As a part of a series of studies on the dynamic rupture processes based on a modern boundary integral equation method, we prove that contribution of direct waves to the Green’s function for a half-space and that to the Green’s function in source layer for a layered half-space, which are both expressed in a cylindrical coordinate system, are strictly equivalent to the well-known analytic Green’s function for full-space. Because all of the hypersingularities in boundary integral equations (BIEs) come from the direct waves and contribution of direct waves can be evaluated analytically, the results obtained in this study are very useful in the simplification of the BIEs, especially for the case of layered half-space, in which the treatment on separation of singular parts is otherwise extremely complicated in mathematics and hence impracticable.

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