Time‐Distance Helioseismology: The Forward Problem for Random Distributed Sources

Abstract

The forward problem of time-distance helioseismology is computingtravel-time perturbations that result from perturbations to a solarmodel. We present a new and physically motivated general frameworkfor calculations of the sensitivity of travel times to small localperturbations to solar properties, taking into account the fact thatthe sources of solar oscillations are spatially distributed. In additionto perturbations in sound speed and flows, this theory can also beapplied to perturbations in the wave excitation and damping mechanisms.Our starting point is a description of the wave field excited bydistributed random sources in the upper convection zone. We employthe first Born approximation to model scattering from local inhomogeneities.We use a clear and practical definition of travel-time perturbation,which allows a connection between observations and theory. In thisframework, travel-time sensitivity kernels depend explicitly on thedetails of the measurement procedure. After developing the generaltheory, we consider the example of the sensitivity of surface gravitywave travel times to local perturbations in the wave excitation anddamping rates. We derive explicit expressions for the two correspondingsensitivity kernels. We show that the simple single-source picture,employed in most time-distance analyses, does not reproduce all ofthe features seen in the distributed-source kernels developed inthis paper.