Using a novel signal processing technique — the method of correlation function of amplitude and phase fluctuations (APCF) — we have obtained the first spectra of equidistant frequency (EF) groups in records of background seismic oscillations. This method has previously been successfully applied to the analysis of resonant oscillations in Earth’s magnetosphere-ionosphere system. In the case of seismic oscillations, all peaks in the EF spectrum can be divided into two groups corresponding to eigenfrequencies of vertical standing waves of P and S types in the Earth’s interior. The upper turning point of these waves lies at the free upper boundary of the Earth’s crust, whereas the lower turning point is located at the boundaries between subsurface layers. We demonstrate that this signal processing technique can serve as a new method for probing the layered structure of the Earth’s subsurface. Specifically, it enables the determination of the depth and thickness of each layer, as well as the estimation of elastic properties (such as Poisson’s ratio) of the geological material composing the layer. The findings have revealed that at the depth of ~2.7 km there are two layers of different solid substance 58 m and 140 m thick with Poisson’s ratios of 0.231 and 0.187.