ABSTRACT
Self-similar uniform moving crack forms a different type of problem which has no characteristic length and the displacements are functions of f(t/x, t/y). The solution method for this class of problems uses the homogeneous solution introduced by Smirnov and Sobolov. Usually the crack is assumed in an infinite medium in this class of problems. In this Chapter the earthquake in an elastic half space is generated by shear faulting on an inclined fault by self-similar crack motion. The main difficulty in getting a solution is complicated due to the presence of surface. Achenbach and Brock solve the problem partially by taking the image solution for the surface effect. Here an exact solution of the surface effect is obtained by considering the body force equivalent for the crack problem. The problem for a two-dimensional self-similar crack on an inclined fault is discussed and the surface motion via determining the body force equivalent for the self-similar crack is derived. The exact surface response for the crack motion on an inclined fault plane is obtained using Cagniard–de Hoop’s technique. The result is valid till the arrival of scattered waves from the crack.
