Potential versus Force

1. Geophysics 1 Potential versus Force The potential is the integral of the force (F) over a displacement path. From above, we obtain a basic definition of the potential (at right) for a unit positive test pole (mt). Note that we consider the 1/4 term =1

2. Thus - H (i.e. F/ptest, the field intensity) can be easily derived from the potential simply by taking the derivative of the potential

3. The Dipole Field Consider the case where the distance to the center of the dipole is much greater than the length of the dipole. This allows us to treat the problem of computing the potential of the dipole at an arbitrary point as one of scalar summation since the directions to each pole fall nearly along parallel lines.

4. If r is much much greater than l (distance between the poles) then the angle  between r+andr- approaches 0 and r, r+andr- can be considered parallel so that the differences in lengths r+andr- from r equal to plus or minus the projections of l/2 into r.

5. r- r r+

6. Thus .. H - monopole = H - dipole This yields the field intensity in the radial direction - i.e. in the direction toward the center of the dipole (along r). However, we can also evaluate the horizontal and vertical components of the total field directly from the potential.

8. Where M = pl and Let’s tie these results back into some observations made earlier in the semester with regard to terrain conductivity data. 32

9. 7.2 nT 0.113 nT For the dipole field, an increase in depth (r) from 4 meters to 16 meters produces a 64 fold decrease in anomaly magnitude

10. Problem 3 To answer this problem we must evaluate - or Take a minute and give it a try.

11. Question 4 Vertically Polarized Horizontal Cylinder

12. Vertical Magnetic Anomaly Vertically Polarized Sphere Question 5 Zmax and ZA refer to the anomalous field, i.e. the field produced by the object in consideration The notation can be confusing at times. In the above, consider H = FE= intensity of earth’s magnetic field at the survey location.

13. Question 5 Vertically Polarized Vertical Cylinder

14. diagnostic distance Sphere vs. Vertical Cylinder; z = __________ The depth 2.17 1.31 0.81 0.9 2.86 3.1 3.35 1.55 2.45

15. Sphere or cylinder?

16. 6. Given that derive an expression for the radius, where I = kHE. Compute the depth to the top of the casing for the anomaly shown below, and then estimate the radius of the casing assuming k = 0.1 and HE=55000nT. Zmax (62.2nT from graph below) is the maximum vertical component of the anomalous field produced by the vertical casing. Which SGO should you use?

17. Review of Due Dates Part 1 Magnetics Problem set TODAY Magnetics Lab Tuesday Dec. 4th or 6th Paper Summaries Thursday Dec. 6th Part 2 Magnetics Problem set Thursday Dec. 6th