TY - JOUR

T1 - Numerical evaluation of time-distance helioseismic sensitivity kernels in spherical geometry

AU - Bhattacharya, Jishnu

N1 - Funding Information:
This work was supported by NYUAD Institute Grant G1502 'NYUAD Center for Space Science'. This research was carried out on the High-Performance Computing resources at New York University Abu Dhabi.
Funding Information:
Acknowledgements. This work was supported by NYUAD Institute Grant G1502 “NYUAD Center for Space Science”. This research was carried out on the High-Performance Computing resources at New York University Abu Dhabi.
Publisher Copyright:
© 2022 EDP Sciences. All rights reserved.

PY - 2022/3/1

Y1 - 2022/3/1

N2 - Context. Helioseismic analysis of large-scale flows and structural inhomogeneities in the Sun requires the computation of sensitivity kernels that account for the spherical geometry of the Sun, as well as systematic effects such as line-of-sight projection. Aims. I aim to develop a code to evaluate helioseismic sensitivity kernels for flows using line-of-sight projected measurements. Methods. I decomposed the velocity field in a basis of vector spherical harmonics and computed the kernel components corresponding to the coefficients of velocity in this basis. The kernels thus computed are radial functions that set up a 1.5D inverse problem to infer the flow from surface measurements. I demonstrate that using the angular momentum addition formalism lets us express the angular dependence of the kernels as bipolar spherical harmonics, which may be evaluated accurately and efficiently. Results. Kernels for line-of-sight projected measurements may differ significantly from those that don't account for projection. Including projection in our analysis does not increase the computational time significantly. We demonstrate that it is possible to evaluate kernels for pairs of points that are related through a rotation by linearly transforming the terms that enter the expression of the kernel, and that this result holds even for line-of-sight projected kernels. Conclusions. I developed a Julia code that may be used to evaluate sensitivity kernels for seismic wave travel times computed using line-of-sight projected measurements, which is made freely available under the MIT license.

AB - Context. Helioseismic analysis of large-scale flows and structural inhomogeneities in the Sun requires the computation of sensitivity kernels that account for the spherical geometry of the Sun, as well as systematic effects such as line-of-sight projection. Aims. I aim to develop a code to evaluate helioseismic sensitivity kernels for flows using line-of-sight projected measurements. Methods. I decomposed the velocity field in a basis of vector spherical harmonics and computed the kernel components corresponding to the coefficients of velocity in this basis. The kernels thus computed are radial functions that set up a 1.5D inverse problem to infer the flow from surface measurements. I demonstrate that using the angular momentum addition formalism lets us express the angular dependence of the kernels as bipolar spherical harmonics, which may be evaluated accurately and efficiently. Results. Kernels for line-of-sight projected measurements may differ significantly from those that don't account for projection. Including projection in our analysis does not increase the computational time significantly. We demonstrate that it is possible to evaluate kernels for pairs of points that are related through a rotation by linearly transforming the terms that enter the expression of the kernel, and that this result holds even for line-of-sight projected kernels. Conclusions. I developed a Julia code that may be used to evaluate sensitivity kernels for seismic wave travel times computed using line-of-sight projected measurements, which is made freely available under the MIT license.

KW - Methods: numerical

KW - Sun: helioseismology

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U2 - 10.1051/0004-6361/202141665

DO - 10.1051/0004-6361/202141665

M3 - Article

AN - SCOPUS:85127372648

VL - 659

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A138

ER -