Frequency dependent attenuation and dispersion in patchy-saturated porous rocks

Huixing Zhang, Kristopher A. Innanen

From seismic wave equations in modified patchy-saturated model established on the basis of the White model, we derive the formulas of reciprocal quality factors and velocities of the two kinds of P-waves and analyze the seismic attenuation and velocity dispersion of the two kinds of P-waves in patchy-saturated rocks within the seismic band. Through comparison of seismic attenuation in modified patchy-saturated, Biot and BISQ models, we find that seismic attenuation in a modified patchy-saturated model is much higher than that in the other two models--about 1000 times higher. Therefore, modified patchy-saturated model can describe seismic propagation more accurately in the seismic band and can be used in seismic exploration. Owing to the importance of porosity, permeability and fluid saturation, we also study and analyze the effects of these three factors on seismic attenuation and velocity dispersion of P-waves in patchy-saturated rocks within the seismic band. The conclusions are: Seismic attenuation of the fast P-wave increases with increasing frequency, while attenuation of the slow P-wave decreases with increasing frequency within the seismic band. As rock porosity goes up with other parameters constant, seismic attenuation and velocity dispersion of the fast P-wave increases with porosity. When the porosity is very low, velocity dispersion is not obvious within seismic band due to insufficient fluid in the pores. As for the effect of permeability on the fast P-wave, the attenuation peaks move to high frequency as rock permeability increases. Moreover, at low frequencies (below about 10Hz), attenuation for low permeability is greater than that for high permeability, and velocity dispersion is also more obvious at low frequencies than that at high frequencies. When water saturation becomes high or gas saturation becomes low with other parameters constant, seismic attenuation and velocity dispersion of the fast P-wave increase within the seismic band. For the slow P-wave, attenuation increases with increasing porosity and gas saturation and decreasing rock permeability. Velocity dispersion is always apparent no matter what porosity, permeability or fluid saturation is within the seismic frequency band.