Michael Leguèbe, Damien Fournier, Aaron C. Birch, Laurent Gizon in Collaboration with Inria team Magique3D

We compute acoustic Green’s functions in an axisymmetric solar background model, which may include a meridional flow and differential rotation. The wave equation is solved in the frequency domain using a finite element solver. A transparent boundary condition for the waves is implemented in the chromosphere, which represents a great improvement in computational efficiency compared to implementations based on ’sponge layers’. We perform various convergence studies that demonstrate that wave travel times can be computed with an accuracy of 0.001 s. This high level of numerical accuracy is required to interpret travel times in the deep interior, and is achieved thanks to a refined mesh in the near surface layers and around the source of excitation. The wave solver presented here lays the ground for future iterative inversion methods for flows in the deep solar interior.

Michael Leguèbe, Damien Fournier, Aaron C. Birch, Laurent Gizon in Collaboration with Inria team Magique3D

Forward problems in local helioseismology have thus far been addressed in a semi-analytical fashion using the Born approximation and normal-mode expansions or direct simulations. However, it has proven difficult to take into account geometrical and instrumental effects. To avoid these difficulties we employ a numerical method to determine the impulse response of a solar model in a 2.5D geometry. Solving the wave equation in the frequency domain avoids the difficulties (instabilities) faced in the time domain. This framework is flexible, computationally efficient, and produces solar-like power spectrum and cross-covariance that agree reasonably with observations, including the high-frequency continuous spectrum. Additionally, we present accurate travel-time sensitivity kernels for perturbations to the solar medium which hint at the promising potential of this framework in future forward and inversion problems.