Magnetotelluric (MT) Method Dr. Hendra Grandis Graduate Program in Applied Geophysics Faculty of Mining and Petroleum Engineering ITB Geophysical Methods Techniques applying physical laws (or theory) to the study of the solid earth Estimation of subsurface physical property distribution by measuring relevant parameters : density gravity susceptibility magnetic field resistivity electric field, electromagnetic field seismic wave travel time velocity 1
Geo-electromagnetic electromagnetic Methods Dependence of electric and magnetic phenomena on the conductivity of the medium can be exploited to study the solid Earth Methods to estimate subsurface electrical property (resistivity)) distribution by measuring EM fields: Magnetotellurics (MT), Controlled-Source Audio-freq. MT (CSAMT), Transient EM, Very Low Freq. EM (VLF-EM), Ground Probing Radar (GPR) Electrical resistivities of rocks 2
What is magnetotellurics (MT) )? MT is a geophysical method to estimate subsurface electrical property (resistivity( or conductivity) distribution by measuring natural EM fields Source of MT signals comes from interaction of Earth s permanent magnetic field with particles from the solar wind and with atmospheric lightning no need for transmitter, simplifies the logistics random signals, low S/N (dead band ~ 1 Hz) Electromagnetic Induction transmitter generates time varying EM fields induce Eddy currents in the conductor (Earth) generate secondary magnetic field electric and magnetic fields sensed at the receiver 3
natural electromagnetic field f > 1 Hz f < 1 Hz Characteristics of MT method Infinite distance of source sounding site plane wave assumption, time invariance of the source simplifies analysis of the governing equations Frequency domain and wide frequency bands intermediate to deep investigation depth Wide range of applications regional scale geological studies/tectonics mineral, geothermal and oil exploration 4
EM induction ~ wave diffusion incident waves surface transmitted waves reflected waves spectral content, not propagation parameters MT field set-up 5
MT field set-up MT time series 6
MT time series MT time series 7
Electric (E) and magnetic (H) fields relationship For a homogeneous or layered (1-D) medium E x = Z H y Z = scalar impedance For a medium with 2-D 2 D symmetry E x = Z xy H y E y = Z yx H x Z xy Z yx For a general 3-D 3 D medium E x = Z xx H x + Z xy H y E = Z H E y = Z yx H x + Z yy H y Z = tensor impedance Data processing To extract impedance tensor Z from observed EM fields (time series of E and H) Spectral analysis and transfer function estimation Analysis of sub- surface properties contained in Z 8
MT framework EM induction theory relationship between electric (E) and magnetic (H) phenomena dependence of EM fields on electrical property (resistivity or conductivity) of the medium Observation of EM fields correlation between horizontal components of EM fields expressed as tensor impedance (Z) Extraction of subsurface parameters from Z EM theory (Maxwell s s equations) electric - magnetic phenomena represented by the Maxwell s s equations B(t) t E(t) E(t) = B(t) t 9
electric - magnetic phenomena represented by the Maxwell s s equations J(t) + D(t) t H(t) H(t) = J(t) + D(t) t Resolving the Maxwell s s equations Constitutive equations: B = µh, J = σe, D = εe Time dependency: exp(+iωt ), ω = 2π f = 2π/ T Neglecting electric displacement term (D) and variation of µ = µ 0 = 4π 10-7 H/m, ε = ε 0 Consider 1-D 1 D medium resistivity varies only with depth: ρ(z) no vertical components of EM fields horizontal components (E x, E y ) and (H x, H y ) vary with z (but do not vary with x and y) 10
