Uniqueness and its application

Unlike prisms, in this class of bodies uniqueness requires knowledge of the density. This theorem was proved by P. Novikov. The simplest example of starshaped bodies is a spherical mass. Of course, prisms are also star-shaped bodies but due to their special form, that causes field singularities at corners, the inverse problem is unique even without knowledge of the density. It is obvious that these two classes of bodies include a wide range of density distributions besides it is very possible that there are other classes of bodies for which the solution of the inverse problem is unique. It seems that this information is already sufficient to think that non-uniqueness is not obvious but rather a paradox. 

Assuming that the measured and calculated fields, caused only by masses of a body, are known exactly it is simple to outline the main steps of interpretation and, as was pointed out earlier, it is a straightforward task. Suppose that we deal with a class of bodies for which uniqueness holds. Then, the main steps of interpretation were formulated above and they are 

Proceeding from an observed field and making use of additional information we approximately define the parameters of the body (first guess). 

Substituting values of these parameters into Equation (4.2) we solve the forward problem and compare the measured and calculated fields. 

This process of comparison allows us to determine how the parameters of the first guess have to be changed in order to decrease the difference between the measured and calculated fields. 

---