Inversion
Information about helioseismic waves (such as mode frequencies and frequency-splitting) collected by transforming the oscillation data can be used to infer numerical details of internal features of the Sun. For example, the internal sound speed, and the internal differential rotation within the Sun. Equations and analytic relations such as integrals can be manipulated to relate the desired internal properties to the transformed data. The numerical methods used are adapted to the particular internal features examined so as to extract the maximum amount of information, with the least error, from the oscillations about the internal features. This process is termed helioseismic inversion.
As an example in slightly more detail, the oscillation frequency splitting can be related, via an integral, to the angular velocity within the sun.
Read more about this topic: Helioseismology