Effect of subsurface hydrological properties on velocity and attenuation of compressional and shear wave in fluid-saturated viscoelastic porous media

Abstract

Summary Over the past years there has been a growing interest in the use of seismic waves to gain required information about the Earth’s subsurface. Despite all achievements, the problem of accurately linking field measurement of seismic attributes to subsurface hydrological properties such as porosity and intrinsic permeability is still ambiguous. The goal of the present paper is to provide a comprehensive study on the effect of subsurface hydrological properties on seismic attributes such as wave attenuation and velocity. This is achieved by using dispersion relations obtained from equations of wave motion that are derived from Biot’s theory of poroelasticity. Since the attenuation predicted from Biot’s theory is only due to relative motion of the solid and fluid phases, viscoelasticity effects are introduced to consider the attenuation caused by grain to grain contact. The dispersion relations for body waves including fast wave, slow wave and shear wave are valid in both low and high frequency ranges where viscous and inertia effects are dominant, respectively. Numerical simulations are performed on sand samples over a wide range of frequencies (1 Hz to 1 MHz). For samples with constant porosity, but different intrinsic permeabilities, it is demonstrated that the velocity of slow wave is higher for the more permeable sample over the full frequency range. The velocity of fast wave and shear wave is higher for the more permeable sample, but the difference is significant only at intermediate frequencies (10–100,000 Hz). However, the corresponding peak velocity and attenuation of each of the wave modes are almost equal for different intrinsic permeability values and, therefore, independent of intrinsic permeability. Another series of numerical simulations are carried out on sand samples with different porosity values. It is shown that the most porous sand has higher slow wave and shear wave velocity, but lower fast wave velocity. Also, the peak attenuation of fast wave and shear wave gets larger as sand porosity increases, but slow wave behavior is opposite. Remarkable result is that all wave modes become more dispersive when porosity increases. Thus, neglecting the dependence of wave velocity on frequency can lead to significant miscalculation of wave velocity for sand samples with high porosity values.