A Brief Introduction to Magnetotellurics and Controlled Source Electromagnetic Methods Frank Morrison U.C. Berkeley With the help of: David Alumbaugh Erika Gasperikova Mike Hoversten Andrea Zirilli
A few equations for MT and CSEM Ohm s Law: J = σe D = εe Ampere s Law: D E H = J + = σe + ε t t For most rocks and for frequencies less than 1.0 MHz Faraday s Law: H E = µ 0 t These equations may be combined to yield: σe E ε t E µ σ = 0 A diffusion equation t 2 E 0
The MT Method The ratio of electric (E) to magnetic (H) fields at a frequency ω is related to the resistivity of the ground by: E H From which: iρωµ = = ρ a = 1 ωµ E H Z (impedance) 2 V L E x = V L J x H y (t)
The fields at the surface attenuate rapidly as they diffuse downward. The depth at which they fall to 1/e their value at the surface is the skin depth, δ. δ H e 0 H 0 2 ρ δ = = 500 µσω f
Low frequencies penetrate more deeply than high frequencies, so ρ A calculated from a range of frequencies produces a sounding. ρ high ρ low ρ a ρ high Frequency
y TM (XY) Strike direction 2-D structure TE (YX) x Profile direction TM mode: Z XY = E X /H Y TE mode: Z YX = E Y /H X
In general the impedance is a tensor. The tensor can be diagonalized over a 2-D structure into the principal TE and TM modes.
) ( )H ( Z ) ( )H ( Z ) ( E ) ( )H ( Z ) ( )H ( Z ) ( E y yy x yx y y xy x xx x ω ω + ω ω = ω ω ω + ω ω = ω y x yy yx xy xx y x H H Z Z Z Z E E =
The vertical contact illustrates some basic behavior of TE and TM modes and the role of boundary conditions in the results. Tangential E and H must be continuous. Normal J must be continuous and so normal E must be discontinuous. Consequently the TE mode apparent resistivity must vary smoothly across the contact while the TM mode is discontinuous. Also because there can be no vertical current then H = J D + t forces Hy to be constant for the TM mode for 2-D models. All the apparent resistivity response is from variations in E.
Apparent Resistivity (Ohm-m) 1000 100 10 1 TM-response TE-response -2000 0 2000 Distance (m) 0-2000 0 2000 (meters) Depth (m) 1000 10 Ohm-m 100 Ohm-m Vertical contact
Vertical contact - TM response
Vertical contact - TE response
The apparent resistivity, and the phase between E and H, for both modes are normally plotted vs. frequency and horizontal location. These sections have a useful relationship to the actual resistivity variations and are more intuitively satisfying than the impedances themselves. They show: For a conductive dike: The TE mode shows the result of the increased current flow in the dike which causes an increased magnetic field over the dike. At low frequencies the effect goes away. The TM mode shows almost no response; the effect of a thin conductive zone normal to current flow is negligible. For a resistive dike: The TE mode shows no response. The dike has no effect on currents flowing parallel to it. The TM mode has essentially no inductive response at high frequencies but does reveal the essentially dc blocking effect of the dike at low frequency when current is forced to flow up and over the dike. Again, H is constant over the dike, the only response is from E. A general rule for thin resistive layers is that they only have a useful response when the current is normal to them, and conductive layers only when the current is parallel. Thus, resistive horizontal layers in a sedimentary section are relatively invisible in MT soundings.
