Sensitivity of acoustic wave travel times to sound-speed perturbations in the solar interior

For time-distance helioseismology, it is important to establish the relationship between the travel times of acoustic waves propagating between different points on the solar surface through the solar interior and local perturbations to the sound speed in the propagation region. We use the Born approximation to derive a general expression for the linear sensitivity of travel times to local sound-speed perturbations in plane-parallel solar models with stochastic wave sources. The results show that the sensitivity of time-distance measurements to perturbations in sound speed depends on the details of the measurement procedure, such as the phase-speed filter used in typical time-distance data analysis. As a result, the details of the measurement procedure should be taken into account in the inversion of time-distance data. Otherwise, the inferred depths of perturbations may be incorrect.