1. Electromagnetic Methods (EM) Basic principle: Transmitter current (Ip) generates primary field (P), which generates ground emf, leading to subsurface “eddy” currents. Subsurface eddy currents then generate a secondary field (S), finally both P and S are measured by the receiver.

3. “Frequency domain” EM: Drive the transmitter with a single frequency Current in transmitter: Primary magnetic field: Subsurface “emf” (voltage):

4. “Frequency domain” EM Important: The “flux” Φ is a measure of the magnetic field passing through a given cross sectional area – this will be large when B is perpendicular to the element of area Subsurface “emf” (voltage): Since B is proportional to H, we may conclude that “Phase shift”

5. “Frequency domain” EM Graphically, the signals look like: The phase difference between primary field and the emf is

6. “Frequency domain” EM Subsurface “emf”: “Phase shift” Subsurface “eddy” currents: Will only flow if there is an electric circuit. Since rocks are both resistive and have self-inductance, a reasonable (“equivalent”) model is: This is a differential equation for I(t), which can be solved for a given ε(t)

7. “Frequency domain” EM This is a differential equation for I(t), which can be solved for a given ε(t) For, the solution to the differential equation is where is the “induction number” “Phase shift”

8. “Frequency domain” EM Summarizing: The total phase difference between the primary and secondary field is

9. “Frequency domain” EM Graphically, the signals look like: The total phase difference between primary and secondary EM fields is

10. I i

11. “Frequency domain” EM Graphically, the signals look like: The total phase difference between primary and secondary EM fields is

12. “Frequency domain” EM Total response at the receiver - phasor diagram The receiver responds to the sum of the primary field and the secondary field:

13. “Frequency domain” EM To determine the secondary field, and the phase angle, the primary field must be subtracted from the response. The primary field strength is known from the separation; the field phase is communicated by wire, radio signal or synchronized beforehand.

14. Recall: This is a differential equation for I(t), which can be solved for a given ε(t) For, the solution to the differential equation is where is the “induction number” “Phase shift”

15. “Frequency domain” EM The key quantity is the response parameter, or “induction number”, given by From the Figure, it may be seen that the induction number is just the ratio of in-phase to out-of-phase components

16. “Frequency domain” EM Good conductors: R << L, tan Φ is large, phase angle is large, in-phase dominates Poor conductors: R>>L, tan Φ is small, phase angle is small, overall magnitude is small

17. “Frequency domain” EM Response of frequency domain EM over a good conductor

18. Response parameters Conductive sphere Vertical sheet Response parameters: Simple R-L circuit Similarities: good conductors have low R (high σ), large response parameters, in-phase will dominate

19. Response parameters Note the variation of real/imaginary parts: with either increasing frequency, or increasing conductivity, the amplitude grows and the phase angle rotates.

20. Next lecture: “Frequency domain” EM: horizontal loop systems Two basic configurations: 1.Fixed transmitter, moving receiver system (eg, Turam system below) 2.Moving transmitter/receiver system, with a fixed separation (eg, Slingram system below) Turam field layoutSlingram “HLEM” field layout