Estimating Seismic Anisotropy: Fluid Substitution Theory, 3D-Printed Inclusion Models, and Multi-Component 3D VSP in the Bakken Shale



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Understanding seismic anisotropy is one of the most important issues in seismic exploration. In this dissertation, I tried to understand how fluids and lithology influence the elastic properties and seismic anisotropy of rocks, theoretically, experimentally, and in the field.

I derived anisotropic fluid-substitution equations for the cases of HTI and orthorhombic media. The derivation was based on the anisotropic Gassmann's equations and linear-slip theory. The results have a similar form as the conventional isotropic Gassmann's equations, but now include two more parameters as normal and tangential weaknesses. To further examine the equations, I created two physical models using 3D-printing methods. The input printing material was thermoplastic with a density of 1.04 g/cc, P-wave velocity of 2167 m/s, and shear-wave velocity of 885 m/s. The first model was a solid-printed cube, and the other was a similarly sized cube, but with many layers of penny-shaped inclusions. Ultrasonic measurements (on the inclusion model) gave P-wave velocities of 1351 m/s and 1706 m/s, and shear-wave velocities of 656 m/s and 812 m/s. A fluid-substitution experiment with water observed 20% to 46% increase in P-wave velocities and 9% to 10% decrease in S-wave velocities. I found that predictions using our equations matched the measurements (within 4%) better than the Hudson's theory (within 10%). I also processed zero-offset, walk-away and walk-around VSP data in the Bakken shale, North Dakota, provided to us by Hess Corporation. I found that there was strong polar anisotropy in evidence from the VSP data in the Mission Canyon, Lodgepole, and Bakken formations. Thomsen’s anisotropy parameters for the Bakken formation were estimated to be 0.27 for ε, and 0.07 for δ. Though the Bakken and its overburden formations exhibited strong polar anisotropy, there was no substantial evidence of azimuthal anisotropy.

The equations I have derived, experiments performed, and the VSP results obtained, provide methods to understand and estimate seismic anisotropy. Seismic anisotropy at different scales and complexity can be useful to characterize reservoir fluids and lithology.



Fluid substitution, Fracture behavior, Bakken shale, Anisotropy


Portions of this document appear in: Huang, Long, Robert R. Stewart, Samik Sil, and Nikolay Dyaur. "Fluid substitution effects on seismic anisotropy." Journal of Geophysical Research: Solid Earth 120, no. 2 (2015): 850-863. DOI: 10.1002/2014JB011246.