A three-dimensional (3D) numerical simulation of scattering of seismic surface Rayleigh and longitudinal waves propagating through the ground, the density and elasticity of which are typical of geomedium. At the soil boundary, there is local unevenness in the form of a hollow hemispherical notch (a truncated sphere). The dependence of the direction of the scattering field on the type of inhomogeneity is shown. From literature it is known that in the transition to another type of heterogeneity, for instance, to covering the boundary with a thin inert (massive) layer in the form of a circle, the forward scattering occurs. A pulsed mode of inhomogeneity probing is considered. As an emitter, it is proposed to use a short pulse source, e.g., a hydroacoustic emitter, or something similar - a pulsating monopole, shallowly immersed under the free boundary. This leads to the generation of such elastic waves as the surface Rayleigh and back-reflected longitudinal waves, which are usually recorded using an array of seismic receivers installed on the free boundary according to the grid pattern. The spatial amplitude distribution of the wave field is analyzed in the vertical (at the center of the inhomogeneity) and horizontal (at the free boundary) sections of the medium. The characteristic features of the wave field are caused by the influence of its scattering on the local inhomogeneity. The features in the image of wave reliefs that arise at the intersection of the wave fronts of longitudinal waves - reflected from the free boundary and scattered on the local inhomogeneity - are studied. Informative signs, indicating the presence of the local heterogeneity and enable diagnostics of its parameters are established. The ways to improve the validity and reliability of algorithms for detection and classification of inhomogeneities and for evaluation of their difficulties using the listed types of waves are discussed. Based on the use of increasingly shorter probing pulses, the possibility of a detailed representation of reliefs and, consequently, the potentially achievable spatial resolution in probing the local subsurface inhomogeneities are demonstrated.