Short note: Three dimensional deconvolution of helioseismic data

Introduction to helioseismology

Helioseismology is a subset of seismology and is unique in the fact that the recorded data is not terrestrial. By recording surface solar oscillations and accounting for Doppler shifts it is possible to constrain information - such as velocities and distances - about the shallow solar interior. This problem is more complex than most terrestrial surveys since there are now problems such as a spherical target, unknown source function and location, and the fact the sun is moving at significant rate (giving a Doppler shift.) However, by using passive data techniques such as cross-correlation and spectral factorisation it is possible to gain valuable insight into solar properties.

Often large scale trends are delineated by decomposing the stochastic wavefields into spherical harmonics (Harvey, 1995), which works well for studying macro solar trends. However to describe small scale events, harmonics of a high order need to be computed, such as is done with cosmic microwave background (CMB) studies, however focusing on smaller areas using this technique is inefficient. What is often done instead is to cross correlate oscillatory dopplergram traces, since the lags acquired from doing this can give information, such as velocity, about ray paths travelling between the two trace locations (Duvall, 1993).

Short note: Three dimensional deconvolution of helioseismic data