AbstractThe problem of vibrations at the free surface of an elastic half‐space due to detonation of a buried source is studied here from the viewpoint of the geophysical seismic technique employed in oil exploration. The fundamental assumption of the theory, therefore, is that the pressure at the source is impulsive and a Dirac delta function of time. The depth of the source below the surface of the medium is considered in the present theory as an additional parameter which has hitherto made the buried source problem formidable and, therefore, has limited almost all previous works to the relatively easy problem of surface blasting.An exact formulation is presented by dividing the half‐space into a stratum above the level of the buried source and a half‐space below it. For boundary conditions at the interface, it is assumed that the vertical displacement and shear stress at the level of the source are continuous while the direct stress is discontinuous. A numerical evaluation of the contour integration in the analysis is presented for the components of vibrations at any point of the free surface for a Poissonian medium. Finally, the analysis provides a theoretical justification for the interesting results obtained from field experiments recorded in an earlier
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