1. Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total field can be derived from other magnetic elements. The formula below represents the anomalous total field in terms of the horizontal and vertical components of the anomalous field.

2. Remember how the proton precession magnetometer works. Protons precess about the earth’s total field with a frequency directly proportional to the earth’s field strength The proton precession magnetometer measures the scalar magnitude of the earth’s main field.

3. In this diagram F ET is is the vector sum of the earth’s main field and the anomalous field associated with a buried dipole field. The proton precession magnetometer measures the magnitude of F ET.

4. Magnetic Elements for your location F is known

5. In most applications the anomalous field F A is much smaller than the main field F E.

6. In this case, the magnetic anomaly is approximated as the difference between the measured field (F ET ) at some point and the predicted value of the earth’s main field (F E ) at that point. This anomaly is often referred to as T. 53

7. When F A (the anomalous field) is small, we consider the difference T = F ET - F E to be equivalent to the projection of vector F A onto the direction of the main field. FAFA

8. In the case where F A is large the projection F AT is significantly different from T.

9. Let’s zoom in for a closer look at the tip of F E.

10. Horizontal line parallel to earth’s surface i is the inclination of the earth’s main magnetic field.  is the angle of F A relative to the earth’s main field F E. T F ET

11. F AT is the projection of F A onto the direction of the main field F E, and is considered equal to T, the scalar difference between F E and F ET.

12. The horizontal and vertical projections of F A

13. The horizontal and vertical projections of F A appear in the expansion of F AT = F A cos(  -i).

14. In summary - F AT is an approximation of T, the scalar difference obtained from measurements of the total field (F ET ) made by the proton precession magnetometer. For the purposes of modeling we work backwards. Given a certain object, we compute the horizontal (H A ) and vertical (Z A ) components of the anomaly and combine them to obtain F AT - the anomaly we obtain from the proton precession magnetometer measurements.