Scaling relations in fragmentation in 1D media

Geophysical sounding data over one-dimensional material profiles are generated throughout a partitioning of original impulse of energy at the boundaries of layers. Horizontally stratified (1D) equal-thickness (Goupillaud-type) models are accepted to have mathematically equivalent descriptions for each geophysical sounding method. A distinction is made between the models having finite, or infinite number of layers, respectively. An extremely complex process of fragmentation under sounding is compared with a simple process of rock fragmentation. For infinitely layered monotone models (monotone behaviour of proper impedance over a profile), a complete analogy to Kolmogorov's rock fragmentation exists. For high frequencies there is a zone of ultraviolet catastrophe, due to the violation of the leading assumption: f --> 0 and/or f --> pi. In the case of finite stratification there is a divergence from the scaling law for low frequencies (the infrared catastrophe), corresponding to non-layered substratum. In the general case of an arbitrary model, the data result from composition of two components, corresponding to both monotone and alternating models, which are mutually convertible one into another.