Efficient and Accurate Algorithm for the Full Modal Green's Kernel of the Scalar Wave Equation in Helioseismology

Abstract

In this work, we provide an algorithm to compute efficiently and accurately the full outgoing modal Green's kernel for the scalar wave equation in local helioseismology under spherical symmetry. Due to the high computational cost of a full Green's function, current helioseismic studies only use its values at a single depth. However, a more realistic modelisation of the helioseismic products (cross-covariance and power spectrum) requires the full Green's kernel. In the classical approach, the Dirac source is discretized and one simulation gives the Green's function on a line. Here, we propose a two-step algorithm which, with two simulations, provides the full kernel on the domain. Moreover, our method is more accurate as the singularity of the solution due to the Dirac source is described exactly. In addition, it is coupled with the exact Dirichlet-to-Neumann boundary condition, providing optimal accuracy in approximating the outgoing Green's kernel, which we demonstrate in our experiments. In addition, we show that high-frequency approximations of the nonlocal radiation boundary conditions can represent accurately the helioseismic products.

Quantitative passive imaging by iterative holography: the example of helioseismic holography

“…function is usually expensive, as the stiffness matrix has to be inverted. The two-step algorithm of [67] allows us to obtain the full modal Green's function from two computations only. Furthermore, this expansion allows us to use a low-rank approximation for the Green's function.…”

hawen: time-harmonic wave modeling and inversion using hybridizable discontinuous Galerkin discretization

“…It combines MPI and OpenMP parallelism, it is deployed on supercomputers and has been used in studies on seismic imaging (Faucher, Alessandrini, et al, 2020;, as well as in helioseismology (Barucq et al, 2019(Barucq et al, , 2020Barucq, Faucher, Fournier, et al, 2020a, 2020b. The software works with an input parameter file: a text file listing the problem configuration (dimension, choice of viscous model, etc.…”