Using a numerical integral method, we deduced a set of formulae for the co-seismic internal deformation in a spherically symmetric earth model, simultaneously taking self-gravitation, compressibility and realistically stratified structure of the Earth into account. Using these formulae, we can calculate the internal deformation at an arbitrary depth caused by an arbitrary seismic source. To demonstrate the correctness of our formulae, we compared our numerical solutions of radial functions with analytical solutions reported by Dong & Sun based on a homogeneous earth model; we found that two sets of results agree well with each other. Our co-seismic internal Green's functions in the near field agree well with the results calculated by the formulae of Okada, which also verifies our Green's functions. Finally, we calculated the Coulomb stress changes on the Japanese Islands and Northeast China induced by the Tohoku-Oki M_w 9.0 earthquake using the methods described above. We found that the effect of layered structure plays a leading role on the near field, while curvature occupies a dominant position on the deep region of the far field. Through a comparison of the Coulomb stress changes at a depth of 10 km on a layered earth model calculated by our method along with the corresponding results of Okada, we found that the discrepancy between them in near field was ∼31.5 per cent, and that of far field was >100 per cent of the signals.

中文翻译：

---

球形层状地球模型中的同震内部变形

使用数值积分方法，我们推导出了一组球对称地球模型中同震内部变形的公式，同时考虑了地球的自重，可压缩性和现实的分层结构。使用这些公式，我们可以计算由任意地震源引起的任意深度处的内部变形。为了证明我们公式的正确性，我们将径向函数的数值解与Dong＆Sun报告的基于均匀地球模型的解析解进行了比较。我们发现两组结果彼此吻合。我们在近场中的内部地震格林函数与由冈田公式计算的结果非常吻合，这也验证了我们的格林函数。最后，中号_瓦特9.0地震使用上文描述的方法。我们发现，分层结构的影响在近场上起主导作用，而曲率在远场的深处占据主导地位。通过比较我们方法计算的分层地球模型在10 km深度处的库仑应力变化以及Okada的相应结果，我们发现它们在近场之间的差异约为31.5％，而远场大于信号的100％。