Numerical study on S-wave scattering attenuation in two-dimensional media with random cracks

Acoustic attenuation demonstrates higher sensitivity to crack identification compared to velocity, thus holding significant potential for applications in unconventional oil and gas exploration and hydraulic fracturing monitoring. Cracked reservoirs exhibit strong heterogeneity, with significant scattering effects. However, the effective medium theory based on the long-wavelength assumption fails to accurately describe the acoustic attenuation caused by scattering. In this study, the propagation of scalar shear waves (SH waves) was simulated on two-dimensional random cracked media using the staggered-grid finite-difference method. The effects of crack scale, density, and intersection on shear wave scattering attenuation were investigated. It was found that when the crack length (l(c)) is less than 1/30 of the background medium wavelength (lambda(0)), scattering attenuation can be neglected. Additionally, attenuation increases with k(0)l(c)/2 when k(0)l(c)/2 < 1, and decreases when k(0)l(c)/2 > 1. The strongest attenuation occurs when l(c) is approximately equal to lambda(0)/3. Cracks intersection amplifies scattering attenuation when k(0)l(c)/2 < 1 while weakening scattering attenuation when k(0)l(c)/2 > 1. The relationship between crack length (l(c)), crack density (gamma), and background medium wave number (k(0)) quantitatively characterizes scattering attenuation. This relationship aids in understanding the shear wave scattering attenuation characteristics of multi-scale cracks, with practical implications for crack identification in sonic logging and exploration seismic.