球体位错理论的基本解

位错理论是现代地震学中计算地球内部位错源引起的地表变形的重要理论模型。诸多学者对准静态位错理论模型进行了研究，其中大量工作是在前人给出的基本解的基础上进行的。回顾了位错理论模型的基本物理方程，包括平衡方程、本构关系和泊松方程，并分别推导了无自重、不可压缩、自重可压缩的地球模型下的通解。给出的基本解可以用于进一步理解和计算一维径向分层的地震变形问题。

Basic Solutions for Spherical Dislocation Theory

In modern seismology, dislocation theory plays an important role in the computation of surface deformation induced by an internal dislocation source. Many researchers have studied quasi-static dislocation theory; however, their works are built on the basic solution of deformation equations given by the classic literature. In this paper, we first review the physical equations of dislocation theory, including the equilibrium equation, constitutive relation, and Poisson’s equation. Then we solve these equations under the non-gravitating, incompressible, and compressible gravitating homogeneous earth model, giving their general solutions including the spheroid and toroid components. The basic solutions under a homogeneous sphere given in this paper can be used to improve understanding and computation of seismic deformations under a layered spherical earth.