Consider a Geonics EM31 with the TX and RX dipoles a distance s = 3 m apart.

Transcription

1 E Near field, frequency domain EM systems E.1 EM responses of 1-D resistivity models E.1.1 Response of a halfspace Consider a Geonics EM31 with the TX and RX dipoles a distance s = 3 m apart. The TX and RX dipoles are oriented vertically This system uses a frequency f = 9.8 k. The conductivity of the Earth is σ = 0.01 S/m. Our goal is to use the magnetic field measurements to compute the conductivity of the Earth in the survey area. Previously we derived expressions for the ratio of total magnetic field to primary magnetic field. Should we use the high or low induction number limit? Using the numbers above can show that the skin depth, δ = 50.5 m. Thus, B = s = (i.e. less than 1) so we should use the low-induction number limit. Previously we showed that k s / p = 1-4 and setting k = iωμσ gives p k s 1 4 is 1 4 Setting the imaginary parts of this equation to be equal gives Im( p s ) 4 and re-arranging, gives an expression for the conductivity of the ground Martyn Unsworth, University of Alberta, September 016 1

2 4 s Im( p ) Notes: (1) If the Earth has a uniform conductivity, the measured conductivity equals the true conductivity. () In general the conductivity of the Earth will vary with horiontal position and/or depth. In this case the measured conductivity can be considered a spatially averaged conductivity (often called the apparent conductivity or terrain conductivity). (3) Calculating the average conductivity of the ground with equation above requires two measurements of the magnetic field. p (a) Measure. This is the magnetic field at the RX when the whole system is far from the influence of the conductive Earth. This usually measured once when the instrument is calibrated at the start of the survey. (b) Measure. This is the magnetic field measured at the RX at each survey location. Both TX and RX are located close to the surface of the Earth. (4) The average conductivity of the ground could be calculated from the equation derived for in section E1 IA = 5 k s k s ( 4 4 k s ) 8 owever, this would require accurate knowledge of I and A. By normaliing with p, this is avoided. Depth of investigation Just as with DC resistivity survey or MT survey, it is important to understand the depth to which the measurement of apparent conductivity extends. Consider the case of vertical TX-RX dipoles. Martyn Unsworth, University of Alberta, September 016

3 At low induction number, the secondary current flow induced in the Earth is a set of horiontal loops, as shown above. This pattern can be derived from Faradays and Len s Laws (McNeill, 1980) In principle, these current loops can induce additional secondary currents in adjacent loops. owever, at low induction number this doesn t happen, which simplifies the physics (McNeill, 1980). The secondary current is induced from the surface to a depth equal to a skin depth. The functions Φ v shows how conductivity at different depths contributes to the apparent conductivity measured by the instrument. This function is called the relative response. The subscript v indicates that the TX and RX dipole axes are pointing in a vertical direction : 4 v ( ) ; 3 (4 1) d Note that is depth in the Earth normalied by the TX-RX distance. s The vertical dipole configuration (V) has ero sensitivity at = 0, and maximum sensitivity at = 0.4 Can integrate this functions to get the cumulative response, which is the sum of the contributions from all layers below a depth For the vertical dipole configuration as: R ( ) ( ) d ; V v 1 R V ( ) ; 1 (4 1) Martyn Unsworth, University of Alberta, September 016 3

4 At low induction number, the depth of penetration is controlled by the TX-RX separation. The skin depth is generally much larger than the TX-RX separation. Vertical and horiontal dipole orientation A second measurement can be made with the TX and RX dipole axes horiontal. When the TX and RX dipoles have their axes horiontal, can show that P iks 3 e {1 [3 3iks k s ] } k s k s A similar analysis can be used to simplify this equation. oriontal dipole configuration () has a relative response Φ that has a maximum value at = 0 and then decreases monotonically with increasing, as plotted above. 4 ( ) (4 1) 3 Again we can integrate these functions to get the cumulative response, which is defined for the horiontal dipole configuration as: R ( ) ( ) d ; R ( ) (4 1) 1 Question : Can you use a sketch of the magnetic fields to explain the differences between Φ () and Φ v ()? Martyn Unsworth, University of Alberta, September 016 4

5 Note that : The vertical dipole configuration gives the greatest depth of penetration. oriontal dipole configuration is most sensitive to shallow structure oriontal dipole configuration is less sensitive to misalignment of the TX-RX coils. In the EM31 the TX and RX are rigidly fixed to a boom. owever in the EM34 they are only connected with a cable and must be oriented for each measurement. In summary Exploration depth for horiontal dipoles ~ 0.75s Exploration depth for vertical dipoles ~ 1.5s EM31, EM34 and EM38 instruments EM38 EM31 EM34 A range of instruments can be used to investigate to different depths oriontal dipoles Vertical dipoles EM38 (s=1 m) 0.75 m 1.5 m EM31 (s=4 m) 3 m 6 m EM34 (s=10 m) 7.5 m 15 m EM34 (s=0 m) 15 m 30 m These depths of investigation are taken from Geonics TN6 by McNeill (1980) and represent the depth at which the peak response occurs. The instrument is sensitive to greater depths (as deep as 6m for the EM31 vertical dipole) Sample calculation Consider the depth extent of an EM31 survey in a region where the subsurface resistivity is 100 Ωm. The TX frequency is Show that the numbers above confirm that the depth of investigation is limited by the TX-RX spacing, rather than skin depth. Martyn Unsworth, University of Alberta, September 016 5

