标题： 远侧地震成像的格林函数：极坐标展开方法 显示英文标题

标题： Green's functions for far-side seismic images: a polar expansion approach

摘要： 我们通过使用地震全息技术，计算了太阳远表面的磁活动地震图像。 与之前的工作类似，该方法基于比较进入和离开太阳某一特定点的波，但在这里，我们从Cowling近似下的绝热波方程的球面极坐标展开中计算格林函数，而不是像之前在远侧全息术中使用的射线路径近似。 展示了使用射线理论和球面极坐标展开得到的结果之间的比较。 在两种情况下，我们都使用了局部平面平行极限下的重力声波方程，而对于后者，我们对格林函数的径向依赖采用了渐近近似。 因此，可以从极坐标展开近似中获得改进的远侧图像，尤其是在结合对应两个和三个跳变的格林函数时。 我们还表明，由于对太阳最上层的错误建模而引起的格林函数中的相位修正，可以从振荡的正常模式的本征频率中估计出来。 显示英文摘要

摘要： We have computed seismic images of magnetic activity on the far surface of the Sun by using a seismic-holography technique. As in previous works, the method is based on the comparison of waves going in and out of a particular point in the Sun but we have computed here the Green's functions from a spherical polar expansion of the adiabatic wave equations in the Cowling approximation instead of using the ray-path approximation previously used in the far-side holography. A comparison between the results obtained using the ray theory and the spherical polar expansion is shown. We use the gravito-acoustic wave equation in the local plane-parallel limit in both cases and for the latter we take the asymptotic approximation for the radial dependencies of the Green's function. As a result, improved images of the far-side can be obtained from the polar-expansion approximation, especially when combining the Green's functions corresponding to two and three skips. We also show that the phase corrections in the Green's functions due to the incorrect modeling of the uppermost layers of the Sun can be estimated from the eigenfrequencies of the normal modes of oscillation.