In this article we provide some analytical solutions of seismic equations with the different sources for a media, consisting of Uniform Half-Space (Air or Water oru2026) & solid Uniform Half-Space (Earth), containing a localized Anomaly. Such solutions allow building the very fast computer-based programs to decipher near-surface caves, karsts, tunnels, engineering applications, etc. This way particularly allows to go along a curved line, discovering already built tunnels without noise detection.We consider sources and model, which are practical for onshore and offshore (in deep water) seismic explorations. One may apply some forms of seismic solutions for a deep exploration of the slightly inclined multi-layer underground structures to find oil-gas-minerals-water-bearing lenses (see for example [9]). Here we apply the found solutions for shallow sounding to describe an effect from Anomaly.Also we showed a math similarity of uniform fluid (within Navier-Stokes equation) with seismic isotropic linear media (excluding the boundary layers). The details of boundary conditions are discussed, as well as the first orders of decomposition theory for the Fourier-Bessel representations of the seismic displacements. It is noted that within reasonable survey parameters an azimuth component can be ignored. Besides, it is observed, that we cannot stitch non-viscous fluid with solids directly, instead of this we must consider a limit transfer of solid-solid interaction. The radial and vertical displacements inside solid half-space are obtained as well as effects from localized Anomalies. For the cases of distributed Anomalies (karsts, tunnels, etc.) a convergence of analytical solutions was shown.