1. GG 450 Modeling Magnetics February 14, 2008

2. TOTAL FIELD ANOMALIES: Recall the components of the earth's field: We can define the field caused by induced anomalies the same way, with F A : TOTAL anomaly field, H A : HORIZONTAL field, Z A : VERTICAL field. When modeling, we calculate H A and Z A, then obtain F A from the sqrt of the sum of the squares. In the field, we measure F A.

3. A key assumption in much of this analysis is that F A is MUCH SMALLER than the earth's field, F E. This is true for most anomalies, but there are exceptions when working with highly magnetic bodies, such as some iron ore bodies and buried steel. Why did we take our survey lines at sea at an azimuth of 010° ? Earth’s Field Anomalous Field

4. This assumption allows us to assume that the direction of the earth's field doesn't change appreciably from magnetic North due to the anomalous body, and that the only evidence of the body will be a change in the total field strength. Thus, we are only interested in the component of the anomalous field in the direction of the earth's field: F AT. IF the anomalous field is in the direction of the earth's field, then F AT is given by: F AT = Z A Sin i + H A Cos i, where i is the inclination of the earth's field.

5. MAGNETIC MONOPOLE MODEL: A magnetic monopole is impossible, but the idea is ok if the matching pole is far away. For a magnetic monopole, equipotential surfaces are spheres and lines of force are radial to the pole.

6. If we immerse a negative magnetic monopole in the earth’s magnetic field, with the strength of the monopole much smaller than the strength of the earth’s field, then we can easily sketch the resulting magnetic anomaly.

7. In directions where the earth’s field and the monopole field are perpendicular to each other, the anomalous field will not change the total field.

8. In directions where the earth’s field and the monopole field are in the same direction, the total field will be high, and the anomaly will be positive.

9. In directions where the earth’s field and the monopole field are in opposite directions, the total field will be be less, and the anomaly will be negative.

10. We can sketch the resulting magnetic anomaly as shown:

11. The ability to sketch magnetic anomalies comes in very handy when trying to predict what type of body is causing the anomaly. You can calculate anomalies with appropriate software, but be sure you understand why an anomaly looks the way it does.

12. When a body with high susceptibility is placed in a magnetic field, a magnetic field is INDUCED in the body. Induced fields are in the same direction as the earth's field, so the pole nearest the surface of the earth for a buried object in the northern hemisphere will be the negative (S) pole and positive (N) in the southern hemisphere:

13. If the location of our pole is at x=0, y=0, z=z. Our observation point is at x,y, then the distance from the pole to the observation point is: √ x 2 +y 2 +z 2 and: recall that the components of the anomaly field are given by: Z A =-dV/dz, H Ax = - dV/dx, and H Ay = -dV/dy, and in general: d/dx (u n )= nu n-1 du/dx, so:

14. We’ll let the +X direction be towards magnetic north, so H Ay won't matter because it is perpendicular to the earth's field, and thus won't change the strength of the field (unless it is very large), so we can get F AT using F AT = Z A Sin i + H A Cos i.

15. Recall that the inclination of the earth’s field at the NORTH magnetic pole is –90° since the North Magnetic Pole is a south pole….. You should understand why the anomalies look the way they do. Note that the anomalies vary strongly with magnetic latitude. An anomaly from an identical buried body near the equator looks much different than one near the pole:

16. meters nT

19. NOTE: The monopole is ALWAYS NEGATIVE in the examples above- it doesn’t change to positive south of the equator as you should expect for an induced pole.