DISPLACEMENTS AND STRESSES INDUCED BY A POINT-SOURCE ACROSS A PLANE INTERFACE SEPARATING 2 ELASTIC SEMIINFINITE SPACES - AN ANALYTICAL SOLUTION

The problem of computing the static deformations and stresses produced by a point source in a homogeneous infinite medium was solved by Volt erra [1907] in a closed analytical form at the beginning of this centu ry. The similar problem of computing fields generated by point sources in a homogeneous half-space bounded by a free surface was later studi ed by Steketee [1958a,b] and several others [see Okada, 1985, 1992], w ho focused on point as well as on rectangular fault sources of interes t in seismology. Here the model taken into account consists of two ela stic half-spaces characterized by different elastic properties (rigidi ty modulus mu and Poisson coefficient nu) and separated by a planar in terface: assuming that a point source is active in one half-space, sta tic deformations and stresses generated by the source in the whole spa ce ate computed. The similar problem of two half-spaces welded togethe r was solved by Heaton and Heaton [1989], but they imposed the simplif ying constraint that both materials are Poissonian (i.e., both have th e same Poisson coefficient nu = 0.25). The present approach, which is based on the Galerkin vector method, is general and applicable to an a rbitrary point source. In this paper the computations have been carrie d out explicitly only for the special case of a dislocation source hav ing the form of a strike-slip double couple. The solution is provided in a closed analytical form by means of expressions involving the sour ce descriptors (position and intensity) as well as the elastic paramet ers of the heterogeneous medium. The solutions have been illustrated a nd discussed with special attention given to the dependence of the dis placement and stress components on the elastic parameters of the model . One interesting finding concerns the Limiting case when the rigidity modulus of the half-space not containing the point source is equalize d to zero. Although the solution in this half-space no longer makes se nse, the solution in the other reduces exactly to the one computed for a halfspace with a free surface, that is, to the solutions computed b y Steketee [1958a] and Okada [1985] following an alternative approach.