Wavefield Evolution and Arrival Behavior of Elastic Wave Propagation in Two-Dimensional Fractional Brownian Fields

The fractional Brownian field is often used to reproduce the fractal properties of complex heterogeneous media, which closely represent real-world geological materials. Studying elastic wave transport in this type of heterogeneous media is essential for advancing knowledge in geophysics, seismology, and rock mechanics. In this paper, we numerically investigate the wavefield evolution and arrival behavior of elastic wave propagation in a two-dimensional fractional Brownian field characterized by the standard deviation (σ) and the Hurst exponent (H). Using a high-fidelity finite element model, we quantify the influence of these parameters on wavefront morphology, wave arrival synchronization, and energy decay. Our results reveal that increased matrix heterogeneity with higher σ and lower H values leads to pronounced wavefront roughness, asynchronous arrival phenomena, and increscent energy decay, attributed to enhanced scattering and modulus variability. For smaller H values, rougher modulus distributions scatter wave energy more intensely, producing more coda waves and distorted wavefronts, while smoother fields with larger H fields promote smoother wave propagation. Higher σ amplifies these effects by increasing modulus variability, resulting in more attenuated wave energy and substantial wavefield disturbance. This study contributes to a quantitative understanding of how fractal heterogeneity modulates wave transport and energy attenuation in random media. Our findings hold practical significance for geophysical exploration and seismic tomography, as well as aiding in subsurface imaging and structural evaluation within fractured or stratified rock formations.