We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are ${\mathcal{C}}^2$ functions representing the solar interior model S, complemented with an isothermal atmospheric model. We solve the equation in vectorial spherical harmonics basis to obtain modal equations for the different components of the unknown wave motions. These equations are then decoupled and written in Schrödinger form, whose coefficients are shown to be ${\mathcal{C}}^2$ apart from at most two regular singular points, and to decay like a Coulomb potential at infinity. These properties allow us to construct an outgoing Green's kernel for each spherical mode. We also compute asymptotic expansions of coefficients up to order $r^{-3}$ as r tends to infinity, and show numerically that their accuracy is improved by including the contribution from the gravity although this term is of order $r^{-3}$.

在日震学的背景下，我们为球对称下的简化Galbrun方程构造了模态输出格林核。该方程的系数为${\mathcal{C}}^{\mathrm{2个}}$代表太阳内部模型S的函数，并补充了等温大气模型。我们以矢量球谐函数为基础求解方程​​，以获得未知波运动不同分量的模态方程。然后将这些方程解耦并以Schrödinger形式编写，其系数显示为${\mathcal{C}}^{\mathrm{2个}}$除了最多两个规则的奇异点之外，它会像无穷远处的库仑势一样衰减。这些属性使我们能够为每个球形模式构造一个传出的格林核。我们还计算了系数的渐近展开式${\mathrm{[R}}^{-3}$因为r趋于无穷大，并通过数字显示了其精确度通过包括重力的贡献而得到了改善，尽管该术语是有序的${\mathrm{[R}}^{-3}$。