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Inversion techniques

The principle of inversions is easy to illustrate.
We look at two oscillations with slightly different *l* and frequency,
corresponding to sound waves that propagate along slightly different
tracks.

The green wave penetrates a little deeper into the Sun, than the
yellow wave and therefore senses conditions in a slightly larger
area. The *difference* in frequency between the two oscillations
corresponding to the green and the yellow wave therefore says something
about that area that only the green wave passed through.

In the same way, different oscillations reach different latitudes.

It turns out that oscillations with *m* = *l* are concentrated
close to the equator, while oscillations with low *m* reach high
latitudes. By studying oscillations with different *m* we can study
how conditions in the Sun vary with latitude. This is particularly
important for measuring the internal rotation rate of the Sun.

Expressed more precisely the observed frequencies are *integral*
measures of the sound speed along the path of the sound waves. When we want
to determine the sound speed itself, we need to *invert* an
integral equation, which is a well-known, but very difficult problem in
mathematics. Therefore we spend a lot of time developing effective
mathematical techniques and computer software to invert the measured
oscillation frequencies.

Some of the results we have obtained are shown on
this page.