Comparing data over simple and complex structures

We learned above what the anomalous magnetic field will be over a buried dipole and over extended bodies of uniform susceptibility, and how those ideas apply to geologic structures (again, assuming uniform susceptibility). How then do we anticipate the fields due to more general geologic models of the earth? In "geophysical" terminology, the question is "how do we forward model the response to an arbitrary distribution of susceptibility?" Here is one approach that has become popular; there are 3 steps:

1. Describe the subsurface as a finite collection of cells, each with uniform susceptibility.
2. Recognize that the response to a single rectangular cell with constant susceptibility in an arbitrary magnetizing field can be calculated relatively easily using expressions from the literature.
3. At each location where a measurement is made above our model of the earth, the responses from all the individual cells must be added up. The result will be the superposition of all those little responses.

The concept is illustrated in the following eight figures selected with the buttons. (Such calculations are introduced in section 10 and details are given in section 11. )

1.	First "discretize" the subsurface under the area in which we are interested.
2.	One cell of susceptible material in the cellular subsurface	4.	Five susceptible cells in the descretized earth
3.	Resulting magnetic anomaly at 50o magnetic north.	5.	Resulting magnetic anomaly at 50o magnetic north.
		6.	The same data set. Not knowing what caused the anomaly, could you tell where susceptibile blocks are, and how susceptible they are?
7.	A complicated earth with all cells susceptible to some degree.	8.	Resulting data over the complicated earth at 50o magnetic north.

1. Total field magnetic anomaly over a single block with susceptibility of 0.1 SI units (corresponds to point 2 in the previous figure). 2. Total field magnetic anomaly over five blocks with varying susceptibility (corresponds to point 6 in the previous figure). 3. Total field magnetic anomaly over a volume with all cells having some finite susceptibility (corresponds to point 8 in the previous figure).