Verification of the Travel Time Measurement Technique and the Helioseismic Inversion Procedure for Sound Speed Using Artificial Data

We performed 3D numerical simulations of the solar surface wave field for the quiet Sun and for three models with different localized sound-speed variations in the interior with: (i) deep, (ii) shallow, and (iii) two-layer structures. We used simulated data generated by two different codes which use the same standard solar model as a background model, but utilize two different integration techniques and use different models of stochastic wave excitation. Acoustic travel times were measured from all data sets using the time-distance helioseismology technique and compared with the ray theory predictions, frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the ray theory in both cases with and without phase-speed filtering for the shallow and deep perturbations. This testing verifies the whole measuring-filtering-inversion procedure for sound-speed anomalies inside the Sun. It is shown, that the phase-speed filtering, frequently used to improve the signal-to-noise ratio does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the background sound-speed profiles in all cases. Due to its smoothing nature, the inversion procedure overestimates sound speed variations in areas with sharp gradients of the sound-speed profile.