Propagation of seismic shear and primary-shear waves in fractal media: the case of Omerelu area and Targy Ocna

Abstract This study investigates seismic wave propagation in fractal-dimensional media using the product-like fractal measure based on the Li and Ostoja-Starzewski approach. The proposed framework incorporates direction-dependent fractal dimensions to model the multiscale heterogeneity, anisotropy, fractures, and pore irregularities present in geological formations. Fractal geometric measures and fractal Fourier transforms are employed to describe anomalous seismic phenomena such as attenuation, dispersion, scattering, and energy localization. The results show that the fractal dimension strongly affects wave propagation characteristics, producing distorted wavefronts and localized energy patterns in heterogeneous media. Applications to geological environments such as the Omerelu Basin in Nigeria and the Târgu Ocna region in Romania demonstrate the relevance of the model to complex subsurface structures. Overall, the study highlights the potential of fractal-dimensional continuum models as effective tools for seismic imaging, earthquake analysis, and geophysical exploration in heterogeneous and anisotropic Earth materials.