NN––thth (or last) layer(or last) layer

ZNN == Z00NN == ((iiωωµµ00ρρNN))1/21/2

→→ calculatecalculate impedance at impedance at ((NN--11))––thth layer using layer using recursive formula, recursive formula, Zjj == ZNN--11 ; ; Zj+j+1 1 == ZNN

→→ proceed upward to obtain impedance at the proceed upward to obtain impedance at the surface of the surface of the NN layered model, layered model, Z11

→→ calculate apparent calculate apparent resistivityresistivity ρρaa and phase and phase φφ from from Z11

→→ proceed for different frequencies proceed for different frequencies f ii or periods or periods Tii

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Impedance at the Impedance at the surface of the Earthsurface of the Earth

. . .. . .

Impedance at the (Impedance at the (NN--1)1)thth layerlayer

impedance at the surface ofimpedance at the surface ofthe last (the last (NNthth) layer, intrinsic ) layer, intrinsic impedanceimpedance

Algorithm for MT 1Algorithm for MT 1--D forward D forward modellingmodelling

surface

ρ 1 h 1

z 1= 0

.

.

.

z 2

z 3

z N-1

z N

ρ 2 h 2

ρ N -1 h N-1

ρ N

ZZNN

ZZNN--11

ZZ33

ZZ22

ZZ11

Algorithm for MT 1Algorithm for MT 1--D D forward forward modellingmodelling

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MTINV1DMTINV1D →→ MT 1MT 1--D D modellingmodelling by Dr. by Dr. MarkuMarku Pirttijärvi, Department of Geosciences University of Oulu, Finland (http://www.gf.oulu.fi/~mpi)

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IP2WIN_MTIP2WIN_MT

→→ MT 1MT 1--D D modellingmodelling by Dr. by Dr. AlexeyAlexey BobachevBobachev, demo , demo version available on internet version available on internet

→→ http://http://geophys.geol.msu.rugeophys.geol.msu.ru

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____√√ TT

ρρaa

φφ

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MT 1MT 1--D smooth D smooth modellingmodelling→→ OCCAM inversion (Constable et al., 1987) OCCAM inversion (Constable et al., 1987) →→ Markov Chain Monte Carlo (MCMC) algorithm (Markov Chain Monte Carlo (MCMC) algorithm (GrandisGrandis et al., 1999)et al., 1999)

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22--D D resistivityresistivity sectionsectionfrom 1from 1--D models on D models on a profilea profile

→→ correlation of correlation of resistivityresistivity unitsunitsfrom station to from station to stationstation

→→ correlation of correlation of resistivityresistivity units with units with geology and geology and lithologylithology