Time-distance helioseismology is a powerful method to study the interior of the Sun by computing travel time of individual acoustic wave packets as they travel through the Sun between two spatially separated locations on its surface. I have contributed to the theoretical development of this field.

Helioseismic tomography is a form of the tomographic techniques adapted to image the interior of the Sun. The important adaptation is the computation of travel time through time-distance helioseismology. Though the technique has a long history in various other fields its adaptation in studying the solar interior has difficulties. I have contributed in the aspects of its adaptation and improvement.

Some important contributions include, (a) a theorem that forbids the use of certain methods used in computing travel time, (b) noting a phenomenon that makes the time-distance diagram lose its uniqueness, making it a function of the frequency width and central frequency of the wave packet, (c) showing . that at high frequencies correlation techniques do not provide the shortest travel time between two spatial locations, (d) in averaging the signal to improve signal to noise ratio, the assumption that travel time of the averaged signal is equal to the average of the individual travel times is erroneous, (e) Duvall's law of traditional helioseismology is equivalent to the phase time-distance curve; the two are connected through a simple transformation. The result is the analytic inversion of local radial sound speed.

These contributions could lead to a reliable understanding of the local and global structures in the solar interior, particularly sunspots and the mechanisms that drive the numerous phenomena at and above the surface of the Sun.