Sensitivity kernels for time-distance helioseismology

Efficient computation for spherically symmetric solar models

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077, Göttingen, Germany
e-mail: fournier@mps.mpg.de
² Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
³ Magique-3D, Inria Bordeaux Sud-Ouest, Université de Pau et des Pays de l’Adour, 64013 Pau, France

Received: 9 April 2018
Accepted: 17 May 2018

Abstract

Context. The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These kernels are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, although it can be computationally expensive.

Aims. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric.

Methods. Kernels are typically expressed as products of Green’s functions that depend upon depth, latitude, and longitude. Here, we compute the spherical harmonic decomposition of the kernels and show that the integrals in latitude and longitude can be performed analytically. In particular, the integrals of the product of three associated Legendre polynomials can be computed.

Results. The computations are fast and accurate and only require the knowledge of the Green’s function where the source is at the pole. The computation time is reduced by two orders of magnitude compared to other recent computational frameworks.

Conclusions. This new method allows flexible and computationally efficient calculations of a large number of kernels, required in addressing key helioseismic problems. For example, the computation of all the kernels required for meridional flow inversion takes less than two hours on 100 cores.