利用球形位错理论研究大地震的地球内部变形及孕震特征

近年来地震的研究一般都局限于地表的变化，而由地震引起的地球内部同震变形研究却很少。地震的发生一般会伴随着孕震、发震、应力调整等过程，并开始新的地震的孕育，故研究地球内部同震变形的特征对下一次地震的孕育过程及机理的分析具有重要意义。考虑了地球的分层构造、重力及曲率影响的球形位错理论在地表同震变形的研究上有很成熟的发展，但是还没有内部变形的完整研究。基于此，我们在现有的震源函数、球心初始条件、内核-外核边界条件、外核-地幔边界条件和地表面自由边界条件组成的积分中加入正交归一的方法以避开变形计算中的高阶不收敛问题。正交归一的方法应用在球函数积分中是个复杂的过程，我们需对每一层计算结果作归一并记忆再还原，从而推出地球内部任意深度处的变形结果，根据地震引起的内部位移变化及应力转移，分析他们对下次地震孕育过程的影响。最后计算2011年日本东北大地震引起的地球内部变形并结合大地测量数据分析它的孕震特征。

The studies on the earthquake are basically focus on the surface deformation recently, while on the internal co-seismic deformation is quite less. Generally, a seismic event accompanied by the procedures of seismogenic process, occurrence of the earthquake and the stress adjustment. Then start the preparation of a new earthquake. Therefore, investigation on the internal co-seismic deformation is significant for the study of the seismogenic process and mechanism of the next earthquake. The study on the surface deformation for the spherical dislocation theory , which take in to account the layered structure, gravity effect and the curvature effect of the earth, has a mature development. But it lacks the study of internal deformation. We add the orthonormalization method into the integration scheme, composed by the source functions, initial conditions, inner-outer core boundary conditions, core- mantle boundary conditions and the free surface boundary conditions. Then we can avoid the problem of high-order non-convergence in the calculation. It is a complicated course to apply the orthonormalization method into the integration of spherical harmonics function. We need to normalize, memory and restore the results of every layer in the earth. Thereby we can get the co-seismic deformation at any depth inside the earth. According to the results of the displacement and the stress transformation, we can discuss the effect on the seismogenic process for the next earthquake. Finally, we calculate the internal deformation of the 2011 Tohoku-Oki earthquake and study the characteristics of the seismogenic, combining the geodetic data.