Seismic waves propagating in heterogeneous Earth materials are subject to intrinsic attenuation where the elastic energy is converted to heat, and scattering attenuation is caused by the redistribution of wavefield energy (Aki & Richard, 1980). Understanding the wave dispersion and attenuation signatures is critical for interpreting multi-scale heterogeneities from geophysical observations in a broad frequency band (Bailly et al., 2019;Sams et al., 1997;Sarout, 2012), ranging from the earthquake seismology (<10 0 Hz), surface seismic (10 0 -10 2 Hz), sonic logs (10 3 -10 4 Hz), to ultrasonic measurements (10 5 -10 6 Hz). Developing the modeling and simulation tools to quantitatively establish the link between the complex heterogeneity features with both the intrinsic and scattering attenuation characteristics are of considerable interest for many Earth-science-related applications (Caspari et al., 2011;Zhao et al., 2017a), including geological storage of CO 2 , geothermal energy exploitation, hydrocarbon reservoir characterization, groundwater and contaminant hydrology, etc. The primary objective of this paper is to develop a new digital rock physics (DRP) modeling technique, stress relaxing simulation (SRS),