Like gravity, the magnetic force varies inversely with distance. In general, the deeper the magnetic object, the broader and gentler the resulting anomaly will be. Alternatively, the shallower the magnetic object, the sharper and narrower the resulting anomaly will be. The strength of the magnetic field, H, of a buried sphere, as measured directly over the sphere can be written as
where r is the radius of the magnetic sphere, d is the depth to the center of the sphere, and k is a constant based on the magnetic properties of the sphere. Let's assume that the sphere has a radius of 100 m. What happens to H in terms of k if we measure directly above the sphere at d=100 m and 400 m? Most ground magnetic surveys place the magnetometer on top of a pole 2.4 m high. Many U.S. Geological Survey aeromagnetic surveys are flown about 300 m above the ground. The amplitude of the magnetic anomaly is much greater when the magnetometer is close to the source.
Now let's see how quickly the anomaly dies off as a function of depth. Below are curves of magnetic field strength for a sphere with a radius of 1 km buried at depths of 2 km, 3km, and 4 km. As you can see, the curve for the more deeply buried sphere is gentler and broader than the curve for the shallowly buried sphere.
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