Are P- and S-wave velocities and attenuations related to permeability?: Ultrasonic seismic data for sandstone samples from the Writing-on-Stone Provincial Park in Alberta

Nicolas Williams Martin

Some experimental results measuring P- and S-wave phase velocities and attenuation coefficients in the laboratory, under dry and water-saturated conditions at a ultrasonic frequency of 1.0 MHz and atmospheric pressure on sandstone samples from the Milk River Formation in the Writing-on-Stone Provincial Park (WOSPP), southern Alberta, are presented and correlated with limited petrophysical data, as clay content, porosity and permeability, obtained from these sandstone samples.

The principal objective of this study is to estimate how the petrophysical properties such as clay content, porosity and permeability, affect the observed behavior of P- and S-wave phase velocities and attenuation coefficients on sandstone samples from WOSPP. Additionally, from this analysis I hope to determine whether, velocity or attenuation is more important for predicting permeability and permeability anisotropy from ultrasonic data.

These sandstone samples present an anisotropic velocity behavior like a transverse isotropy (TI) after analyzing its measured P-wave phase velocities under dry conditions, along three orthogonal axis oriented parallel and perpendicular to the layering in these samples.

In addition, these sandstone samples present different degree of permeability anisotropy, with the axis perpendicular to the layering having lower permeability than permeability measured along two axes parallel to the layering.

An analysis of the effect of polarization direction for S waves on phase velocity and attenuation is included, showing that for these sandstone samples the estimated S-wave phase velocities and attenuations are not significantly affected by the polarization direction. Also, the effect of the internal pressure on P-wave phase velocity and attenuation for a sandstone sample is analyzed. The experimental result shows a total agreement with experimental results obtained by other authors.

The most important conclusion obtained from this study is that the attenuation coefficient for P and S waves is more affected by permeability than phase velocity. For the same permeability range the variation of the P- and S-wave attenuation coefficient is higher than the corresponding variation in phase velocity for both waves. For P waves the phase velocity tends to show dependence on permeability above some critical permeability, but S-wave phase velocity tends to increase when permeability is increased beyond this critical permeability.