A viscoelastic representation of wave attenuation and velocity dispersion in fractured porous media

Analyzing and understanding the seismic response from the fractured porous media is essential for fractured reservoirs characterization and hydrocarbon exploration. In response to passing seismic waves in the fractured porous media, there is fluid exchange between fractures and pore space, seismic waves are subject to attenuation and dispersion, thus, the media behave viscoelasticity, the stiffnesses involved in the stress-strain relation become complex and frequency dependent. In order to compute synthetic seismograms in the time domain with the purpose of studying seismic response of the media, an efficient approach is to approximate the stiffnesses by suitable viscoelastic models and then solve viscoelastic differential equations. In this paper, based on the poroelastic model of Chapman (2003), we use the Zener model to fit the stiffnesses, and solve the complex Christoffel equation to obtain attenuation and velocity dispersion curves and their corresponding Zener model best fits. We consider three selected models filled with different fluids, and there are two scales fractures in each model. The results show that the Zener model provides a good representation for viscoelasticity of fractured porous media.