Closed form analytical expressions for the static strain and stress fields caused by a compensated linear vector dipole at any point of an elastic half-space in welded contact with another half-space are first obtained. The correspondence principle of viscoelasticity is then used to calculate the quasi-static field when the medium is linearly viscoelastic. The rheology of the lower half-space has been taken as Maxwell, a Kelvin or a Standard Linear Solid (SLS). The expressions obtained can be used to calculate the static and quasi-static field at depth caused by explosions. Detailed numerical computations are performed to examine the effect of rigidity contrast and the relaxation time on the strain and stress field. The study of the deformation of the two half-space in welded contact has a large number of applications in the fields of engineering and science.

compensated linear vector dipole, viscoelastic, deformation, relaxation time.