6 E.1. Response of a two-layer resistivity model To calculate the conductivity that would be measured over a layered Earth, need to average the contributions from each layer. At low induction number McNeil (1980) showed that for a two layer model with conductivity σ 1 and σ where the upper layer has a thickness d, the average conductivity measured by vertical dipoles is _ 1 R v ( )) R ( 1 v v ( ) Note that = d/s where s is the TX-RX distance. With the dipoles horiontal _ h 1( 1 Rh ( )) Rh ( ) Depth sounding with a loop-loop EM system These equations are evaluated in the figure below. Increasing the value of s corresponds to deeper exploration. In principle could use a system to measure depth variation of conductivity in a similar way to the Wenner array owever, a wide range of s values is difficult to implement because this requires a wide dynamic range for the RX. This method is not used at present (although possible with an instrument such as Geonics EM34) Often the depth character of the near surface is modelled by loop-loop EM systems using measurements from two different instruments, each with a different spacing s. Equations derived above are not valid at high values of conductivity (e.g. seawater). This is because the low induction number assumption is not valid. Figure below shows a layer Earth with the TX and RX placed on the surface at = 0. The upper layer has ρ 1 = 100 Ωm and is 1 m thick. The lower layer has resistivity values ρ = [10000, 1000, 100, 10, 1 Ωm] 1 Conductivity is the reciprocal of resistivity ( ) Martyn Unsworth, University of Alberta, September 016 6

7 Generated with MATLAB script : em_sounding layer.m Solid lines are for vertical dipoles. Dashed lines are for horiontal dipoles Profiling with a loop-loop EM system oriontal lines show the exploration depth for s = 1 m (Geonics EM38) and s = 4 m (Geonics EM31) with horiontal (dashed) and vertical (solid) dipole orientation. Blue layer, ρ = 10 Ωm ; White layer ρ = 100 Ωm Martyn Unsworth, University of Alberta, September 016 7

8 In upper panel, the horiontal lines show the 0.75s and 1.5s depths for horiontal and vertical dipoles. With small s value in the figure above, this survey has a very limited depth of exploration. Can only measure the resistivity at the surface. Deeper exploration of the same model is possible with s = 4 m using an EM31 Everywhere on the profile can see that resistivity increases with depth. To see this, compare the vertical and horiontal measurements. MATLAB script : em_profiling layer.m Sample calculation 1 An EM31 survey takes place where a surface layer of glacial till is 4 m thick. The resistivity of the till is 5 Ωm The crystalline bedrock has a resistivity 400 Ωm The EM31 is placed on the ground at = 0 with dipoles oriented vertically. What resistivity value will the EM31 read? Sample calculation An EM34 survey is being used to map the depth of the water table in a sand layer. The TX and RX are placed on the surface of the Earth at =0. Dry sand has a resistivity of 800 Ωm and the wet sand has a resistivity of 100 Ωm. The EM34 gives a reading of 350 Ωm when s = 0 m What is the depth of the water table? Martyn Unsworth, University of Alberta, September 016 8

9 E.1.3 Response of multi-layer resistivity models This approach is simple to extend to multiple layers. Conductivity values,, ] with interfaces at depths d d 1, d ] [ 1 3 These depths are normalied to give d1 1 ; s d ; s 3 d s 3 [ Can show that: _ v 1( 1 Rv ( 1)) ( Rv ( 1) Rv ( )) 3Rv ( ) _ h 1( 1 Rh ( 1)) ( Rh ( 1) Rh ( )) 3Rh ( ) In the following example the model consists of blue layer (ρ = 10 Ωm) in white halfspace (ρ = 100 Ωm) This survey has limited depth of exploration, as expected for s = 1 m oriontal dipoles (dashed line) and vertical dipoles (solid line) This EM38 survey detects an increase in apparent resistivity with depth in some areas and a decrease in others. To see this compare the horiontal (dashed line) and vertical dipole (solid line) measurements. Remember that vertical dipoles sample deeper in the Earth than horiontal dipoles. Martyn Unsworth, University of Alberta, September 016 9

