### 3.6 Tests of Born approximation for sound speed and flow perturbations

The range of validity of the Born approximation is an important question for local helioseismology, as
the linear forward problem proceeds naturally in the Born approximation.
Birch et al. (2001) simulated the scattering of sound waves by a spherical region of perturbed
sound speed. The geometry and the essential result are shown in Figure 5. The main result,
which was also found by Hung et al. (2001) in the context of geophysics, is that in the limit
of weak perturbations the Born approximation is valid, while the ray approximation can fail
badly. The Born approximation becomes less accurate as the strength, or spatial extent, of the
perturbation is increased. Notice that there have not yet been any studies, in the context of
helioseismology, on the accuracy of waveforms, rather than travel times, computed in the Born
approximation.

Birch et al. (2004) studied the validity of the Born approximation for the effect of flows on
time-distance travel times. Figure 6 shows the geometry for the numerical experiment, and Figure 7 shows
the basic results. For weak flows, the Born approximation is valid as long as the acoustic waves were not
traveling nearly upstream or downstream. They also found that strong flows can reflect incoming waves,
which leads to a failure of the Born approximation.