100 m 10 Ohm-m 100 Ohm-m 50 m 1 Ohm-m Distance (m) Distance (m) 1000-2000 -1000 0 1000 2000 1000-2000 -1000 0 1000 2000 100 Resitivity (Ohm-m) 100 Phase (deg) 100-135 10 10 Frequency (Hz) 1 30 10 Frequency (Hz) 1-140 -145 0.1 0.1 3-150 0.01 0.01 1-155 0.001 0.001 TE response of conductive dike
100 m 10 Ohm-m 100 Ohm-m 50 m 1 Ohm-m Distance (m) Distance (m) 1000-2000 -1000 0 1000 2000 1000-2000 -1000 0 1000 2000 100 Resitivity (Ohm-m) 100 Phase (deg) 100 45 10 10 Frequency (Hz) 1 30 10 Frequency (Hz) 1 40 35 0.1 0.1 3 30 0.01 0.01 1 25 0.001 0.001 TM response of conductive dike
100 m 10 Ohm-m 100 Ohm-m 50 m 1000 Ohm-m Distance (m) Distance (m) 1000-2000 -1000 0 1000 2000 1000-2000 -1000 0 1000 2000 100 Resitivity (Ohm-m) 100 Phase (deg) 1000-135 Frequency (Hz) 10 1 0.1 300 100 30 Frequency (Hz) 10 1 0.1-140 -145-150 0.01 10 0.01-155 0.001 0.001 TE response of resistive dike
100 m 10 Ohm-m 100 Ohm-m 50 m 1000 Ohm-m 1000 Distance (m) -2000-1000 0 1000 2000 1000 Distance (m) -2000-1000 0 1000 2000 100 Resitivity (Ohm-m) 1000 100 Phase (deg) 45 Frequency (Hz) 10 1 0.1 300 100 Frequency (Hz) 10 1 0.1 40 35 30 30 0.01 0.01 10 25 0.001 0.001 TM response of resistive dike
MT and CSEM data are interpreted by the process of inversion: 1) A model is chosen to represent the subsurface resistivity distribution. 2) The parameters of the model are systematically varied in a numerical calculation of the response of the em system to the model until the numerical data match the observed data. A common generic model is the representation of the resistivity distribution by a discrete volume element grid or mesh: σ ij
Smooth vs. Sharp Inversion Node j-1 Node j Node j+1 ρ Boundary 2 ρ 2, j-1 ρ ij 2, j ρ 2, j+1 Boundary 3 ρ 3, j-1 ρ 3,j ρ 3,j+1 Smooth inversion - smoothing on ρ of adjacent cells Sharp inversion - smoothing on node z & lateral ρ within a region
3D View of Gemini Salt Structure
MMT Survey Line Shaded Area Represents Salt Thickness > 500m
Occam TM-mode Inversion
SBI TM-mode Inversion
The MT response over the well known Eloise ore body in Australia is an excellent example of the behavior of the TE and TM modes over a buried vertical conductive body.
100 Distance (m) 0 500 1000 Resistivity (Ohm-m) 100 Distance (m) 0 500 1000 Phase (deg 60 Frequency (Hz) 10 1 0.1 60 20 Frequency (Hz) 10 1 0.1 40 20 0.01 0 0.01 0 Eloise - TM response
Distance (m) 0 500 1000 Resistivity (Ohm-m) Distance (m) 0 500 1000 Phase (deg 100 100 Frequency (Hz) 10 1 0.1 60 20 Frequency (Hz) 10 1 0.1 224 212 200 0.01 0 0.01 188 Eloise - TE response
Distance (m) 0 500 1000 0 Resistivity (Ohm-m) 60 Depth (m) -500 20-1000 0 Eloise - RRI TM & TE Inversion
Controlled Source EM (CSEM)
Controlled source methods usually employ either two current electrodes, an electric dipole, or a loop of current carrying wire, a magnetic dipole. In the following figure the changing magnetic field from a horizontal loop source induces horizontal loop currents in the ground. As we have seen these currents would be unaffected by a thin horizontal resistive layer but would respond to a thin conductive layer. The electric dipole produces largely vertical current flow at dc and low frequency. As the frequency increases the changing magnetic field of the injected current produces counter fields which oppose the inducing fields and have the effect of distorting the current pattern and forcing it closer to the surface (see current flow vectors in later slide). The thin resistive layer has a big effect on the response because it blocks the vertical current flow.
