A Brief Introduction to Magnetotellurics and Controlled Source Electromagnetic Methods

Transcription

1 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

2 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

3

4 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)

5 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

6 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

7 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

8 In general the impedance is a tensor. The tensor can be diagonalized over a 2-D structure into the principal TE and TM modes.

9 ) ( )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 =

10 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.

11 Apparent Resistivity (Ohm-m) TM-response TE-response Distance (m) (meters) Depth (m) Ohm-m 100 Ohm-m Vertical contact

12 Vertical contact - TM response

13 Vertical contact - TE response

14 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.

15 100 m 10 Ohm-m 100 Ohm-m 50 m 1 Ohm-m Distance (m) Distance (m) Resitivity (Ohm-m) 100 Phase (deg) Frequency (Hz) Frequency (Hz) TE response of conductive dike

16 100 m 10 Ohm-m 100 Ohm-m 50 m 1 Ohm-m Distance (m) Distance (m) Resitivity (Ohm-m) 100 Phase (deg) Frequency (Hz) Frequency (Hz) TM response of conductive dike

17 100 m 10 Ohm-m 100 Ohm-m 50 m 1000 Ohm-m Distance (m) Distance (m) Resitivity (Ohm-m) 100 Phase (deg) Frequency (Hz) Frequency (Hz) TE response of resistive dike

18 100 m 10 Ohm-m 100 Ohm-m 50 m 1000 Ohm-m 1000 Distance (m) Distance (m) Resitivity (Ohm-m) Phase (deg) 45 Frequency (Hz) Frequency (Hz) TM response of resistive dike

19 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

20 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

21 3D View of Gemini Salt Structure

22 MMT Survey Line Shaded Area Represents Salt Thickness > 500m

23 Occam TM-mode Inversion

24 SBI TM-mode Inversion

25 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.

26 100 Distance (m) Resistivity (Ohm-m) 100 Distance (m) Phase (deg 60 Frequency (Hz) Frequency (Hz) Eloise - TM response

27 Distance (m) Resistivity (Ohm-m) Distance (m) Phase (deg Frequency (Hz) Frequency (Hz) Eloise - TE response

28 Distance (m) Resistivity (Ohm-m) 60 Depth (m) Eloise - RRI TM & TE Inversion

29 Controlled Source EM (CSEM)

30 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.

31 Magnetic and Electric Sources for CSEM B field line +I I Current Loop Current Current

32 Magnetic and Electric Sources with thin resistive layer B field line +I I Current Loop Current

33 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.

34 E-field amplitude as a function of offset

35 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.

36 Percent difference in E-field w/without resistive layer 10 Offset, r (m) Frequency (Hz) km m Ohm-m T r Ex 1 km 1 Ohm-m 50 m 100 Ohm-m 1 Ohm-m % Difference

37 Current flow vectors Sea water over half space 0.3 Ohm-m 1.0 km 0.7 Ohm-m

38 f=1x10-3 Hz

39 f=1x10-2 Hz

40 f=2.15x10-2 Hz

41 f=4.64x10-2 Hz

42 f=1x10-1 Hz

43 f=2.15x10-1 Hz

44 f=4.64x10-1 Hz

45 f=1hz

46 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

47 f=1x10-3 Hz

48 f=1x10-2 Hz

49 f=2.15x10-2 Hz

50 f=4.64x10-2 Hz

51 f=1x10-1 Hz

52 f=2.15x10-1 Hz

53 f=4.64x10-1 Hz

54 f=1hz

55 Comparison of current flow vectors without and with resistive layer

56 f=1x10-6 Hz

57 f=1x10-6 Hz

58 f=1x10-3 Hz

59 f=1x10-3 Hz

60 f=1x10-2 Hz

61 f=1x10-2 Hz

62 f=2.15x10-2 Hz

63 f=2.15x10-2 Hz

64 f=4.64x10-2 Hz

65 f=4.64x10-2 Hz

66 f=1x10-1 Hz

67 f=1x10-1 Hz

68 f=2.15x10-1 Hz

69 f=2.15x10-1 Hz

70 f=4.64x10-1 Hz

71 f=4.64x10-1 Hz

72 f=1hz

73 f=1hz

74

75 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., 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, 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, 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, Smith,T., Hoversten, M., Gasperikova, E., and Morrison, H.F., 1998, Sharp Boundary Inversion of 2D Magnetotelluric Data: Geophysical Prospecting, 47,