component of ( E(t) = ) The x component of 2 E x z 2 = iωµ 0 σ E x The y component of E x z (1) component of ( ) = iωµ 0 H y E(t) = (2) B(t) Elementary solution to diffusion equation (1) t B(t) E x = A exp( kz) + B exp(+kz) k = (iωµ 0 /ρ) 1/2 t Elementary solution to Maxwell s s equations in 1-D1 E x = A exp ( k( z) + B exp (+k( z) k H y = (A exp ( k( z) B exp (+k( z)) i ωµ 0 EM fields as function of depth (z( > 0 downwards) terms with A represent attenuation of EM fields with increasing depth terms with B represent attenuation of EM fields with decreasing depth ("reflected" waves) A and B are constants to be determined from boundary conditions 11
Amplitude attenuation of EM fields attenuation with increasing depth (z( > 0) attenuation with decreasing depth (z( < 0) Homogeneous half-space medium (with external sources, i.e. MT) no resistivity interface at depth, i.e. no "reflection EM fields tend to zero at great depth no terms with B E x = A exp ( k( z) k H y = A exp ( k( z) i ωµ 0 attenuation with increasing depth (z( > 0) 12
Homogeneous half-space medium k = (iωµ 0 /ρ) 1/2 = α + i α α = ( 0.5 ωµ 0 /ρ) 1/2 E x = A exp ( α( z) ) exp ( iα( z) amplitude decay A(z) sinusoidal term amplitude of EM fields decays exponentially with depth and becomes negligible at certain depth Skin effect and penetration depth Skin effect = exponential EM wave attenuation with depth Skin depth (δ)( ) = depth in a homogeneous medium at which the amplitude becomes 1/e of that at the surface A(δ) = A exp ( α( δ) = A exp ( 1)( δ = (2ρ/ωµ 0 ) 1/2 500 (ρt ) 1/2 δ in meter, ρ in Ohm.m, Τ in seconds Skin depth is associated to penetration depth of EM 13
Skin effect and penetration depth δ 500 (ρt ) 1/2 Lower frequency (or higher period) and higher resistivity ~ slower attenuation ~ deeper penetration Principles of MT sounding, i.e. wide frequency band measurement probes different parts (depths) of the subsurface z Homogeneous half-space medium impedance, proportionality between E and H E x = A exp ( k( z) k H y = A exp ( k( z) i ωµ 0 Z xy E x H y i ωµ xy = = 0 = k (i ωµ 0 ρ) 1/2 Z 0 = intrinsic impedance 14
Homogeneous half-space medium intrinsic impedance Z 0 = (i ωµ 0 ρ) 1/2 Z 0 = ( 0.5 ωµ + i ( 0.5 ωµ 0 ρ) 1/2 0 ρ) 1/2 resistivity and impedance phase 1 ρ = Z 0 2 ωµ 0 φ = tan Im (Z 0 ) tan [ ] 1 Re (Z 0 ) Homogeneous half-space medium intrinsic impedance Z 0 = (i ωµ 0 ρ) 1/2 impedance (theoretical) homogeneous half-space resistivity and phase 1 ρ = Z 0 2 ωµ 0 φ = tan Im (Z 0 ) tan [ ] 1 Re (Z 0 ) resistivity (inferred) impedance (measured) 15
Measurement and data processing Measurement of orthogonal EM fields (time series) E x, E y, H x, H y Data processing to extract impedance tensor E x = Z xx E y = Z yx H x + Z xy H y H x + Z yy H y E = Z H Apparent resistivity and phase ρ a(ij ij) = 1 ωµ 0 Z ij 2 φ (ij ij) tan [ ] 1 = tan Im (Z ij ij ) Re (Z ij ij ) Apparent resistivity and phase sounding curves plot of log 10 ρ a vs. T and φ vs. T qualitatively represent resistivity as function of depth 16
Apparent resistivity and phase sounding curves APP. RESISTIVITY (Ohm.m) 1000 100 10 1 90 obs. data calc. data DEPTH (m) RESISTIVITY (Ohm.m) 1 10 100 1000 100? 1000 PHASE (deg.) 45 0 0.001 0.01 0.1 1 10 100 1000 PERIOD (sec.) 10000 Summary Electromagnetic induction concepts MT framework: Measured parameters model parameters relationship Maxwell s s equations: solution for simplest medium skin effect and penetration depth MT sounding principles MT raw data MT sounding curve 17