Magnetic and Electric Sources for CSEM B field line +I I Current Loop Current Current
Magnetic and Electric Sources with thin resistive layer B field line +I I Current Loop Current
The response of a submerged electric dipole is described by the superposition of the source dipole and an image dipole located an equal distance above the interface. In the following slide the figure on the left shows the Ex fields as a transmitter comes closer to the surface from within a uniform conducting half space. At depth we see the initial 1/R 3 falloff transitioning to the exponential falloff as induction kicks in (with a little image effect at the greatest separation). As the dipole approaches the surface the image dipole acts to increase the subsurface fields and so to lessen their fall-off until we get to the halfspace fall off when the depth is zero. The second figure on the right shows the modification to the response when there is an ocean layer over a slightly more resistive bottom. The shape of the decay is modified but the general halfspace-image dipole character is unchanged. The second figure also shows the distortion in the E response, for a seawater layer of 1.0 km, caused by a resistive layer in the ocean bottom.
E-field amplitude as a function of offset
The effects of the thin resistive layer can be summarized in plots of the percentage change in the field caused by the introduction of the layer as a function of frequency and transmitter-receiver offset for a given depth of sea water.
Percent difference in E-field w/without resistive layer 10 Offset, r (m) 2000 6000 10000 14000 18000 1 Frequency (Hz) 0.1 1001 km m 0.3 10 Ohm-m T r Ex 1 km 1 Ohm-m 50 m 100 Ohm-m 1 Ohm-m 0.01 0.001-30 0 30 60 90 120 150 180 % Difference
Current flow vectors Sea water over half space 0.3 Ohm-m 1.0 km 0.7 Ohm-m
f=1x10-3 Hz
f=1x10-2 Hz
f=2.15x10-2 Hz
f=4.64x10-2 Hz
f=1x10-1 Hz
f=2.15x10-1 Hz
f=4.64x10-1 Hz
f=1hz
Current flow vectors Sea water over half space with resistive layer 0.3 Ohm-m 1.0 km 50 m 100 Ohm-m 0.7 Ohm-m
f=1x10-3 Hz
f=1x10-2 Hz
f=2.15x10-2 Hz
f=4.64x10-2 Hz
f=1x10-1 Hz
f=2.15x10-1 Hz
f=4.64x10-1 Hz
f=1hz
Comparison of current flow vectors without and with resistive layer
f=1x10-6 Hz
f=1x10-6 Hz
f=1x10-3 Hz
f=1x10-3 Hz
f=1x10-2 Hz
f=1x10-2 Hz
f=2.15x10-2 Hz
f=2.15x10-2 Hz
f=4.64x10-2 Hz
f=4.64x10-2 Hz
f=1x10-1 Hz
f=1x10-1 Hz
f=2.15x10-1 Hz
f=2.15x10-1 Hz
f=4.64x10-1 Hz
f=4.64x10-1 Hz
f=1hz
f=1hz
A few References Chave, A. D., Constable, S. C. and Edwards, R. N., 1991, Electrical exploration methods for the seafloor: in Nabighian, M. N., Ed., Electromagnetic methods in applied geophysics, 02, Soc. of Expl. Geophys., 931-966 Constable, S.C., Orange, A., Hoversten, G.M., and Morrison, H.F., 1998, Marine magnetotellurics for petroleum exploration, part 1 : A marine equipment system: Geophysics, 63, 816-825 Hoversten,G. M., Morrison, H.F., and Constable, S.C., 1998, Marine magnetotellurics for petroleum exploration, part 2: Numerical analysis of subsalt resolution: Geophysics, 63, 826-840 Hoversten, G.M., Constable, S., and Morrison, H.F., 2000, Marine magnetotellurics for base salt mapping: Gulf of Mexico field test at the Gemini structure: Geophysics, 65, 1476-1488 Smith,T., Hoversten, M., Gasperikova, E., and Morrison, H.F., 1998, Sharp Boundary Inversion of 2D Magnetotelluric Data: Geophysical Prospecting, 47, 469-486