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Context: Helioseismic analysis of large-scale flows and structuralinhomogeneities in the Sun requires the computation of sensitivity kernels thataccount for the spherical geometry of the Sun, as well as systematic effectssuch as line-of-sight projection. Aim: I aim to develop a code to evaluatehelioseismic sensitivity kernels for flows using line-of-sight projectedmeasurements. Methods: I decomposed the velocity field in a basis of vectorspherical harmonics and computed the kernel components corresponding to thecoefficients of velocity in this basis. The kernels thus computed are radialfunctions that set up a 1.5D inverse problem to infer the flow from surfacemeasurements. I demonstrate that using the angular momentum addition formalismlets us express the angular dependence of the kernels as bipolar sphericalharmonics, which may be evaluated accurately and efficiently. Results: Kernelsfor line-of-sight projected measurements may differ significantly from thosethat don't account for projection. Including projection in our analysis doesnot increase the computational time significantly. We demonstrate that it ispossible to evaluate kernels for pairs of points that are related through arotation by linearly transforming the terms that enter the expression of thekernel, and that this result holds even for line-of-sight projected kernels.Conclusion: I developed a Julia code that may be used to evaluate sensitivitykernels for seismic wave travel times computed using line-of-sight projectedmeasurements, which is made freely available under the MIT license.

Numerical evaluation of time-distance helioseismic sensitivity kernels in spherical geometry