Comparison Between Gravity and Magnetic Anomalies
Unlike the gravitational anomalies caused by subsurface density variations, the magnetic anomalies caused by subsurface variations in magnetic susceptibility are difficult to intuitively construct. This is because there are more factors involved in controlling the shape of a magnetic anomaly than there are in controlling the shape of a gravity anomaly.
In the case of a given subsurface density distribution, the shape of the resulting gravity anomaly is a function of the subsurface density distribution only. In fact, knowing the gravitational anomaly produced by a simple shape such as a point mass is often enough to guess what the shape of the gravity anomaly would be over a much more complicated density distribution. Once you've determined the shape of the gravity anomaly that the density distribution will produce, then you can make reasonable guesses about how the anomaly will change as the density constrast is varied or as the depth to the density contrast is varied. In addition, the anomaly will not change shape if the density distribution is moved to a different location on the Earth, say from the equator to the north pole. The gravity anomaly is a function of density only.
Magnetic anomalies, on the other hand, are a function of two independent parameters: the subsurface distribution of susceptibility and the orientation of the Earth's main magnetic field. Change one of these parameters and you change the resulting magnetic anomaly. What this means in practice is that magnetic anomalies over the same susceptibility distribution will be different if the distribution is in a different location, say one located beneath the equator versus one located beneath the north pole. Additionally, the magnetic anomaly over a two-dimensional body such as a tunnel will look different depending on the orientation of the tunnel, say east-west or north-south, even if the magnetic profile is always taken perpendicular to the trend of the tunnel.
With these complexities in mind, we will not spend a great deal of time analyzing the shapes of magnetic anomalies over simple structures; there are many computer programs available that do this quite well. Rather, we will look at several simple examples and qualitatively construct the magnetic anomalies over them so that you can get a better feeling for the complexities involved and for how it might be done in the computer.