Acoustic imaging in helioseismology

The time-variant acoustic signal at a point in the solar interior can be constructed from observations at the surface, based on the knowledge of how acoustic waves travel in the Sun: the time-distance relation of the p-modes. The basic principle and properties of this imaging technique are discussed in detail. The helioseismic data used in this study were taken with the Taiwan Oscillation Network (TON). The time series of observed acoustic signals on the solar surface is treated as a phased array. The time-distance relation provides the phase information among the phased array elements. The signal at any location at any time can be reconstructed by summing the observed signal at array elements in phase and with a proper normalization. The time series of the constructed acoustic signal contains information on frequency, phase, and intensity. We use the constructed intensity to obtain three-dimensional acoustic absorption images. The features in the absorption images correlate with the magnetic field in the active region. The vertical extension of absorption features in the active region is smaller in images constructed with shorter wavelengths. This indicates that the vertical resolution of the three-dimensional images depends on the range of modes used in constructing the signal. The actual depths of the absorption features in the active region may be smaller than those shown in the three-dimensional images.