Comprehensive modeling of elastic wave propagation in porous viscoelastic media incorporating fractional-order derivative under welded and loose boundary conditions

The complexity and diversity of Earth materials pose significant challenges to seismic detection techniques, especially in oil and gas exploration. The development and application of the viscoelastic theory and microscopic flow theory of porous fluids have made the analysis of elastic wave propagation information one of the main methods of detection. This study investigates the propagation characteristics of elastic waves in a sandwich structure, which comprises of layers of elastic, porous viscoelastic and viscoelastic solids, placed on top of each other. The fractional order Zener model, Biot-squirt flow (BISQ) model, and non-Newtonian fluid theory are employed to describe the viscoelasticity of the solid frame, microscopic flow of porous fluids, and viscosity of porous fluids, respectively. To our knowledge, existing studies on unwelded bonded boundary conditions have not yet incorporated the BISQ model and fractional derivative theory. We aim to address this critical knowledge gap. Both welded and loose boundary conditions have been taken into account in our model. Graphical representations illustrate the numerical simulation findings. Our study suggests that the viscoelasticity of solid frame, the flow characteristics of porous fluids, welded and loose boundary condition have significant impact on the propagation properties of elastic waves. Hence, the study of the above factors in Earth materials will appropriately describe the subsequent dissipation of seismic wave energy and the analysis of stratigraphic structures and soil properties.