We use the method of small perturbation to study the scattered waves generated by an arbitrary 3D inhomogeneous medium around a spherically symmetric compressional source. We consider two models of the medium inside the source: a homogeneous solid and a fluid. The results from these two models differ only when scattering occurs within a few source's radii from the explosion. We find that there is a simple relation between the structure of the first order scattered waves and the structure of the medium, namely that a given harmonic of the medium parameters excites only the same harmonic of the two spheroidal potentials. When scattering occurs within a wavelength from the source, we find that the quadrantal terms in the spherical harmonic decomposition of the field have the lowest frequency dependence. They depend on frequency only through the spectrum of the source. Thus, in the far field, the dominant scattered waves generated near an explosion are similar to the primary waves generated by an earthquake. However, when the displacement field is observed in the near field of the explosion, the static solution reveals that a complete set of harmonics may be required to properly account for the displacement field. We compare the perturbation solution with the exact solution of the scattering by a sphere located within a wavelength from the source. This suggests that the perturbation solution has a fairly wide domain of practical applicability. We attempt to apply these results to the Love wave generated near the Boxcar nuclear explosion.