The Frequency (or Time) -Temperature Equivalence of Relaxation in Saturated Rocks

Abstract

Laboratory data on dry and saturated rocks show that pore fluid has the most important effect on rock attenuation. It is known that viscous and inertial coupling between the frame of a porous rock and its pore fluid dissipates seismic energy by conversion to heat and hence cause attenuation. We show that attenuation peaks, in saturated rock have the same property as that of typical thermally activated relaxations. In the frequency domain, a plot of attenuation versus frequency shows an obvious systematic shift to higher frequencies with increasing temperatures. Similarly, the attenuation versus temperature curve moves to higher temperature with increasing frequencies. The attenuation peaks are somewhat broader than that for a Zener relaxation. A Cole-Cole distribution of relaxation times closely matches the attenuations. This behavior can be explained theoretically by local flow mechanisms.

Wave propagation analysis of porous rocks with the thermal activated relaxation mechanism

“…The attenuation results, such as the attenuation peak value, the peak position and width, are pleasantly coincident with the experimental data (Batzle, et al, 2006;Xi, et al, 2007). The variations of velocity with frequency or temperature are also evidenced by some experiment results (Jones and Nur, 1983;Xi, et al, 2007). The characteristics of velocity and attenuation are more apparent for rock samples with higher porosity.…”

“…Review of the experiments in the temperature and frequency field Xi et al (2007) conducted series of experiments to investigate the wave attenuation and dispersion of porous rocks under various temperatures and frequencies. Measurements of frequency-dependent and temperature-dependent attenuation in rock samples are performed in three types of mode on two types of apparatus (detailed in Table 1).…”

On the relative importance of global and squirt flow in cracked porous media

“…A change in the viscosity may lead to a shift of the attenuation peak towards lower or higher frequencies, depending on the mechanism of wave-induced fluid flow. The influence of viscosity on attenuation peaks of the global and squirt flow is different depending on the type of mechanism involved (Xi et al 2007). Also the experimental observations show that the high fluid viscosity can act to shift the relaxation towards lower frequencies (Winkler et al 1985;Dvorkin et al 1994).…”

Temperature Effect on the Velocity‐Porosity Relationship in Rocks

“…Several studies about the effect of temperature on the attenuation and dispersion characteristics of seismic waves in complex reservoirs have been carried out (Jaya et al., 2010; Rabbani et al., 2017; Xi et al., 2007; Zhu & Pan, 1993). These studies offer some insights to understand the link between temperature and wave attenuation in rocks.…”

“…Xi et al. (2007) found that the attenuation peak shifts to higher frequencies with increasing temperatures. Rabbani et al.…”