10 Martyn Unsworth, University of Alberta, September

11 E.1.4 Applications of near field EM systems E Mineral exploration Figures above show a test of the EM31 at the Cavendish test site (McNeill, 1980). The bedrock is high resistivity gneiss and limestone. Two ones of sulphide mineraliation are crossed on Line C and show a high conductivity. Note that a swamp also shows up as a one of low resistivity (high conductivity) The mho is a unit of conductivity and is ohm spelt backwards. 0 milli-mhos = 0.0 S/m = 50 Ωm Martyn Unsworth, University of Alberta, September

12 E.1.4. Environmental geophysics EM instruments are commonly used to pinpoint areas of interest, which are than explored further using DC resistivity and/or ground truth (drilling or digging). Comparison of EM34 and DC resistivity Wenner array for mapping a contaminant plume. The EM34 survey took days, in contrast to 1 days for the Wenner survey. In addition, the EM34 does not require direct contact with the ground through the electrodes, since it couples inductively. Martyn Unsworth, University of Alberta, September 016 1

13 These maps are made by measured ground conductivity on a grid of points and contouring the results. Modern instruments use a built-in GPS system, thereby removing the need to independently survey the grid points. Example of mapping the horiontal extent of a landfill with EM data Estimate of thickness of waste layer using EM instrument. Requires assumption of the layer conductivity Both above figures are from utchinson et al, (000) In environmental surveys such as this one, the data is often explored further with boreholes and pieometers to find the cause of the high conductivites (high sulphide content, chlorides, metallic debris, etc) Martyn Unsworth, University of Alberta, September

14 E Sea-ice thickness Ice has a high resistivity and seawater has a very low resistivity. This allows EM31 measurements to be used to measure sea-ice thickness. Equations developed in E.1. are not exact in this case because the high conductivity of the seawater means that the induction number is not low. Method described by Kovacs and Morey (1991) and aas et al., (1997). oriontal dipoles used to give maximum sensitivity to near surface structure. Figure 3 from aas et al., (1997) is shown below and confirms the empirical relationship between the apparent conductivity measured by the EM31 and ice thickness. Ice resistivity changes from summer to winter but does not have a significant effect. Figure 4 from the same paper shows ground truth obtained by comparing geophysical estimate of ice thickness with direct measurement from coring. Martyn Unsworth, University of Alberta, September

15 See later that helicopter measurements can use a similar technique to measure sea ice thickness. elicopter and ground level estimates give consistent results. The airborne measurements allow large areas to be surveyed. Monitoring sea ice extent and thickness has become an important method for monitoring climate change in the Arctic For more information see webpage of Dr. Christian aas in EAS Martyn Unsworth, University of Alberta, September

16 Other studies have monitored changes in thickness over a field season In this case the EM31 was mounted inside a kayak Accuracy of EM31 instrument is ~0.001 S/m, so if Sea ice is 3 m thick, this gives m precision. If sea ice is 5 m thick, this gives 0.09 m This approach has also been used by deploying an EM31 from the bow of an icebreaker! See movie courtesy of Christian aas. E Agriculture Ground based surveys that generally need to be calibrated with some ground truth to work in each location. Commonly used system is the Geonics EM38 Ground Conductivity Meter. Martyn Unsworth, University of Alberta, September

17 For agriculture they work well since they are non-invasive and the instrument can be mounted on a tractor. Applications include mapping salinity variations in a field mapping moisture variations in a field mapping depth of soil mapping depth of flood deposits Mapping sand content of soil Study of EM38 conductivity and crop yield in Australia Rampant, P., and M. Abuar, (004) Professional Agricultural Consulting Education and Research This plots shows the correlation between wheat yield and EM38 conductivity (a proxy for water content) Monitoring saliniation at Stettler, Alberta, (McKenie et al., 1997) Martyn Unsworth, University of Alberta, September

18 E.1.5 References aas, C., S. Gerland,. Eicken,. Miller, Comparison of sea-ice thickness measurements under summer and winter conditions in the Arctic using a small electromagnetic induction device, Geophysics, 6, , utchinson et al, Geophysical Applications to Solid waster analysis, in Proceedings of the Sixteenth International Conference on Solid Waste Technology and Management Philadelphia, PA U.S.A., December 10-13, 000 Editors: Zandi, I.; Mersky, R.L.; Shieh W.K. Pp. -68 to -78 ISSN PDF available at under Case Studies. Kovacs, A., and Morey, R. M., 1991, Sounding sea-ice thickness using a portable electromagnetic induction instrument: Geophysics, 56, McKenie, R.C., R.J. George, S.A. Woods, M.E. Cannon, D.L. Bennett, Use of the Electromagnetic-Induction Meter (EM38) as a tool in managing salinisation, ydrogeology Journal, 5 (1), Palacky and West (1991), chapter 10 in Electromagnetic methods in Applied Geophysics Volume - Applications Part B, edited by Misac Nabighian, and published by the SEG. More details can be found at where the review by McNeill, (1980) can be downloaded as a PDF. Martyn Unsworth, University of Alberta, September