The phenomenon of wave dispersion and its causes are a hot topic in the study of rock physics and acoustics of porous media. Based on the Biot theory and Darcy-Brinkman law

Maxwell-Brinkman and Kelvin-Brinkman viscoelastic porous media mechanical models were proposed

and the dispersion relationship of compression waves was established. The dispersion and attenuation laws of waves were revealed

and the effects of stress relaxation and creep on wave propagation velocity and inverse quality factor were analyzed. At low frequencies

the dispersion and attenuation of compression waves predicted by the Kelvin- Brinkman model and the Darcy-Brinkman-Biot model are consistent. While

at high frequencies

the dispersion and attenuation of compression waves predicted by the Maxwell-Brinkman model agree well with those by the Darcy-Brinkman-Biot model. The reliability of the physical model was verified using experimental data from the Gulf of Mexico. Through parameter sensitivity analysis

the method for optimizing medium parameters based on measured data was discussed.