Bulletin of the Seismological Society of America

We consider the problem of reflection and refraction of purely compressional waves incident on an interface separating identical solid half-spaces in which the condition of continuity of shear displacement at the boundary is generalized to one that allows slippage. The problem is solved using the Cagniard-de Hoop technique. It is found that the generation of reflected P and $ waves, as well as transmitted S waves, is most effective in the case of perfectly unbonded halfspaces. We discuss the implications of this model for the generation of $ waves by block movement in the vicinity of an underground explosion. INTRODUCTION Considerable effort has been devoted to the understanding of SH radiation from underground explosive sources. A variety of possible mechanisms have been proposed, as reviewed by Aki and Tsai (1972). They include (I) mode conversion at irregular interfaces (e.g., All and Lamer, 1970), (2) cracking in the vicinity of the shot point (e.g., Kiss]inger et al., 1961), (3) prestress relaxation associated with the creation of the cavity (e.g., Archambeau, 1972, 1973), and (4) triggering of an actual earthquake with large scale faulting, a mode] favored by Aki and Tsai (1972). It is likely that a combination of these mechanisms acts to produce the observed SHand Love-wave radiation from underground explosions. The relative contributions of various mechanisms will of course depend on local characteristics of the site. Nevertheless, it may be noted that the two last mechanisms listed above involve the release of strain energy stored in the medium prior to the experiment, and therefore require the presence of sufficient prestress. On the other hand, the two first mechanisms can operate even in the absence of significant initial stress, as evidenced by the observations of Kiss]inger et al. (1961). These authors observed SH radiation generated by small scale explosions detonated in mud, and suggested that near-source cracking was the most likely cause of shear-wave radiation. In order to better understand the influence of site characteristics and prestress on SHand Love-wave generation, an improved assessment of the phenomena which do not require prestress is needed. Cracking and block motions in the vicinity of explosions fall in this category; a review of these problems is provided by Bache and Lambert (1976). T h e purpose of this pape r is to demons t ra t e tha t the presence of imperfec t ly bonded interfaces and joints near a pure ly dflatat ional source could account for far* Present address: Sierra Geophysics, Inc., 150 N. Santa Anita Blvd., Suite 880, Arcadia, California 91006. 659 660 CARLOS SALVADO AND d. BERNARD MINSTER field transverse components of displacement and thus, with a suitable geometry, for SHand Love-wave radiation. The problem is greatly simplified because we restrict ourselves to linear boundary conditions, and solve the problem in the far-field, first-motion approximation. It appears that if the bonding is sufficiently weak, and if the geometry is favorable, at least a portion of the observed shear radiation could be explained by this mechanism. 1. S ta tement of the problem, and boundary conditions. Consider the simple geometry depicted on Figure 1: a purely dilatational point source is located at a height h above the plane interface between two elastic half-spaces. To simplify the problem, we restrict our attention to the case when the two half-spaces are identical. The boundary conditions usually adopted in seismology involve continuity of tractions and displacements, and in this case, the problem reduces to that of a point source in an infinite space. We shall now relax the boundary conditions, and request continuity of tractions and of normal displacement but allow a jump in the tangential displacement. In other words, slippage is allowed between the two half-spaces. Sezawa and Kanai (1940), Kanai (1961), and Murty (1975, 1976) proposed a boundary condition which